PRESSURE VESSEL
HANDBOOK
PRESSURE VESSEL
HANDBOOK
Twelfth Edition
with foreword by
Paul Buthod
Professor of Chemical Engineering
University of Tulsa
Tulsa, Oklahoma
Eugene F. Megyesy
PRESSURE VESSEL PUBLISHING, INC.
P.O. Box 35365· Tulsa, Oklahoma 74153
Copyright © by Eugene F. Megyesy
Copyright 1972, 1973 by Pressure Vessel Handbook Publishing, Inc.
All rights reserved. No part of this book may be reproduced in any
form or by any means including information storage and retrieval
systems - without permission of the publisher.
Library of Congress Control
Number: 2001130059
ISBN 0-914458-21-3
COPYRIGHT©
1972,1973,1974,1975,1977,1979,1981,1982,1983, 1986, 1989,
1992,1995,1998,2001
Printed and bound in the United States of America.
NOTE: This new edition of the Pressure Vessel Handbook supersedes all previous editions, effective July 1,2001.
The changes over the previous Eleventh Edition have been made
necessary by the revision of Codes, Standards, Specifications, etc.
FOREWORD
Engineers who design equipment for the chemical process industry
are sooner or later confronted with the design of pressure vessels and
mounting requirements for them.
This is very often a frustrating
experience for anyone who has not kept up with current literature
in the field of code requirements and design equations.
First he must familiarize himself with the latest version of the
applicable code.
Then he must search the literature for techniques
used in design to meet these codes. Finally he must select material
properties and dimensional data from various handbooks and company
catalogs for use in the design equations.
Mr. Megyesy has recognized this problem.
For several years he
has been accumulating data on code requirements and calculational
methods.
He has been presenting this information first in the form
of his "Calculation Form Sheets" and now has put it all together in
one place in the Pressure Vessel Handbook.
I believe that this fills a real need in the pressure vessel industry
and that readers will find it extremely useful.
Paul Buthod
PREFACE
This reference book is prepared for the purpose of making fonnulas,
technical data, design and construction methods readily available for the
designer, detailer, layoutmen and others dealing with pressure vessels.
Practical men in this industry often have difficulty finding the required
data and solutions, these being scattered throughout extensive literature
or advanced studies. The author's aim was to bring together all of the
above material under one cover and present it in a convenient fonn.
The design procedures and fonnulas of the AS ME Code for Pressure
Vessels, Section VIII Division I have been utilized as well as those
generally accepted sources which are not covered by this Code. From
among the alternative construction methods described by the Code the
author has selected those which are most frequently used in practice.
In order to provide the greatest serviceability with this Handbook,
rarely occurring loadings, special construction methods or materials have
been excluded from its scope. Due to the same reason this Handbook
deals only with vessels constructed from ferrous material by welding,
since the vast majority of the pressure vessels are in this category.
A large part of this book was taken from the works of others, with some
of the material placed in different arrangement, and some unchanged.
The author wishes to acknowledge his indebtedness to Professor
Sandor Kalinszky, Janos Bodor, Laszl6 Felegyhazy and J6zsef Gyorfi for
their material and valuable suggestions, to the American Society of
Mechanical Engineers and to the publishers, who generously pennitted
the author to include material from their publications.
The author wishes also to thank all those who helped to improve this
new edition by their suggestions and corrections.
Suggestions and criticism concerning some errors which may remain
in spite of all precautions shall be greatly appreciated. They contribute to
the further improvement of this Handbook.
Eugene F. Megyesy
7
ASME CODE vs. THIS HANDBOOK
The ASME BOILER AND PRESSURE
VESSEL CODE - 2001, Sect. VIII, Div. 1
The American Society of Mechanical Engineers set up a Committee in 1911 for the
purpose of formulating standard rules for
the construction of steam boilers and other
pressure vessels that will perfonn in a safe
and reliable manner.
The Code comprises these rules.
It's scope includes vessels:
1. made of nonferrous materials, cast iron,
high alloy and carbon steel,
2. made by welding, forging, bracing, and
3. applying a wide variety of construction
methods and details.
It includes all vessels where the question
of safety is concerned.
PRESSURE VESSEL HANDBOOK2001, Twelfth Edition
The Handbook covers design and construction methods of pressure vessels:
1. made of carbon steel,
2. made by welding
3. applying construction methods and
details which are the most economical
and practical, which are in accordance
with the Code rules, and thus generally followed by the industry.
The vast majority of the pressure vessels
today fall into this category.
For construction rules and details which
are excluded from the scope of the Handbook, references are made to the applicable
Code paragraphs to avoid neglecting them.
The Code - as it is stated in paragraph UG2 - "does not contain rules to cover all
details of design and construction ... "
"where details are not given, it is intended
that the Manufacturer ... shall provide details of design and construction."
Details of design and construction not
covered by the Code are offered by the
Handbook including: Design of tall towers, wind load, earthquake, vibration, eccentric load, elastic stability, deflection,
combination of stresses, nozzle loads, reaction of supports, lugs, saddles, and rectangular tanks.
"The Code is not a handbook." "It is not
intended that this Section be used as a design handbook" as it is stated in the Foreword of the Code.
The updated and revised Code is published
in three years intervals. Addenda, which
also include revisions to the Code, are published annually. Revisions and additions
become mandatory six (6) months after the
date of issuance, except for boilers and pressure vessels contracted for prior to the end
ofthe 6 month period. (Code Foreword)
The aim of this Handbook is to be easily
handled and consulted. Tables, charts eliminate the necessity of calculations, Geometry, layout of vessels, piping codes, API
storage tanks, standard appurtenances,
painting of steel surfaces, weights, measurements, conversion tables, literature,
definitions, specification for vessels, design of steel structures, center of gravity,
design of welded joints, boIted connections, boiler and pressure vessel laws,
chemical resistance of metals, volumes, and
surfaces of vessels, provide good serviceability.
The Handbook is updated and revised in
three years intervals, reflecting the changes
of Code rules, new developments in the design and construction method, and includes the revisions of its sources.
8
THE ASME CODE
ASME Boiler and Pressure Vessel Code, Section VIII, Division 1
An internationally recognized Code published by
The American Society of Mechanical Engineers.
PRESSURE VESSEL - is a containment of solid, liquid or gaseous material under
internal or external pressure, capable of withstanding also various other loadings.
BOILER - is a part of a steam generator in which water is converted into steam
under pressure.
RULES OF DESIGN AND CONSTRUCTION - Boiler explosions around the turn
of the century made apparent the need for rules governing the design and construction of vessels. The first ASME Code was published in 1914.
ISSUE TIME - The updated and revised Code is published in three years intervals
(2001 and so on). Addenda, which also include revisions to the Code, are published annually. Revisions and additions become mandatory 6 months after the
date of issuance, except for boilers and pressure vessels contracted for prior to
the end of the 6 month period. (Code Foreword)
SCOPE OF THE CODE - The rules of this Division have been formulated on the
basis of design principles and construction practices applicable to vessels designed for pressures not exceeding 3000 psi. Code U-l (d)
Vessels, which are not included in the scope of this Division, may be stamped
with the Code U Symbol if they meet all the applicable requirements of this Division. Code U-2(g)
THE DESIGN METHOD - The Code rules concerning design of pressure parts
are based on the maximum stress theory, i.e., elastic failure in a ductile metal
vessel occurs when the maximum tensile stress becomes equal to the yield strength
ofthe material.
OTHER COUNTRIES' Codes deviate from each other considerably, mainly because of differences in the basic allowable design stresses. The ASME Code's
regulations may be considered to be at midway between conservative and
unconservative design.
COMPUTER PROGRAMS - Designers and engineers using computer programs
for design or analysis are cautioned that they are responsible for all technical
assumptions inherent in the programs they use and they are solely responsible
for the application of these programs to their design. (Code, Foreword)
DESIGN AND CONSTRUCTION NOT COVERED - This Division ofthe Code
does not contain rules to cover all details of design and construction. Where
complete details are not given, it is intended that the Manufacturer shall provide
details which will be as safe as those provided by the rules of this Division.
Code U-2(g)
CONTENTS
PART I
Design and Construction of Pressure Vessels ............. 11
PART II
Geometry and Layout of Pressure Vessels .............. 257
PART III
Measures and Weights ............................................ 321
PART IV
Design of Steel Structures ....................................... 447
PART V
Miscellaneous .......................................................... 465
11
PART I.
DESIGN AND CONSTRUCTIONS OF PRESSURE VESSEL
1. Vessels Under Internal Pressure ............................................
Stresses in Cylindrical Shell, Definitions, Formulas, Pressure of Fluid, Pressure-Temperature Ratings of American
Standard Carbon Steel Pipe Flanges.
15
2. Vessels Under External Pressure ............................................
Definitions, Formulas, Minimum Required Thickness of
Cylindrical Shell, Chart for Determining Thickness of
Cylindrical and Spherical Vessels under External Pressure
when Constructed of Carbon Steel.
31
3. Design of Tall Towers ............................................................
Wind Load, Weight of Vessel, Seismic Load, Vibration,
Eccentric Load, Elastic Stability, Deflection, Combination
of Stresses, Design of Skirt Support, Design of Anchor
Bolts (approximate method), Design of Base Ring (approximate method), Design ofAnchor Boltand Base Ring,
Anchor Bolt Chair for Tall Towers.
52
4. Vessel Supports........... ............... ....... .............. ......................
Stresses in Large Horizontal Vessels Supported by Two
Saddles, Stresses in Vessels on Leg Support, Stresses in
Vessels Due to Lug Support, Lifting Attachments, Safe
Loads for Ropes and Chains.
86
5. Openings ......................................... :......................................
Inspection Openings, Openings without Reinforcing Pad,
Opening with Reinforcing Pad, Extension of Openings,
Reinforcement of Openings, Strength of Attachments,
Joining Openings to Vessels, Length of Couplings and
Pipes for Openings.
122
6. Nozzle Loads ..........................................................................
153
7. Reinforcement at the Junction of Cone to Cylinder ...............
159
8. Welding of Pressure Vessels .................................................
Welded Joints, Butt Welded Joint of Plates of Unequal
Thicknesses, Application of Welding Symbols.
170
9. Regulations, Specifications ....................................................
Code Rules Related to Various Services, Code Rules
Related to Various Plate Thicknesses of Vessel, Tanks
and Vessels Containing Flammable and Combustible Liquids, Properties of Materials, Description of Materials,
Specification for the Design and Fabrication of Pressure
Vesels, Fabrication Tolerances.
181
12
10. Materials of Foreign Countries ..............................................
194
11. Welded Tanks ........................................................................
203
12. Piping Codes ..................... ................ ......................... ............
208
13. Rectangular Tanks .................................................. ................
213
14. Corrosion ................................................................................
221
15. Miscellaneous .......................................................................
Fabricating Capacities, Pipe and Tube Bending, Pipe
Engagement, Drill Sizes for Pipe Taps, Bend Allowances, Length of Stud Bolts, Pressure Vessell Detailing, Preferred Locations, Common Errors, Transportation of Vessels.
232
16. Painting of Steel Surfaces .....................................................
247
IN REFERENCES THROUGHOUT THIS BOOK "CODE" STANDS FOR ASME
BOILER AND PRESSURE VESSEL CODE SECTION VIII, DIVISION 1 - AN
AMERICAN STANDARD.
2001 EDITION
13
STRESSES IN PRESSURE VESSELS
Pressure vessels are subject to various loadings, which exert stresses of
different intensities in the vessel components. The category and intensity
of stresses are the function of the nature ofloadings, the geometry and construction of the vessel components.
LOADINGS (Code UG-22)
a. Internal or external pressure
b. Weight of the vessel and contents
c. Static reactions from attached equipment, piping, lining, insulation,
d. The attachment of internals, vessel supports, lugs, saddles, skirts, legs
e. Cyclic and dynamic reactions due to pressure or thermal variations
f. Wind pressure and seismic forces
g. Impact reactions due to fluid shock
h. Temperature gradients and differential thermal expansion
1.
Abnormal pressures caused by deflagration.
STRESSES (Code UG-23)
a.
Tensile stress
b. Lingitudinal
compressive stress
c. General primary membrane stress
induced by any combination of
loadings. Primary membrane stress
plus primary bending stress induced
by combination of loadings, except
as provided in d. below.
d. General primary membrane stress
induced by combination of earthquake or wind pressure with other
loadings. Seismic force and wind
pressure need not be considered to
act simulta neously.
MAXIMUM ALLOWABLE STRESS
Sa = Maximum allowable stress in
tension for carbon and low alloy steel
Code Table UCS-23; for high alloy
steel Code Table UHA-23., psi. (See
properties of materials page 186-190.)
The smaller of Sa or the value of
factor B determined by the procedure
described in Code UG 23 (b) (2)
1.5 Sa
Sa = (see above)
1.2 times the stress permitted in a., b.,
or c. This rule applicable to stresses
exerted by internal or external pressure
or axial compressive load on a cylinder.
14
STRESSES IN CYLINDRICAL SHELL
Unifonn internal or external pressure induces in the longitudinal seam two times larger unit
stress than in the circumferential seam because of the geometry of the cylinder.
A vessel under external pressure, when other forces (wind, earthquake, etc.) are not
factors, must be designed to resist the circumferential buckling only. The Code
provides the method of design to meet this requirement. When other loadings are
present, these combined loadings may govern and heavier plate will be required
than the plate which was satisfactory to resist the circumferential buckling only.
The compressive stress due to external pressure and tensile stress due to internal pressure
shall be detennined by the fonnulas:
FORMULAS
LONGITUDINAL
JOINT
CIRCUMFERENTIAL
JOINT
S _ PD
2t
2 -
D
p
51
52
t
=
=
=
=
=
NOTATION
Mean diameter of vessel, inches
Internal or external pressure, psi
Longitudinal stress, psi
Circumferential (hoop) stress, psi
Thickness of shell, corrosion allowance
excluded, inches
EXAMPLE
Given
D
p
t
=
=
=
96 inches
15 psi
0.25 inches
PD
SI = 4t
=
15 x 96
4 x 0.25
15 x 96
=
1440 psi
=
2880 psi
2 x 0.25
For towers under internal pressure and wind load the critical height above which compressive stress governs can be approximated by the formula:
H
=
PD
12t
where H = Critical height of tower, ft.
15
INTERNAL PRESSURE
1.
OPERA TING PRESSURE
The pressure which is required for the process, served by the vessel, at wh ich
the vessel is normally operated.
2.
DESIGN PRESSURE
The pressure used in the design of a vessel. It is recommended to design a
vessel and its parts for a higher pressure than the operating pressure. A
design pressure higher than the operating pressure with 30 psi or 10 percent,
whichever is the greater, will satisfy this requirement. The pressure of the
fluid and other contents of the vessel should also be taken into consideration.
See tables on page 29 for pressure of fluid.
3.
MAXIMUM ALLOWABLE WORKING PRESSURE
The internal pressure at which the weakest element of the vessel is loaded
to the ultimate permissible point, when the vessel is assumed to be:
(a)
(b)
(c)
(d)
in corroded condition
under the effect of a designated temperature
in normal operating position at the top
underthe effect of other loadings (wind load, external pressure, hydrostatic pressure, etc.) which are additive to the internal pressure.
When calculations are not made, the design pressure may be used as the
maximum allowable working pressure (MA WP) code 3-2.
A common practice followed by many users and manufacturers of pressure
vessels is to limit the maximum allowable working pressure by the head or
shell, not by small elements as flanges, openings, etc.
See tables on page 28 for maximum allowable pressure for flanges.
See tables on page 142 for maximum allowable pressure for pipes.
The term, maximum allowable pressure, new and cold, is used very often. It
means the pressure at which the weakest element of the vessel is loaded to
the ultimate permissible point, when the vessel:
(a) is not corroded (new)
(b) the temperature does not affect its strength (room temperature ) (cold)
and the other conditions (c and d above) also need not to be taken
into consideration.
4.
HYDROSTATIC TEST PRESSURE
At least 1.3 times the maximum allowable working pressure or the design
pressure to be marked on the vessel when calculations are not made to
determine the maximum allowable working pressure.
Ifthe stress value of the vessel material at the design temperature is less than
at the test temperature, the hydrostatic test pressure should be increased
proportionally.
Hydrostatic test shall be conducted after all fabrication has been completed.
16
In this case, the test pressure shall be:
1.5 X
Stress Value S At Test Temperature
Max. Allow. W. Press.
(Or Design Press.)
X
Stress Value S At Design Temperature
Vessels where the maximum allowable working pressure limited by the
flanges, shall be tested at a pressure shown in the table:
Primary Service
Pressure Rating
1501b
300lb 400lb
600lb
9001b 1500lb
Hydrostatic Shell Test
Pressure
425
1100
2175
3250
1450
5400
25001b
9000
Hydrostatic test of multi-chamber vessels: Code UG-99 (e)
A Pneumatic test may be used in lieu of a hydrostatic test per Code UG-I 00
Proof tests to establish maximum allowable working pressure when the
strength of any part of the vessel cannot be computed with satisfactory
assurance of safety, prescribed in Code UG-I 0 1.
5. MAXIMUM ALLOWABLE STRESS V ALVES
The maximum allowable tensile stress values permitted for different materials
are given in table on page 189. The maximum allowable compressive stress
to be used in the design of cylindrical shells subjected to loading that produce
longitudinal compressive stress in the shell shall be determined according to
Code par. UG-23 b, c, & d.
6. JOINT EFFICIENCY
The efficiency of different types of welded joints are given in table on page
172. The efficiency of seamless heads is tabulated on page 176.
The following pages contain formulas used to compute the required wall
thickness and the maximum allowable working pressure for the most
frequently used types of shell and head. The formulas of cylindrical shell are
given for the longitudinal seam, since usually this governs.
The stress in the girth seam will govern only when the circumferential joint
efficiency is less than one-half the longitudinal joint efficiency, or when
besides the internal pressure additional loadings (wind load, reaction of
saddles) are causing longitudinal bending or tension. The reason for it is
that the stress arising in the girth seam pound per square inch is one-half of
the stress in the longitudinal seam.
The formulas for the girth seam accordingly:
PR
1 =
2SE
See notation on page 22.
+ O.4P
P =
2SEI
R - 0.41
17
NOTES
18
INTERNAL PRESSURE
FORMULAS IN TERMS OF INSJDE DIMENSIONS
NOTATION
P
5
E
=
Design pressure or max. allowable
working pressure psi
= Stress value of material psi. page
189
A
R
= Joint efficiency. page 172
= Inside radius. inches
D = Inside
diameter. inches
Wall thickness. inches
CA. = Corrosion allowance. inches
t
=
CYLINDRICAL SHELL (LONG SEAM) 1
r
/
\
\
t
+--.f-- l~
'~
PR
SE-O.6P
t
R
P=
SE~_
R+O.6t
I.
Usually the stress in the long seam is governing. See
preceding page.
2.
When the wall thickness exceeds one half of the inside
radius or P exceeds 0.385 SE, the formulas given in
the Code Appendix 1-2 shall be applied.
B
SPHERE
6
and
HEMISPHERICAL HEAD
PR
2SE-O.2P
t
P
2SE t
R+O.2t
~"","~
l
R
f
I.
For heads without a straight flange. use the efficiency
of the head to shell joint if it less than the efficiency
of the seams in the head.
2. When the wall thickness exceeds 0.356 R or P exceeds
0.665 SE. the formulas given in the Code Appendix
1-3, shall be applied.
C
2: 1 ELLIPSOIDAL HEAD
hS-~
I.
]\1
0
h = 0/4
t
I.
PD
2SE-O.2P
P=
2SEt
D+O.2t
For ellipsoidal heads, where the ratio of the major
and minor axis is other than 2: I, see Code Appendix
1-4(c).
19
EXAMPLES
E
DESIGN DATA:
p = 100 psi design pressure
S = 20,000 psi stress value of
SA 515-70 plate @ 500°F
E = 0.85, efficiency of spot-examined
joints of shell and hem is. head to
shell
1.00, joint efficiency of seamless
heads
R = 48 inches inside radius*
D = 96 inches inside diameter*
t = required wall thickness, inches
CA. = 0.125 inches corrosion allowance
* in corroded condition greater
with the corrosion allowance.
SEE DESIGN DATA ABOVE
SEE DESIGN DATA ABOVE
Determine the required thickness,
t of a shell
Determine the maximum allowable
working pressure P for 0.500 in. thick
shell when the vessel is in new condition.
100 X 48.125
.
t=20,000 X 0.85 -0.6XIOO =0.284 m.
+CA.
=
P=20,000 X 0.85 X 0.500
48 + 0.6 X 0.500
0.125 in.
0.409 in.
176 psi
Use 0.500 in. plate
SEE DESIGN DATA ABOVE
SEE DESIGN DATA ABOVE
The head furnished without straight
flange.
Determine the required thickness,
t ofa hemispherical head.
t
100X48.125
=0.142 in.
2 X 20,000 X 0.85 -0.2 XI 00
+C A.
0.125 in.
0.267 in.
Determine the maximum allowable
working pressure, P for 0.3125 in. thick
head, when it is in new condition.
P 2 X 20,000 X 0.85 X 0.3125 -221
48+0.2XO.3125
-
.
pSI
Use OJ 125 in. plate
SEE DESIGN DATA ABOVE
Determine the required thickness ofa
seamless ellipsoidal head.
100 X 96.25
.
t 2 X 20,000 X 1.0-0.2 X 100 =0.241 m.
+CA.
0.125 in.
OJ66 in.
Use 0.375 in. min. thk. head
SEE DESIGN DATA ABOVE
Determine the maximum allowable
working pressure, P for 0.250 in. thick
seamless head, when it is in corroded
condition.
P
2 X 20,000 X 1.0 X 0.250 -103 .
96.25 + 0.2 X 0.250
pSI
20
INTERNAL PRESSURE
FORMULAS IN TERMS OF INSIDE DIMENSIONS
D = Inside diameter, inches
NOTATION
a = One half of the included (apex)
angle, degrees
L = Inside radius of dish, inches
r = Inside knuckle radius. inches
I = Wall thickness, inches
C.A. = Corrosion allowance. inches
P = Design pressure or max. allowable
working pressure psi
S = Stress value of material psi, page
189
E = Joint efficiency, page 172
R = Inside radius. inches
D
CONE
AND
CONICAL SECTION
PD
t=~~----~~~~:7
2 cos a (SE-O.6P)
P= 2SEt cos a
D+ 1.2t cos a
I. The half apex angle, a not greater than 30°
2. When a is greater than 30 ~ special analysis is required.
(Code Appendix 1-5(g))
ASME FLANGED AND DISHED HEAD
E
(TORISPHERICAL HEAD)
0.885PL
t
SEt
SE-O.IP
P
=-=0--=.8=85-=-=L=-+-0-=-."'-1t
When lIr less than 16 2/3
\
When the min. t~nsile strength
of material exceeds 70,000 psi.
see Code UG-32(e)
PLM
p=
t = -=-2=SE=--=0-=.2-=P
2SEt
LM+0.2t
VALUES OF FACTOR "M"
L/r
M
L/r
M
*
1.00
1.50
1.25
1.00
1.06
1.08
1.03
7.00
8.00
1.46
2.00
2.25
1.10
2.50
2.75
1.15
1.13
1.17
10.0
9.00
8.50
7.50
1.41
I. 75
19·50
3.00
1.18
3.25
1.20
11.0
10.5
3.50
4.00
1.22
1.25
12.0
11.5
4.50
1.28
5.00
1.31
14.0
13.0
5.50
6.00
1.34
1.36
16.0
15.0
2
16]"
1.54
1.50
1.58
1.62
1.69
I. 75
1.48
1.52
1.56
I.~Q
1.65
1.72
1.77
THE MAXIMUM ALLOWED RATIO: L - D + 2t
(see note 2 on facing page)
1.44
6.50
1.39
•
21
EXAMPLES
DESIGN DATA:
P = 100 psi design pressure
S = 20,000 psi stress value of
SA 515-70 plate @ 500°F
E = 0.85, efficiency of spot-examined
I
joints
'
E = 1.00, joint efficiency of seamless
heads
SEE DESIGN DATA ABOVE
cos 30°= 0.866
Determine the required thickness,
t of a cone
L = 96 inches inside radius of dish*
D = 96 inches inside diameter*
t = required wall thickness, inches
a = 300 0ne half ofthe apex angle
CA. = 0.125 inches corrosion allowance
* in corroded condition greater with
the corrosion allowance
SEE DESIGN DATA ABOVE
I
!
100 X 96.25
-0 "28 .
t 2XO.866 (20,000 X 0.85 _0.6XlOO) - . J m.
+C.A.
Q 125 jn
Determine the maximum allowable
working pressure, P for 0.500 in. thick
cone, when the vessel is in new
condition.
P 2X20,000XO.85XO.500XO.866
96 + 1.2 X 0.500 X 0.866
152psi
0.453 in.
Use 0.500 in. plate
SEE DESIGN DATA ABOVE
SEE DESIGN DATA ABOVE
Llr = 16~
Determine the required thickness, t of a
seamless ASME flanged and dished
head.
0.885 x 100 x 96.125
.
t=20,OOO x 1.0-0.1 XI 00 0.426 m.
+CA.
0.125 in.
0.551 in.
Determine the maximum allowable
working pressure, P for 0.5625 in. thick
seamless head, when the vessel is in
new condition.
P=
20,000 X 1.0 X 0.5625
132 psi
0.885 X 96 + 0.1 X 0.5625
Use 0.5625 in. plate
SEE DESIGN DA T A ABOVE
Knuckle radius r = 6 in. Llr = ~ = 16
M= 1.75 from table.
Determine the required thickness t of a
seamless ASME flanged and dished
head.
100 X96.125 X 1.75
.
t= 2 X 20,000 - 0.2 X 100 -0.421 m.
0.125 in.
0.54610.
Use 0.5625 in. min. thick head
+CA.
SEE DESIGN DATA ABOVE
Knuckle radius r = 6 in. Llr = 9£ = 16
M= 1.75 from table
Determine the maximum allowable
working pressure, P for a 0.5625 in.
thick seamless head when the vessel is
in corroded condition.
p= 2x20,000xl.OxO.5625 104 .
96.125x1.75+0.2 x0.4375
pSI
NOTE: When the ratio of Llr is greater than 161, fupn-Code construction) the values of
M may be calculated by the formula: M = Y4 (3 + Wr)
22
INTERNAL PRESSURE
FORMULAS IN TERMS OF OUTSIDE DIMENSIONS
NOTATION
= Joint efficiency, page 172
= Outside radius, inches
D = Outside· diameter, inches
t = Wall thickness, inches
C.A. = Corrosion allowance. inches
E
P = Design pressure or max. allowable
R
working pressure psi
S
= Stress va'ue of material psi, page
189
A
CYLINDRICAL SHELL (LONG SEAM)I
PR
1-
SE
+ 0.4P
SEI
P - R - O.4t
1. Usually the stress in the long seam is governing. See
page 14
2. When the wall thickness exceeds one half of the inside
radius or P exceeds 0.385 SE, the formulas givencin
the Code Appendix 1-2 shall be applied.
B
SPHERE and HEMISPHERICAL HEAD
PR
1 -
2SE
+ 0.8P
2SEI
P - R - 0.81
1. For heads without a straight flange, use the efficiency
of the head to shell joint if it is less than the efficiency
of the seams in the head.
2. When the wall thickness exceeds 0.356 R or P exceeds
0.665 SE, the formulas given in the Code Appendix
1-3, shall be applied.
C
2:1 ELLIPSOIDAL HEAD
PD
t=""'2"""'S=E-+--:"1-".8~P
2SEt
P= ..- - D· -1.8t
1. For ellipsoidal heads, where the ratio of the major and
minor axis is other than 2:1, see Code Appendix 1-4(c).
h = 0/4
23
EXAMPLES
DESIGN DATA:
P = 100 psi design pressure
S = 20,000 psi stress value of
SA 515-70 plate @ 500°F
E = 0.85, efficiency of spot-examined
joints of shell and hemis. head to
shell
R
D
t
CA.
1.00, joint efficiency ofseamless
heads
= 48 inches outside radius
= 96 inches outside diameter
= Required wall thickness, inches
= 0.125 inches corrosion allowance
=
SEE DESIGN DATA ABOVE
SEE DESIGN DATA ABOVE
Determine the required thickness, t
of a shell
100 X 48
0.283 in
t 20,000 X 0.85 - 0.4 X 100
+C.A.
E
0.125 in.
0.408 in.
Determine the maximum allowable
working pressure, P for 0.4375 in. thick
shell when the vessel is in new condition.
20,000 X 0.85 X 0.4375
p=
155psi
48 - 0.4 X 0.4375
Use: 0.4375 in. thick plate
SEE DESIGN DATA ABOVE
SEE DESIGN DATA ABOVE
Head furnished without straight flange.
Determine the required thickness, t of a
hemispherical head.
100X48
0.141 in.
2 X20,000XO.85 +0.8 X 100
t
+CA.
0.125 in.
0.266 in.
Determine the maximum allowable
wOFking pressure, P for 0.3125 in. thick
head, when the vessel is in new
condition.
p=2 X 20,000 X 0.85 X 0.3125 222 psi
48-0.8 XO.3125
Use: 0.3125 in. min. thick head
SEE DESIGN DA T A ABOVE
SEE DESIGN DATA ABOVE
Determine the required thickness t of a
seamless ellipsoidal head.
Determine the maximum allowable
working pressure, P for 0.375 in. thick
head, when it is in new condition.
t
100X96
0.239 in.
2 X 20,000 X l.0+ l.8X 100
+CA.
Use 0.375 in. min. thick head
0.125 in.
0.364 in.
P
2 X 20,000 X 1.0 X 0.375
96-1.8 X 0.375
157psi
24
INTERNAL PRESSURE
FORMULAS IN TERMS OF OUTSIDE DIMENSIONS
NaTATION
D = Outside diameter, inches
a = One half of the included (apex)
angle. degrees
L = Outside radius of dish, inches
r = Inside knuckle radius. inches
t = Wall thickness, inches
C.A. = Corrosion allowance. inches
P = Design pressure or max. allowable
working pressure psi
S = Stress value of material psi, page
189
E = Joinl efficiency. page 172
R = OUlside radius, inches
D
CONE
AND
CONICAL SECTION
~
!
[
~
t=
1
PD
P=
2 cos a (SE +0.4P)
2SEt cos a
D -0.8t cos a
~
Ii::
T
0
1-
-oj
'r-'-
I. The half apex angle, a not greater than 30°
2. When a is greater than 30°,. special analysis is
required. (Code Appendix 1-5(g»
E
ASME FLANGED AND DISHED HEAD
(TORISPHERICAL HEAD)
WhenL/r= 16 2 /3
<,(l
~
--f t:
~
i
\!.I
t
0.885PL
SE+0.8P
P
SEt
0.885L-0.8t
When L/r Less Than 16 2/3
0
\
t
When the min. tensile strength
of material exceeds 70,000 psi.
see Code UG-32(e)
PLM
2SE+P(M-0.2)'
2SEt
P= ML -t(M-0.2)
V ALUES OF FACTOR M
L/r
M
L/r
M
•
1.00
1.50
1.25
1.06
1.00
11.03
7.00
1.08
144
1.10
8.50
1.46
2.25
1.13
9.00
8.00
17.50
1.41
1.75
2.00
11.48
2.50
1.15
1.17
10.0
9.50
1.50
2.75
1.52
3.00
1.18
1.20
11.0
10.5
1.54
3.25
1.56
3.50
1.22
THE MAXIMUM ALLOWED RATIO : L - t
=D
1.25
12.0
11.5
1.58
4.00
1.60
4.50
1.28
1.31
14.0
13.0
1.62
5.00
11.65
5.50
1.34
16.0
15.0
1.69
11.72
1.75
6.00
1.36
16t
1.77
(see note on facing page)
6.50
1.39
•
25
EXAMPLES
heads
48 inches outside radius
96 inches outside diameter
30° one half of the apex angle
96 inches outside radius of dish
Required wall thickness, inches
0.125 inches corrosion allowance
DESIGN DATA:
P = 100 psi design pressure
S = 20,000 psi stress value of
SA 515-70 plate @ 500°F
E = 0.85, efficiency of spot-examined
joints
E = 1.00, joint efficiency of seamless
t =
CA. =
SEE DESIGN DATA ABOVE
SEE DESIGN DATA ABOVE
cos 30° = 0.866
Determine the required thickness, t
of a cone
l00X %
.
t=2XO.866X(20,OOOXO.85+O.4Xl (0)=0.326 m.
0.125 in.
0.451 in.
+CA.
R
=
D =
ex =
L =
Determine the maximum allowable
working pressure, P for 0.500 in. thick
cone in new condition.
p=2 X 20,000 X 0.85 X 0.500 X 0.866 153 psi
96 -(0.85 X 0.500 X 0.866)
Use: 0.500 in. thick plate
SEE DESIGN DATA ABOVE
SEE DESIGN DATA ABOVE
Llr = 16~
Determine the required thickness, t of a
seamless ASME flanged and dished
head.
0.885 X 100 X96
.
t= 20,000 X 1.0 + 0.8 X 100=0.423 m.
+C.A.
0.125 in.
0.548 in.
Determine the maximum allowable
working pressure, P for 0.5625 in. thick
seamless head, when the vessel is in
corroded condition.
(=0.5625-0.125 =0.4375
P
20,000 X 1.0 X 0.4375
0.885 X96-0.8 X0.4375
10"" .
,) pSI
Use: 0.5625 in. min. thick head
SEE DESIGN DATA ABOVE
Knuckle radius r = 6 in. Llr = 96 = 16
6
M= 1.75 from table.
Determine the required thickness t of a
seamless ASME flanged and dished
head.
100X96X 1.75
.
t=2 X 20,000 X 1.0+ 100(1.75-0.2) 0.419m.
+CA.
0.125 in.
0.544 in.
SEE DESIGN DATA ABOVE
Knuckle radius r = 6 in. Llr =
~
= 16
M= 1.75 from table.
Determine the maximum allowable
working pressure, P for a 0.5625 in.
thick seamless head when the vessel is
in corroded condition.
2 X 20,000 X 1.0 X 0.4375
P 1.75 X96-0.4375(1.75 _0.2) 104 psi
Use 0.5625 in. min. thick head
NOTE: When the ratio ofLir is greater than l6~ , (non-Code construction) the values of
M may be calculated by the formula: M = 14 (3 + Wr)
26
INTERNAL OR EXTERNAL PRESSURE
FORMULAS
NOTATION
P = Internal or external design pressure psi
d
E=joint efficiency
= Inside diameter of shell, in.
S = Maximum allowable stress value of material, psi
t
= Minimum required thickness of head, exclusive of corrosion allowance, in.
th = Actual thickness of head exclusive of corrosion allowance, in.
tr = Minimum required thickness of seamless shell for pressure, in.
ts = Actual thickness of shell, exclusive of corrosion allowance, in.
A
CIRCULAR FLAT HEADS
t = d
0.13 P/SE
V
This formula shall be applied:
1. When d does not exceed 24 in.
2. thld is not less than 0.05
nor greater than 0.25
3. The head thickness, th is not less than
the shell thickness, ts
B
t=dVCPISE
C = 0.33tr/ ts
c
D
C min. = 0.20
2 t,min. nor less than 1.25ts
need not be greater than t
If a value of tr/ ts less than 1 is used in
calculating t, the shell thickness t s shall be
maintained along a distance inwardly from
the inside face of the head equal to at least
2..[cii:
Non-circular, bolted flat heads, covers,
blind flanges Code UG-34; other types
of closures Code UG-35
27
INTERNAL OR EXTERNAL PRESSURE
EXAMPLES
DESIGN DATA
P = 300 psi design pressure
E =joint efficiency
d = 24 in. inside diameter of shell
S = 17,100 psi maximum allowable stress value of SA-515-60 plate
tr = 0.243 in. required thickness of seamless shell for pressure.
ts = 0.3125 in. actual thickness of shell.
DETERMINE THE MINIMUM REQUIRED THICKNESS, t
=
t
=
d "0.13 P/SE
1.146in.
24 " 0.13 x 300117,100x 1
Use 1.25 in. head
Checking the limitation of
l.25
24
d
= 0.052
The ratio of head thickness to the diameter of the shell is satisfactory
SEE DESIGN DATA ABOVE
0.243
tr
=
C
0.33 -[
=
0.33
0.3125
s
=
t
d
JCP/SE
=
24
=
0.26
~ 0.26 x 300/17,100'(
1
=
l.620 in.
Use 1.625 in. plate
Using thicker plate for shell, lesser thickness will be satisfactory for
the head.
Is =
C
=
I =
0.375 in.
tr
0.33 -t- = 0.33
s
d .jCP/SE
=
24
0.243
0.375
=
0.214
oJ 0.214 x 30<V17,IOOx 1 = l.471 in.
Use 1.625 in. plate
The shell thickness shall be maintained along a distance 2 ~ from the
inside face of the head
2 "24 x 0.375 = 6 in.
28
PRESSURE - TEMPERATURE RATINGS
FOR STEEL PIPE FLANGES AND FLANGED FITTINGS
American National Standard ANSI B 16.5-199611998 ADDENDA
Class
150 lb. 300 lb. 400 lb. 600 lb. 900 lb. 1,500 lb. 2,5001b
Hydrostatic
test
450
1,125
1,500
2,225
3,350
5,575
9,275
pressure, psig
Temperature, F MAXIMUM ALLOWABLE NON-SHOCK PRESSURE PSIG.
-20 to 100
285
740
990
1,480
2,220
3,705
6,170
200
260
675
900
1,350
2,025
3,375
5,625
3,280
5,470
300
230
655
875
1,315
1,970
400
1,900
3,170
845
1,270
200
5,280
635
500
600
650
700
170
140
125
110
600
550
535
535
800
730
715
710
1,200
1,095
1,075
1,065
1,795
1,640
1,610
1,600
2,995
2,735
2,685
2,665
4,990
4,560
4,475
4,440
750
800
850
900
95
80
65
50
505
410
270
170
670
550
355
230
1,010
825
535
345
1,510
1,235
805
515
2,520
2,060
1,340
860
4,200
3,430
2,230
1,430
950
1,000
35
20
105
50
140
70
205
105
310
155
515
260
860
430
Ratings apply to NPS Yz trough NPS 24 and to materials:
A 105 (1) A 350 Gr. LF2 (1) A 350 Gr. LF6 Cl. 1 (4) A 216 Gr. WCB (1)
A 515 Gr. 70 (1) A 516 Gr. 70 (1) (2) A 537 Cl. 1 (3)
NOTES:
(1) Permissible, but not recommended for prolonged use above 800 OF.
(2) Not to be used over 850 OF.
(3) Not to be used over 700 oF.
(4) Not to be used over 500 oF.
Flanges of ANSI B 16. 5 shall not be used for higher ratings except where it
is justified by the design methods of the Code.
Ratings are maximum allowable non-shock working pressures expressed
as gage pressure, at the tabulated temperatures and may be interpolated
between temperatures shown.
Temperatures are those on the inside of the pressure-containing shell of the
flange. In general, it is the same as that of the contained material.
Flanged fittings shall be hydrostatically tested.
29
PRESSURE OF FLUID
STATIC HEAD
The fluid in the vessel exerts pressure on the vessel wall. The intensity of the
pressure when the fluid is at rest is equal in all directions on the sides or at bottom
of the vessel and is due to the height of the fluid above the point at which the
pressure is considered.
The static head when applicable shall be added to the design pressure of the
vessel.
The tables below when applicable shall be added to the design pressure of the
water.
To find the pressure for any other fluids than water, the given in the tables shall
be be mUltiplied with the specific gravity of the fluid in consideration.
Pressure in Pounds per Square Inch for Different Heads of Water
I
Head
Feet
0
10
20
30
40
50
(i)
70
00
'Xl
0
4.33
8.66
12.99
17.32
21.65
25.98
30.31
34.64
38.97
1
0.43
4.76
9.09
13.42
17.75
22.08
26.41
30.74
35.07
39.40
2
0.87
5.20
9.53
13.86
18.19
22.52
26.85
31.18
35.51
39.84
3
1.30
5.63
9.96
14.29
18.62
22.95
27.28
31.61
35.94
40.27
4
1.73
6.06
10.39
14.72
19.05
23.38
27.71
32.04
36.37
40.70
5
2.16
6.49
10.82
15.15
19.48
23.81
28.14
32.47
36.80
41.13
6
2.60
6.93
11.26
15.59
19.92
24.25
28.58
32.91
37.24
41.57
7
3.03
7.36
11.69
16.02
20.35
24.68
29.01
33.34
37.67
42.00
8
3.46
7.79
12.12
16.45
20.78
25.11
29.44
33.77
38.10
42.43
9
3.90
8.23
12.56
16.89
21.22
25.55
29.88
34.21
38.54
42.87
NOTE: One foot of water at 62° Fahrenheit equals .433 pound pressure per square
inch. To find the pressure per square inch for any feet head not given in the table
above, multiply the feet times .433.
Heads of Water in Feet Corresponding to
Certain Pressure in Pounds per Square Inch
Pressure,
Lbs.
0
0
1
2
3
4
5
6
7
8
9
18.5
4.6
2.3
11.5
13.9
16.2
20.8
6.9
9.2
23.1
25.4
27.7
30.0
32.3
34.6
36.9
39.3
41.6
43.9
48.5
50.8
53.l
55.4
57.7
60.0
62.4
64.7
46.2
67.0
20
71.6
73.9
78.5
80.8
83.l
85.4
87.8
69.3
90.1
76.2
30
92.4
94.7
97.0
99.3 101.6 103.9 106.2 108.5 110.8 113.2
40
115.5 117.8 120.1 122.4 124.7 127.0 129.3 131.6 133.9 136.3
50
(i)
138.6 140.9 143.2 145.5 147.8 150.l 152.4 154.7 157.0 159.3
70
161.7 164.0 166.3 168.6 170.9 173.2 175.5 177.8 180.1 182.4
184.8 187.l 189.4 191.7 194.0 196.3 198.6 200.9 203.2 205.5
00
207.9 210.2 212.5 214.8 217.l 219.4 221.7 224.0 226.3 228.6
'Xl
NOTE: One pound of pressure per square inch of water equals 2.309 feet of water
at 62° Farenheit. Therefore, to find the feet head of water for any pressure not
given in the table above, multipy the pressure pounds per square inch by 2.309.
10
30
TABLES
F or quick comparison of required plate thickness and weight for various
materials and at a different degree of radiographic examination.
A Stress values at temperature -20° to 500 OF.
SA53 B
SA 515-60
SA 516-60
14,535
17,100
SA285 C
85% J. E.
100% J. E.
13,345
15,700
SA515-70
SA 516-70
17,000
20,000
B Ratios of Stress Values
13,345
13,345
14,535
15,700
17,000
17,100
20,000
-
0.92
0.85
0.79
0.78
0.67
14,535
1.09
-
0.92
0.86
0.85
0.73
-
17,000
1.27
1.17
1.08
0.93
0.92
0.79
-
17,100
1.28
1.18
1.09
1.01
0.99
0.85
0.86
15,700
1.18
1.08
-
20,000
1.49
1.37
1.27
1.18
1.17
-
Table A shows the stress value of the most frequently used shell and head
materials.
Table B shows the ratios of these stress values.
EXAMPLE:
1. For a wessel using SA 515-70 plate, when spot radiographed, the required
thickness 0.4426 inches and the weight of the vessel 12600 lbs.
2. What plate thickenss will be required, and what will the weight of the
vessel be using SA 285-C plate and full radiographic examination:
In case 1. The stress value of the material 17,000
In case 2. The stress value of the material 15,700
The ratio of the two stress values from Table B= 1.08 In this proportion the
required plate thickness and the weight of the vessel will be increased.
0.4426 x 1.08 = 0.4780 in.
12600 x 1.08 = 13608 lb.
31
EXTERNAL PRESSURE
DESIGN PRESSURE
When Code Symbol is to be applied, the vessel shall be designed and
stamped with the maximum allowable external working pressure. It is
recommended that a suitable margin is provided when establishing the
maximum allowable external pressure to allow for pressure variation in
service. Code UG-28(f).
Vessels intended for service under external working pressure of 15 psi
and less may be stamped with the Code Symbol denoting compliance
with the rules for external pressure provided all the applicable rules of
this Division are also satisfied. Code UG-28(f).
This shall not be applied if the vessel is operated at a temperature below minus 20° F, and the design pressure is determined by the Code
UCS-66(c)(2) or Code UHA-51(b) to avoid the necessity of impact
test.
Vessels with lap joints: Code UG-28(g) Non-cylindrical vessel, jacket:
Code UG-28(i).
TEST PRESSURE
Single-wall vessels designed for vacuum or partial vacuum only, shall
be subjected to an internal hydrostatic test or when a hydrostatic test is
not practicable, to a pneumatic test. Code UG-99(f).
Either type of test shall be made at a pressure not less than 1Yz times
the difference between normal atmospheric pressure and the minimum
design internal absolute pressure. Code UG-99(f).
Pneumatic test: Code UG-l 00.
The design method on the following pages conform to ASME Code for
Pressure Vessels Section VIII, Div. 1. The charts on pages 42-47 are
excerpted from this Code.
32
EXTERNAL PRESSURE
FORMULAS
NOTATION
P
External design pressure, psig.
~ ~_ Maximum allowable working pressure, psig.
ll.
Outside diameter, in.
L0
the length, in. of vessel section between:
1. circumferential line on a head at one-third the depth of the
head-tangent line,
2. stiffening rings
3. jacket closure
4. cone-to-cylinder junction or knuckle-to-cylinder junction of
a toriconical head or section,
5. tube sheets (see page 39)
t
Minimum required wall thickness, in.
=
=
=
A.
1"1
~
,-"----' -
....---1111- r-
CYLINDRICAL SHELL
Seamless or with Longitudinal Butt Joints
When D/ / equal to or greater than 10
the maximum allowable pressure:
Pa=
48
3eD o Il)
The value of B shall be determined by the following procedure:
1. Assume a value for t; (See pages 49-511)
Determine LI Do and D ~ 1/
VESSEL
WITHOUT STIFFENING RING
B.
~
~
a:::
iii
~-:..--:
"'"
--~
Do
~
z
Z
~
\I.
\I.
~
~H-----~----H--~--~
~'
-----,..
2. Enter Fig. G (Page 42) at the value of LIDo'
Enter at 50 when LIDo is greater than 50, and
at 0.05 when LIDo is less than 0.05.
3. Move horizontally to the line representing
Dolt. From the point of intersection move vertically to determine the value of factor A .
4. Enter the applicable material chart (pages
43-47) at the value of A. Move vertically to the
appltcable temperature line-.
5. From the intersection move horizontally and
read the value of B.
Compute the maximum allowable working pressure, P
If the maximum allowable working pressure is
smaller than the design pressure, the design
procedure must be repeated increasing the vessel thickness or decreasing L by stiffening ring.
-For values of A falling to the left of the
applicable temperature line, the value of P
can be calculated by the formula:
Q'
Q
Pa =
VESSEL
WITH STIFFENING RING
2AE
3(D.lt)
When the value of Dolt is less than 10, the
formulas given in the Code UG-28(c)(2) shall
be applied.
33
EXAMPLES
DESIGN DATA
P = IS psig. external design pressure
Do = 96 in. outside diatmeter of the sheIl
Length of the vessel from tangent line to tangent line: 48 ft. 0 in. = 576 in.
Heads 2: I e11ipsoidal
Material of shell SA - 285 C plate
Temperature 500 0 F
E = Modulus of elasticity of material, 27,000,000 psi. @ 500 of (see chart
on page 43)
Determine the required sheil thickness.
Assume a shell thickness: t = 0.50 in. (see page 49)
Length L = 592 in. (length of shell 576 in. and one third of the depth of
heads 16 in.)
LlDo= 592/96=6.17
D/I= 96/0.5 = 192
A=0.00007 from chart (page 42)determined by the procedure described on
the facing page.
Since the value of A is falling to the left of the applicable temperature-line in
Fig. CS-2 (pg. 43),
P" _ 2AE/3(D/ I) = 2 x 0.00007 x 27,000,000/3 x 192 = 6.56 psi.
Since the maximum allowable pressure Pais smaller than the design pressure
P stiffening rings shall be provided.
Using 2 stiffening rings equally spaced between the tangent lines of the heads,
Length of one vessel section, L = 200 in. (length of shell 192 in. plus one third
of depth of head 8 in.)
.
..,-1
co
\0
B = 3000 from chart (page 43 )
"0 ,
determined by the procedure described on
facing page.
-
I::
'",
II::
'"
I-
"
•'-Ci
"0
co
'00
v
'-Ci
~\...
~
V
N
..j
Jco
Dolt = 96/0.5 = 192
LlD.= 200/96 = 2.08
A = 0.00022 from chart (page 42)
Po = 4B/3(D/I)
= 4 x 3000/3 x
192 = 20.8 psi.
Since the maximum allowable pressure Po is
greater than the design pressure P, the assumed
thickness of shell using two stiffening rings,
is satisfactory.
See page 40 for design of stiffening rings.
34
EXTERNAL PRESSURE
FORMULAS
NOTATION
P
External design pressure psig.
P
Maximum allowable working pressure psig.
Do
Outside diameter of the head, in.
Ra
Outside radius of sphere or hemisphereical head, O.9Do for ellipsoidal
heads, inside crown radius of flanged and dished heads, in.
t
Minimum required wall thickness, inches.
E
Modulus of elasticity of material, psi. (page 43)
Q
SPHERE and HEMISPHERICAL HEAD
The maximum
p =
B
allowable pressure:
(Ro / I)
The value of B shall be determined by the following procedure:
1. Assume the value for t and calculate the value of
A using the formula: AF--Q. 125/( R n / I ) (see page 49)
2. Enter the applicable material chart (pages 43-47) at
the value of A. Move vertically to the applicable
temperature line. *
3. From the intersection move horizontally and read
the value of B.
*For values of A faIling to the left of the applicable temperature line, the value of Pa can be calculated by the formula:P n = O.0625E/{R o I t)~
If the maximum allowable working pressure P computed by the formula above, is smaller than the design
pressure, 'a greater value for t must be selected and
the design procedure repeated.
Q
Q
2:1 ELLIPSOIDAL HEAD
The required thickness shall be the greater ot the
following thicknesses.
(1) The thickness as computed by the formulas
given for internal pressure using a design pressure 1.67 times the external pressure and joint
efficiency E =1.00.
(2) The thickness proofed by formula Pa= BIRo It
whereR,,=0.9 Du , and B to be determined as for
sphere.
ASME FLANGED AND DISHED HEAD
TORISPHERICAL HEAD
The required thickness and maximum allowable pressure shall be computed by the procedures given for
ellipsoidal heads. (See above)Romaximum=D"
35
EXAMPLES
DESIGN DATA:
P = 15 psig external design pressure
Do = 96 inches outside diameter of head
Material of the head SA-285C plate
500 0 F design temperature
Determine the required head thickness.
SEE DESIGN DATA ABOVE
Assume a head thickness:
A
=
Ro
= 48.00 in.
0.125/( 48.00/0.25)~0.00065
From Fig. CS-2 (page 43) B
facing page.
Pa
t. = 0.25 in.
=
8500/(48.00/0.25)
=
8500 determined by the procedure described on the
= 44.27 psi.
Since the maximum allowable working pressure Pais exceedingly greater than
the design pressure P, a lesser thickness would be satisfactory.
For a second trial, assume a head thickness: t = 0.1.875 in.
Ro = 48.00 in.
A
B
= 0.125/(48.00/0.1875) = 0.0005
= 6700, from chart (page 43), Pa = BI(R/I) = 67001256 = 26.2 psi.
The assumed thickness: t = 0.1875 in. is
SEE DESIGN DATA ABOVE.
sati~factory.
Procedure (2.)
Assume a head thickness: (= 0.3125 in.. Ru = 0.9 x 96 = 86.4 in.
A = 0.125/(86.4/0.3125) = 0.00045
B = 6100 from chart (page 43 ),p .. - BI(Ra/ 1)1= 6100/276 = 22.1 psi.
Since the maximum allowable pressure p .. is greater than the design pressure
P the assumed thickness is satisfactory.
SEE DESIGN DATA ABOVE.
Procedure (2.)
Assume a head thickness: t =0.3125 in., Ra=.Do = 96 in.
A =0.125/(96/0.3125) =0.0004
B = 5200 from chart (page 43), P = BI (Ro / t) = 5200/307 = 16.93 psi.
Q
Since the maximum allowable pressure p .. is greater than the design pressure
P the assumed thickness is satisfactory.
36
EXTERNAL PRESSURE
FORMULAS
CONE
AND
CONICAL SECfION
Seamless or with Bull Joints
WHEN a IS EQUAL TO OR LESS THAN 60·
and Dlte ~ 10
The maximum allowable pressure:
P"
=
48
3(D,/t,.)
I. Assume a value for thickness,
I~
The values of B shall be determined by the
following procedure:
2. Determine fe' Lt<, and the ratios Lei DJ and
Dltt
3. Enter chart G (page 42) at the value of LI
D, (LID,) (Enter at 50 when LID, is, greater
than 50) Move horizontally to the lme representing Dr/t. From the point of intersection move vertically and read the value
of A.
4. Enter the applicable material chan at
NOTATION
A
B
a
determined from
= factor
fig.UGO-2B.O (page 42
factor determined from
= charts
(pages 43-47)
= one half of the included
(apex) angle, degrees
D{= outside diameter at the
large end, in.
D.= outside diameter at the
small end, in.
E = modulus of elasticity of
material (page 43)
L = length of cone, in. (see
page 39)
Le = equivalent length of
conical section,
in.(L/2)(l +DsfDt )
external design pressure,
P
psi.
Pa = Maximum allowable
working pressure, psi
t
minimum required
thickness, in.
effective thickness, in.
te
=
=
= =t cos a
the value of A· and move vertically to the
line of applicable temperature. From the
intersection move horizontally and read
the value of B .
S. Compute the maximum allowable working
pressure, P /I •
If P /I is smaller than the design pressure, the
design, the design procedure must be repeated
increasing the thickness or decreasing L by
using of stiffening rings.
-For values of A falling to the left of the applicable line, the value of P can be calculated
by the formula:
P" - 2A£/3(D,II,.)
For cones having D /t ratio smaller than 10,
see Code UG-33 (O(b)
WHEN a IS GREATER THAN 60°
The thickness of the cones shall be the same as
the required thickness for a flat head. the
diameter of which equals the largest outside
diameter of the cone.
Provide adequate reinforcing of the cone-tocylinder juncture. See page I S9
37
EXAMPLES
DESIGN DATA
P = 15 psi external design pressure
Material of the cone SA 285-C plate
500 F design temperature
CONICAL HEAD
O(
=
96 in.
Ds =0
a = 22.5 degrees
Determine the required thickness, t
Length, L = (O,I2)/tana= 48/ .4142 = 115.8, say 116 in
1. Assume a head thickness, t, 0.3125 in.
2.te =t cosa=0.3125 x .9239 = 0.288;
L~ =Ll2 (l+D lOt> = 11612 x (1 + 0/96) = 58
L./O,=58/96 =0.6
D(lle = 96/.288 = 333
3. A = 0.00037 (from chart, page 42)
4. B = 5,200 (from chart, page 43)
5
_
. P" -
48
3(/),/(,)
D,
4 x 5,200
20 8 .
3(333)
= . pSI.
Since the maximum allowable pressure is greater than the design pressure, the
assumed plate thickness is satisfactory.
CONICAL SECTION (See design data above)
0, = 144 in.
Os =96 in.
a =30 deg. Determine the required thickness,
Length, L=[(DrD,)I2]/tana =24/.5774=41.6 in.
1. Assume a head thickness, t, 0.375 in.
2. Ie = t cosa.=0.375 x 0.866=0.324
Le=(L/2)(l
+ D/D,) =41.612 x
+ 96/144) = 34.67
(l
LeID, =34.67/144=0.241
D[it e = 144/0.324=444
3. A =0.00065 (from chart, page 42,
4. B = 8,600 (from chart, page 43)
24
144-96
5
_
48
4 x 8600
2
. p .. - 3(01/t e)
3 X (144/0.324)
144
= 25.8 psi.
Since the maximum allowable pressure P is greater than the design pressure
P, the assumed thickness is satisfactory.
Q
EXAMPLES FOR CONICAL HEAD. WHEN
ex
IS GREATER THAN 60°
ARE GIVEN AT FLAT HEADS
38
NOTES
39
EXTERNAL PRESSURE
FORMULAS
t
L
\.-.J~
Use L in calculation as shown when
the strength of joints of cone to cylinder does not meet the requirements
described on pages 163 - 169 It will
result the thickness for the cone not
less than the minimum required thickness for the joining cylindrical shell.
l
L
t----IJ
f
L
L
I
Use L in calculation as shown when
the strength of joints of cone to cylinder meets the requirements described
on pages 163-169
"
40
EXTERNAL PRESSURE
DESIGN OF STIFFENING RINGS
NOTATION
A
:= Factor determined from the chart (page 42) for the material used in the
stiffening ring.
As
=
Cross sectional area of the stiffening ring, sq. in.
Do
=
Outside Diameter of shell, in.
E
= Modulus of elasticity of material (see chart on page 43)
Is
=
Required moment of inertia of the stiffening ring about its neutral axis parallel
to the axis of the shell, in.4.
I',.
=
Required moment of inertia of the stiffening ring combined with the shell
section which is taken as contributing to the moment of inertia. The width of
the shell section 1.10 Wt
in.4.
o
Ls
=
The sum of one-half of the distances on both sides of the stiffening ring from
the center line of the ring to the (1) next stiffening ring, (2) to the head line at
113 depth, (3) to a jacket connection, or (4) to cone-to-cylinder junction, in.
P
=
External design pressure, psi.
t
=
Minimum required wall thickness of shell, in.
I. Select the type of stiffening ring and determine its cross sectional area A.
II. Assume the required number of rings and distribute them equally between
jacketed section, cone-to-shell junction, or head line at 113 of its depth and
determine dimension, Ls
III. Calculate the moment of inertia of the selected ring or the moment of inertia of
the ring combined with the shell section (see page 95).
IV. The available moment of inertia of a circumferential stiffening ring shall not be
less than determined by one of the following formulas:
l' = Do 2L s (t+A/L)A
I = Do 2Ls (t+A/L)A
\'
10.9
.v
14
The value of A shall be determined by the following procedure:
1. Calculate factor B using the formula:
B= 3/. [ PDo ]
,
4 t+AlLs
2. Enter the applicable material chart (pages 43 _A7) at the value of B and move
horizontally to the curve of design temperature. When the value of B is less than
2500, A can be calculated by the formula: A = 2BIE.
3. From the intersection point move vertically to the bottom of the chart and read the
value of A.
4. Calculate the required moment of inertia using the formulas above.
If the moment ofinertia ofthe ring or the ring combined with the shell section is greater
than the required moment of inertia, the stiffening ofthe shell is satisfactory. Otherwise
stiffening ring with larger moment of inertia must be selected, or the number of rings
shall be increased.
Stiffening ring for jacketed vessel: Code UG-29 (f)
41
EXAMPLES
DESIGN DATA:
P = 15 psi, external design pressure.
Do = 96 in., outside diameter of the shell.
Length of the vessel from tangent line to tangent line: 47 ft. 8 in. = 572 in.
Heads 2: 1 ellipsoidal
Material of the stiffening ring SA-36
Temperature SOO°F
E
Modulus of elasticity of material, 27,000,000 psi, @ SOO°F (see chart on
page 43)
t = 0.500 in. thickness of shell
96"
~
I. An angle of 6 x 4
As = 3.03 sq. in.
N
V
00
in
~
~
-r-.-
~
-.:t
~
~
ctI
-
""\
-
~
rt
f - _ . _ - -f-
-I- -
t-
--
selected.
II. Using 2 stiffening rings equally
-.:t
~
- -
spaced between one-third the
depths of heads (see figure),
Ls = 196 in.
III. The moment of intertia of the
selected angle: 11.4 in.
~
--~-
\0
00
-.:t
5h6
-
1. The value of Factor B:
B = lit [PDol(t + AILs)] =
y.. [15x96/(0.S + 3.03/196)]
;:::2095
00
in
2. Since the value of B is less
than 2500,
A =2BIE=
2 x 209S127,000,000 = 0.00015
IV. The required moment of inertia:
I ;::: [Do 2L s(t+ AslLl A];::: 96 2 x 196 x (O.S + 3.03/196) x 0.00015;::: 997· 4
s
14
14
. m.
Since the required moment of inertia (9 t97 in.4) is smaller than the moment of
inertia of the selected angle (11.4 in.4) the vessel is adequately stiffened.
Stiffening rings may be subject to lateral buckling. This should be considered
in addition to the required moment of inertia.
See pages 95-97 for stiffening ring calculations.
42
I
50.0
40.0
P p_p .....0 . 0
35.0
;;- ;--;;
30.0 2S.0
8 g
0;
I\)
I
J.
J. i
I
p P P ,....p P
~r-~
::.
4-::'
; - 11- =;:-- ;- II -11-11- I\)
I I - r - _II§ ....-Q)--.+...g) ~ ~ _1:l t:;; C-r- '"
[\)
~
~_
.0
J
.1
6
P
I- t::l
1
0 ,p
:;.
~:;.
::.
:;.
11-
II-r-
II
II
II
C5+tTQ)-t-tt-O)-+i~01+-t~~+t
H+-Ift-Hf--t--t;-t+++t-+-+++Hf+++++tf-+++H-H-+-H-H-l-H--+++-+fH-++-H+-H
20.0 t-J\rt--~t-t--++t-ttt-HH-t++t--Jrtt+t-ttl:+++H-it--+-t+t+1H+-++t-+iH-I+-H1-H
18.0 ~~,+-!-+-++-i-ftt++H-++-+-+--H+-H+HH-++H+-++++-Hf++-++t--+-IH-++-H+-H
16.0 t---+--+--+-+-+-t-1-ttt++-t-+-t+-+f-t-t++t++ir-++t+-t-ft--+-++t+1r++-++t--H+-t-it-+-if+H
14.0
J\ \
12.0
'-'
\
1\
\
~\I\\
\
<> "6
\.'
\
? .~ +PI\.rl-'H-\+ru--'l,~H-tt\+-tt+ittirt--H-tt-H-+-Hf+t-+t-Hf-H-+-tt-+-tl-t-HtH
10.0
9.0
\~,1\
8.0
1\ ~ l\
\
\
7.0
6.0
<>f6~
~\'i~a~~~l*~~"\~~=l!1:nl*=!$S=tnm$$la*$ala
.\
5.0
0
o\t-~\.-t-Hd-flH-~\~\H~\+~l\.*Hd-~H-!I.\M-!+\H-lH++-H-+++-+-IH-H-H
?
l>. 1\ "
~,~.\~~~~~~\~\~~~~~~-4~~+-~H44+~+#-~t+~~~
1\
1\ I\.
\ \
1\
\
4.0~\~J\
i\ 1\
\ \ ' 1\1\
~\
\
3.5
? ~ 1\ \
\ 1\ i\ "1\
1\:\
1\
\ 1\
1
3.0
\\ .If--H:--lt","*rH~rlH.ld-\--fr+.lH*I-\--f\--HrI\-+\++-\+t+--1..l.~f\Ll+-if-.4l~t+-+~
r-- ~\~~-\tl\~t-H+I\~I\~H[\d-1\-fM\-\+t1I\-.~*-++\\,,*1\-\--fi~f+-~l\'t-+-+-+-1\f-+H.l
1\
[\
l\ \ 1\ 1\ 1\ 1\ 1\ \ ~ \1\ 1\
\
[\
~~
2.5
1\
2.0
1\
1.8
~O~:~
~
\ \ \ \
1\ \
1\
i\ 1\1,1\
I\.
1\
\
~
1\1\
[\
1\ ~
\
\.
\
I\t\ \
"1\
I
~
,
~
I'~ lj~X
\
~
\ l'1
~ ~
1\
.N
\
~ ~ I' ~I
.OO~;-~~-rI\~~+pr;\r\~I~\~\+I'~+Nl~\+~~I\~~\~~\~~~~~~~\I\~~~~I'~O\~
:::
\
[\
[\
.80
.70
\
"
\
1\
1\ 1\
\
"
i\ 1\
\
1\
t \
1\ I\~
1\
\
\
\,
\
1\
"'\
-0
l),
t1"\
" "\
.OO~+=~+=t+~~~~~~~~~~~~~~~t=~~~t~tj±~~
SO
1\
\ \ 1\
1\ \
I\....'!..J _\
1\ <?...L
.
1\
1\ ~
1\'
\
\
.40
.35
\
1\ 1\
1\ 1\
1\
I\.
\
1\
1\
'\
1\
1'.1\
\ 1\
I\~
~
?'.'
~\~
"'~~
1\
1\ 1\ 1\ .'\ 1\ 1\ '\
l\ 1\ K{J
'.: t---1r-t--H-T-t-t-t1>tt-....,I\:-1rI\t--ft-l\-to.I\-++t+ld~\:+~
\~'+-TI\~HJ~
\~-N"'~~l\.+--I\:o~~3
\
\
I' \
.20
.10
.080
r-..
\1\ ~ r\~~
\
';~ , >~:~ :<' ,~\ L~t~
~!
.090
\~I\ \
r'."
\
1\
FIG. G
1\
\
\
"
r\. '\
t--t-+-1h-""-T"T-rrTT'"--'T-+-f-,H--ftI:-k>a~~~
\J:Ir.!.,I\'~~ ....
";. ~\~~\~ ~9 ~~_'.
\
'\
~ ~
• ~o
\\
:0
~1
~ ~-!r
:O~:O L~o
"~~~~~~~'';:r "\~~~~-:~,:~~~:~T
-~"""::t;~"l.: ~
.070
.060
I.~
.ll1I.
~
2
.0001
3
4 5 6789
.0001
"
~
2
3
.~
4 5 6 789
.001
r\
~
L....
"
2
"to~~~~ ~~~1\.db
3
l\,' ....
II
4 5 8789
2
3456789
.01
FACTOR A
THE VALUES OF FACTOR A
USED IN FORMULAS FOR VESSELS UNDER EXTERNAL PRESSURE
.1
I toI3~J1~ _
I7
I
UP
V
./
V
V
IIi.- i............. V
i
~
III
. / .-
V
1-'1010-
~
..... 100-
.....
~ .....
~
~ i""'"
.....
~
-- -
~ I--'"
l.--
~
~
l-
I-
14,000
900 F
E=24.5xl06
E = 22.8 x 10 6
E = 20.B)( 10 e
11 U I
23456789
.00001
.0001
j...,
10,000
~
9,000
V
-.
-
~
B,OOO
o
7,000
U
6,000
-
~
-<~
5,000
VII
4.000
~W
FIG.CS-2
r--....... ~ ~rt
o (])
I I II
3456789
.001
2
3
456789
.01
2
3
4
5 6 7 89
0..
-
~;:;
(])
........... t<::l C
(;r:E:.:::
;> (]) 0
(])
0.. N ~
~ E .;:: B
.....
(])
0
t<::l
(])
(])
(])
0..
U
(])
~"""..c
~
..c-5..c E
::: 4- ..... (])
o ..c
......
en
..... (])
(]) "0 .- ..c
en C ::: .....
t<::l (])
4c ..c
-.......,
•• 4-
C 0
.S
.........
"0
U
(])
~
(])
s:::::
3,500
~
3,000
O ..c(])o..
..... 0..
:z .;::on .S
:::l
Eo-<
17.~ V
2
4-:':::2
12.000
~V
J. rll
III VV '"'
r---.... .......
......
en
0
t<::l ._
......
u
....... (]) (])
. . . . . c ......
<...,;;
~
80p ~_
rIP""
E = 29.0 x 10 6
E=27.0xl0 6
-t<::l
16,000
I
./
1/
(])
~ ~ c
18.000
700 F-
V
C
B E '0
20.000
I I
I
(])
..ct<::l..c
...... (]) ......
500 F_
-""".VV
.....
V
l..- i---'I"""
t.,.....- L-
.- ~
L-o
V
J rI
-
25,000
0
......
~
~
2.500
.1
FACTOR A
THE VALUES OF FACTOR B
USED IN FORMULAS FOR VESSELS UNDER EXTERNAL PRESSURE
The values of the chart are applicable when the vessel is constructed of carbon steel and the specified yield
strenth 30,000 psi. and over. To this category belong the following most frequently used materials:
SA - 283 C
SA - 515} II
d
SA - 53 - B
Type 405 } S . I
S I
SA - 285 C
SA - 516 A Gra es
SA _ 106 _ B
Type 410
tam ess tee
DESIGN
I~
I i JT
up to 300
F
V
V
1/'"
II
III
V
~
~
~
J rJ'
~
~
./
l,.-I.-
V
--....
V
I-"'"
~
l.,....-- ~
~
...... ......
V-
--
V
V
V-
I--'
~
j..-Ioo-
-I-' I--"
....1- I--"
V
~
~
j.....-
l-
I
(!)
,..t::
-
700 F-
16,000
800 F_
14.000
I
V
I
I
10,000
~
9,000
8,000
./
L,;o
V
rlJ'~
I. rII
E ; 29.0 x 10 6
E;27.0xl0 6
E;24.Sxl0 6
22.8
x
10 6
E ; 20,8
x
10 e
E;
I IIII
2
.00001
3456789
,0001
[71
~
r-.. !2
~
2
~
~
o~
u
6,000
~
<
o (!) 0..
(!)
'::s ::s - ..... ro
ro
;>
lJ 1/1
FIG.HA-I
~'I
3,500
f- I- H
I I Ii
3456789
,001
2
3456789
.01
2
3
4
t::
-5 8
(!)
.....
(!)
,..t::
.....
'1:
(!)
'(!)
,..t::
'(!)
(!)
0..
,..t::,:::::
rfJ
0
~ 4-
(!)
~
0
,..t::
.....
Q)
,..t::
.....
(!)
-0 .-;::
t::
(!)
(!)
B
ro
~-5
4-
.5 -5
t::
.~ -0
0
4-
U
t::
~
0
(!)
(!)
rfJ
'r",..t::'-(!)
t.......
I
~
'
(!)
ro
'- ~
t : :"--
(!)
0
(!)
(!)o..N'-
u
4,000
0
4-:"::0
7,000
5,000
rill
1'-.....1"-..
~
v. . . v
L,;o
t
(!)
,..t::
~ ~ t::
rfJ
0
tZ: ro ';::
.A'
o.i
U
........
,....
(!)
12,000
j..-~
ro
..... 8
I
900 F
t::
~(!):
:l0.000
18,000
I I-
.- j....V
~
./
I
SOO F
25,000
3,000
1
OCJ)~§:
Z '1: ._ ::s
S 6 7 89
2,500
,1
FACTOR A
THE VALUES OF FACTOR B
USED IN FORMULAS FOR VESSELS UNDER EXTERNAL PRESSURE
*The values of the chart are applicable when the vessel is constructed of austenitic steel (18Cr-8Ni, Type 304)
(Table 1 on page 190)
25.000
Q)
C
Q)
..c:ee..c:
......
......
Q)
.8 S t;
:;>0.000
~ ~ C
- ee
Vl ._
0
ee
18.000
up to 100 F
-II
......
./
V
~
~
./
~~ ~V
~
l/
E
E
E
E
E
= 28.0
= 25.9
= 23.8
= 22.4
= 20.3
II
2
.00001
3456789
.0001
x 106 _
x lOS' ....
x
10~~ I
x 106~
x 106 -..l11,7
y&
2
j 'J
'I, ~J''''''
'/I 1/
I--"~
~
.....
~
.....
.- l -II--
L....- """-
/"
~
~
~ I--~
....
.... 1-'
L.-- I-
,40? ,F,_
~I-' 10-1---
I--- ~
..... i---
I---
I---- I---
~
I- 700 F
9il I
F
16,000
1,200 F
12.000
4-:':::2
Q)
0-
9,000
8,000
L....- ~
7,000
V
6,000
~
5.000
"<,
o
~
~
oE--
U
<
~
Q).....
1I FIG. HA-2
~
;>
3456789
.001
2
3456789
.01
2
3
5 6 789
Q)
~
...... ..c:
Q)
Q)
Q)
~
0-
..c:-5..c:s
::: 4 - ......
Q)
o ..c:
......
Vl
......
Q)
Q) "0 ,- ..c:
Vl
C ::: ......
ee
Q)
4Q)
C
0
C ..c: ,S "0
---~~=
3,500
~
••
~
4
0
a
-5;)s'(;j
Q)
Q) §',~
4,000
3,000
I
<l.i
=.2eec
C;;~c:':::
U
W)
......
• U
Q)
Q)
C ......
......
10.000
1-1-'
<,..<
14,000
4-UQ)
0
~
.....
......
.....
Q)
..c:Q)O01)...... 0Z'C ,5
O
=
2,500
.1
FACTOR A
THE VALUES OF FACTOR B
USED IN FORMULAS FOR VESSELS UNDER EXTERNAL PRESSURE
*The values of the chart are applicable when the vessel is constructed of austenitic steel (18CR-8Ni-Mo, Type
316)(Table 3 on page 190)
~------------------------------------------------------------------------------------------------~I~
DESIGN
I
I
~
vv
I:::: ~r-
r
J JJ 1
--
......
I
~r
~
...
I
r--
I, .......
'/
E ; 2B.0 x 106~J
E ; 25.9 x 10 6 of...
E = 24.5 x 106 -...,
E = 23.1 x 106
....... 1-"'"
~
f-'""i""'"
f-'""
f-'"~
~
.c.
r--
~
1
r" 600 F
9.000
B,OOC
Bod F
7,00e
~
~
6,00e
..::::::: I-"'"
5,000
4,000
3,500
..........
FIG.HA-3
3,000
-.J
2
.00001
3
ill
456789
.0001
~
11 I
2
I
3456789
2
01
......
U
....... Q)" Q)
4-:':::2
o Q) 0.
~
~
o
E-U
-<
~
Q)5~Q)
;::l ......
ro s::
~e=:.:::
> Q) 0 Q)
~
a0. .;::
N
.1
FACTOR A
THE VALUES OF FACTOR B
USED IN FORMULAS FOR VESSELS UNDER EXTERNAL PRESSURE
*The values of the chart are applicable when the vessel is constructed of custenitic steel (lSCR-SNI-O, 03 max.
carbon, Type 304L) (Table 2 on page 190)
;...
B
...... Q) 0 ro
~ ...... ..s:::: ~
Q) Q) Q) 0.
..s::::-:5..s::::a
~ 4- ...... Q)
o ..s::::
......
U'J
......
Q)
Q) "'0 .- ..s::::
U'J
s::
~ ......
ro Q)
4U Q) s:: 0
s:: ..s::::.S "'0
~ c::
.. 4-UQ)
~ 0 ~ ;...
E-o ...... ;... Q)
..s::::Q)o.
O OJ)...... 0.
.......-Ij
"""""'
Z ';::.5
2,000
3456789
3456789
.001
2,500
I1 I
I
0
ro U'J
ro ._
~
<,..;;
10.000
.... 400 F
~I-"
'1
a '0
"" s:: ......
.......... f--"'"
I,.....-f-'"'
.8
~ ~ s::
12.000
~
rr
16.000
14.000
I
15\
Q) s:: Q)
..s::::ro..s::::
...... Q) ......
IB.OOO
up to 100 F
..- I -
/~
b:::::::
20.000
111 1
I
;::l
I
~
"..
~
"..
-
II
~r'"
"..
.....
-"
..............
II .... fo-"
IL ..- lo-':r-""
~
E = 28.0 x 106 E = 26.4 x 106 _
E = 24.5 x 106 ......
E
23.1 x 106_ i'"
b-
2
.00001
3
456789
.0001
"..
fo-"r'"
~
.........
~
"..
r-
r- joci
.....
~
".r--: l - f-
I-"'r--~
---
I-'""
I,...--"t"'"'
r-
l..- I - -
F'
.8 S
~OO'
<.+-<
-
I- 800 F
9.000
8.000
7.000
6.000
C':S
.......
<Il
C':S
~
0
....
.....
u
--... .....
~ ....
0
--1-0
o (\) 0.
(\)
(\)
.,
10.000
F'-
(\)
....
'0
12.000
460 IF
111
~
(\)
~ ~ ~
~
~
o
~
u
(\)
->
::1
C':S
1-0
B
~
~
S
.... (\)
~
(\)
C':S
~
~
(\) 0
0. N
1-0
'C
0
-<
~
::: "- ....
(\)
..s:::
4,000
FIG. HA-4
~
~v
2
3456789
.001
.01
1I Ij
2
3,000
2,500
<Il
......
(\) "0 .....
<Il
~
C':S
(\)
U (\)
~ ..s:::
........
.. "~ 0
~
Eo- ......
O
~
......
.......
(\)
1-0
B
C':S
~
: ; ..s:::
..s:::
(\)
0.
.... ..s:::S
O..s:::
3,500
3456789
(\)
....
..s:::C':S..s:::
14.000
5.000
'1.'iJ
2
20.000
18.000
16.000
11
~
'"'~
I--'"
up to 100 F
/I,.,.
r-.
1II
~
~r-
...... V
-
~ r-
fo-" ........
...... ~~
V
V
rJ
...... ,.,..
I--'" I-"'t--
f.-
J 1J j
(\)
......
(\)
..s:::
:::
....
~
"-
0
"0
~
u (\)
~ 1-0
.S
~
1-0
(\)
..s:::(\)o.
OJ)......
0.
Z ·c.5
::1
2.000
3456789
.1
FACTOR A
THE VALUES OF FACTOR B
USED IN FORMULAS FOR VESSELS UNDER EXTERNAL PRESSURE
*The values of the chart are applicable when the vessel is constructed of austenitic steel (I SCR-SNi-Mo-O.03
max. carbon, Types 316L and 317L) (Table 4 on page 190)
~------------------------------------------------------------------------------------~I~
DESIGN
48
EXTERNAL PRESSURE
CONSTRUCTION OF STIFFENING RINGS
LOCATION
Stiffening rings may be placed on the inside or au tside of a vessel.
SHAPE OF RINGS
The rings may be of rectangUlar or any other sections.
CONSTRUCTION
It is preferable to use plates in constructing a composite-section stiffener ring,
rather than using standard structural shapes. The reason for this lies not only in
the difficulties of rolling heavy structural shapes, but also because of the necessity to adjust the ring to the curvature of the shell. For large diameter vessels the
maximum permissible out of roundness can result in a 1 - 2 inch gap between
the shell and the ring. This can be eliminated if the vertical member of the ring is
cut out of the plate in sections. The sections can be flame cut, instead of rolled
and then butt-welded together in place.
DRAIN AND VENT
Stiffener rings placed in the inside of horizontal shells have a hole or gap at the
bottom for drainage and at the top for vent. Practically one half of a 3 inch
diameter hole at the bottom and I V2 inch diameter hole at the top is satisfactory
and does not affect the stress conditions. Figure A.
For the maximum arc of shell left unsupported because of gap in stiffening
ring, see Code Figure UG.29.2.
WELDING
According to the ASME Code (UG 30): Stiffener rings may be attached to the
shell by continuous or intermittent welding. The total length of intermittent
welding on each side of the stiffener ring shall be:
1. for rings on the outside, not less than one half the outside circumference
of the vessel;
2. for rings on the inside of the vessel, not less than one third of the circumference of the vessel.
Where corrosion allowance is to be provided, the stiffening ring shall be attached
to the shell with continuous fillet or seal weld.ASME. Code (UG.30.)
Max. Spacing
12 t for internal ring
8 t for external ring
Figure A
EXAMPLE:
RINGS OUTSIDE
RINGS INSIDE
1
J:
Figure B
Y4" x 3" 19. fillet weld on 6" ctrs.
Y4" x 2" 19. fillet weld on 6" ctrs.
The fillet weld leg-size shall be not less than the smallest of the following: 1/4 in,
the thickness of vessel wall or stiffener at the joint.
49
CHARTS FOR DETERMINING THE WALL THICKNESS FOR
FORMED HEADS SUBJECTED TO FULL VACUUM
Using the charts, trials with different assumed thicknesses can be avoided.
The charts has been developed in accordance with the design method of ASME
Code, Section VIII, Division 1.
. 70
.65
.60
.55
300
.50
.45
:~
Y
1
i~
700 •
.40
Isoo
.35
'JIll
. 30
&
.
. i,;.l.
I
.25
.20
.....
. 15
•
.10
.05
.00 10 20
30
40
50
60
70
80
90
100 110 120 130140 150 160170 180 190200
SPHERICAL, ELLIPSOIDAL, FLANGED AND DISHED HEADS
(Specified yield strength 30,000 to 38,000 psi, inclusive)
To find the required head thickness: 1. Determine R, 2. Enter the chart at the value
of R, 3. Move vertically to tempeTature line, 4. Move horizontally and read t.
t
R
Do
Required head thickness, in.
For hemispherical heads, the inside radius, in.
For 2: 1 ellipsoidal heads 0.9xDo
For flanged and dished heads, the inside crown radius, in. Rmax=Do
Outside diameter of the head, in.
50
CHARTS FOR DETERMINING THE WALL THICKNESS FOR
VESSELS SUBJECTED TO FULL VACUUM
I'"
500.
.0-.
.~~
EO.
~ ~ f---
300 of
....-- c-- c- 500 of
~" ~~f'-.,.
....... f- -700 of
~
,./
..--800 of
"~ ~
.;;:<
0
~
~ 900 of
~ ~ ~ ./
NK~
~~
~
~~~
-.....::::
~~
400.
"'' '\
ns.
215.
315.
215.
"""
115.
3
..
130.
120.
10.
50.
&
1
~
•
I.
2
3
4
5
&
LID
~
iJj ~ ~1 /1 I~ 1I 11/ I I /
I /
~t.:
/1/// ~ ~ bI fcI I i / / / / V
//; ~/; ~/ II't~Vi 10/' leo.: ¥.1 j' ./ /
/ /
v
VI
V
V /
W2 ~VI 'II J y l?~I ~
W 0 ~ j / / /;/ .;//
/ /
/
yv
~ ~v/ / V / L/
?
~ V / ~/ / / / / J v
v
.~
~ / . /V /' / ......./ ' /
.~
v .........-v /"..,/
.........- ~
--::v k ..-vV .--
«
,/
125.
100.
10.
!/
140.
~
5
I
rlJ '/ ,/1/ / If I /' II' /
II VJ II, 11/II II I I I I I I I I I I
Ij~ III Z ,/1 If I I / V / / _1/
-~ ~ (II 'II IlL illl II J I II
/ I
150.
100.
150.
--..::::::~~
125.
100.
115.
~ ~~
I !SO.
150.
If'
140.
130.
120.
110.
100.
~.
80.
10.
e
T
•
---
0
A
CYLINDRICAL SHELL
(See facing page for explanation)
5
~
0
....l
....l
"':t"
[/)
....
&0-
0
:t
50.
40.
30.
EU
Z
"'....l"
II
.....l
20.
I-"'
5
U
"'"
,./
..
Z
0
1=
[/)
,/
..,-
i
e
7
•
Q
10.
10.
51
CHARTS FOR DETERMINING THE WALL THICKNESS FOR
VESSELS SUBJECTED TO FULL VACUUM
.10
.1$
.20
.25
.30
.35
.45
.4)
.50
.eo
.55
.&5
.70
.15
.80
.85
,go
.SJ5
S2S.
500.
415.
A6O.
oG5.
400.
315.
350.
.....
-0
0
325.
lOO.
215.
250.
225.
200.
115.
ISO.
\ \ \\ \\ \\ l\ \
i\ \ 1\ \ 1\ \ 1\ \ 1\\ .~.
\ \ ~\ 1\ \ 1,\ \ Io~ .f€.
!\ \ \ \ 1\.\ ~~ ~. ~~
-1 1\ \ \ \ 1\ \ \ ~ ~~ ~~ I'<.,~ ~
\ \ \ 1\ \ 1\" f<1."<. ~'" v'~ ""-" ~
\ \ 1\ \ \ I\o~ .~ ~" ~'" ~ f'o..-~ ~ ~
f'o..-""-.. ~ ~
~\
\ \ \ 1\ ~ "~ ~~ ~'
~ ~ ~ "'-....' '""""""- 0
f'<..'
~
\ \ f\
-~
1'
-."""
\b '"
,,"""- ~ ~ ~ ~ t': ~
f'o..-"
\ \ ~ ~. ~ f\v ~
r-... .....
\ \ \
\ 1\ \ 1\ \
\ \ \ \
~\ \ \
\
'y
\
'\ .}
\
~.
1\.,.,.
~ ~
.10
.15
.20
~
'\
rx ~
'\
\: '\
125.
100.
~,.,
1'0
§\
.>
"""
""
,25
r-.....,
.30
~
""
~
f'o..-
'" " '"
"" '"""
t-.....
.........
t-.....
~
r--....
.............. 1--..
~
.35
.4)
.45
'"
"" ."" ""
,"""I"-.. ~'
"'-....
"r--
"
~ .............. r-..............
........
r---
...............
I--I-- r-.:::-.......
i--- r--. r-... r--
['---...... '-.....
'"-...
r-- h-. r-- 1-;,.,.. r--- ~
.SO
.55
500.
415.
315.
215.
~...... --......:::~ ~ r--::::
~
I'--..... ~ :::-...... ~ ~ r--:::: ~
""--
i'--.
1.00
S2S.
.eo
.e5
.10
.15
I--
r::- r-:::
r-- .:::=
-- --
------ r-- ::----
.80
~=
~
.85
,go
.Q5
115.
,so.
'25.
'00.
1.00
t = REQUIRED SHELL THICKNESS, IN.
CYLINDRICAL SHELL
(Specified yield strength 30,000 to 38,000 psi, inclusive)
To find the required shell thickness:
1. Enter lower chart (facing page) at the value of L
2. Move horizontally to curves representing Do
3. Move vertically to temperature line
4. Move horizontally and read Dolt
5. Enter chart above at the value of Dolt
6. Move horizontally to curve D
7. Move vertically down and read the value of t
NOTATION
Do
L
Required shell thickness, in.
Outside diameter of shell, in.
Length of the vessel or vessel section, taken as the largest of the following:
1. Distance between the tangent lines of the heads plus one third of the depth of
the heads if stiffening rings are not used, in.
2. The greatest distance between any two akjacent stiffening rings, in.
3. The distance from the center of the first stiffening ring to the head tangent
line plus one third of the head depth, in.
The charts are from:
Logan, P. 1., "Based on New ASME Code Addenda ... Chart Finds Vessel Thickness,"
HYDROCARBON PROCESSING, 55 No.5, May 1976 p. 217.
Logan, P. J., "A Simplified Approach to . . . Pressure Vessel Head Design," HYDROCARBON PROCESSING, 55 No. 11, November 1976 p. 265.
Copyrighted Gulf Publishing Co. Houston. Used with permission.
52
DESIGN OF TALL TOWERS
WIND LOAD
The computation of wind load is based on Standard ANSIIASCE 7-95, approved
1996.
The basic wind speed shall be taken from the map on the following pages.
The basic wind speed is 105 mph. in Hawaii and 125 mph. in Puerto Rico.
The minimum design wind pressure shall not be less than 10 lb.lsq. ft.
When records and experience indicates that the wind speeds are higher than
those reflected in the map, the higher values of wind speed shall be applied.
The wind pressure on the projected area of a cylindrical tower shall be calculated
by the following formula.
F = qz G e{A{
Table 6-1 ANSI/ASCE 7-95 STANDARD
(Numbers of tables and paragraphs are references to this
Standard.)
L
(D x H)
I
I
Projected area oft ower, sq. ft.
height oflower considered. ft.
outside diameter of tower, ft.
L...-_ _
Shape factor = 0.8 for cylindrical tower (Table 6-7)
'---- Gust response factor = (G h & GJ* (Para. 6.6)
When the tower is located:
in urban, suburban areas, Exposure B 0.8;
in open terrain with scattered obstruction, Exposure
in flat, unobstructed areas, Exposure D 0.85.
L...-_ _ _
e 0.85;
Velocity pressure at height z above ground, lb.lsq. in.
0.00256 KzKzt V2 I, lb./sq. ft. (Table 6-1)
II
~ Design Wind Force. lb.
on projected area of
tower. (Para. 6.2)
Importance factor ~ 1. 0 for structures that
present low hazard to human life in event
offailure (Para. 6.2).
Wind speed, mph. (Map 6-1)
'- Topographic factor = 1.0 when wind speed-up
over hills and escarpment is not present.
(Para. 6.5.5)
'--
Velocity Pressure
Exposure Coefficient*
Exposures B, e & D (Table 6-3)
* See tables below for values of q and for combined values
of Gh, G z, and Kz in Exposures B, e, and D.
VELOCITY PRESSURE, q
Basic wind speed, mph, V
1 70 I 80 I <x) 1100 1110
Velocity Pressure psfO.00256 V2, q
I 13 I 171 21 I 26 I 31
J120
I
37
1130
44
I
I
I
53
DESIGN OF TALL TOWERS
WIND LOAD
(Continued)
COEFFICIENT G (Gust response factor combined with Exposure Coefficient)
HEIGHT
Above Ground, ft.
0-15
20
40
60
80
100
140
200
300
500
EXPOSUREB
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.4
1.6
1.9
EXPOSUREC
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.9
2.0
2.3
EXPOSURED
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.4
The area of caged ladder may be approximated as 1 sq. ft. per lineal ft. Projected area
of platform 8 sq. ft.
Users of vessels usually specify wind pressure for manufacturers without reference
to the height zones or map areas. For example: 30 lb. per sq. ft. This specified pressure shall be considered to be uniform on the whole vessel.
The total pressure on a tower is the product of the unit pressure and the projected
area of the tower. With good arrangement ofth-e equipment, the exposed area of the
wind can be reduced considerably. For example, by locating the ladder 90 degrees
from the vapor line.
EXAMPLE:
Determine the wind load, F
DESIGN DATA:
the wind speed, V
= kOOm.p.h
=
6 ft.
diameter of tower, D
= 80 ft.
height of tower, H
the tower located in flat,
unobstructed area, exposure: D
I
I
The wind load, F=qz xG x CI AI
=
q from table
=
G from table
=
Shape factor
26 psf
1.8
0.8
Area, Ar= DH = 6 x 80 = 480 sq. ft.
F = 26 x 1.8 x 0.8 x 480 = 17,971 lbs.
54
MAP OF WIND SPEED, V
(miles per hour)
Alaska Note:
For coastal areas and islands,
use nearest contour.
. \140
100
130
110120
ANSI/AASCE STANDARD 7-95
Courtesy of American Society of Civil Engineers
55
MAP OF WIND SPEED, V
(miles per hour)
90
100
110
120
Special Wind Region
•
Population Center
Location
Hawaii
Puerto Rico
Guam
Virgin Islands
American Samoa
Notes:
1. Values are 3-second gust speeds in miles per hour at 33 ft.
above ground for Exposure C category and are associated with
an annual probability of 0.02.
2. Linear interpolation between wind speed contours is permitted.
3. Islands and coastal areas shall use wind speed contour of
coastal area.
4. Mountainous terrain, gorges, ocean promotories, and special
wind regions shall be examined for unusual wind conditions.
V, mph
105
125
170
125
125
56
DESIGN OF TALL TOWERS
WIND LOAD
Computation of wind load as alternate method based on standard ASA A5S.1-1955.
This standard is obsolete but still used in some codes and foreign countries.
The wind pressure at 30 ft. level above ground for the United States is shown on the
map on the facing page.
The table below gives the wind pressures for various heights above ground for the
areas indicated by the map.
WIND PRESSURE Pw WHEN THE HORIZONTAL
CROSS SECTION SQUARE OR RECTANGULAR*
MAP AREAS
HEIGHT
ZONE ft. 20 25
30
40 45
50
35
25
40
25
30 35
less than 30 15 20
30
35
40 45
50
30 to 49
20 25
45
50 55
60
50 to 99
25 30 40
45
55
60 70
75
100 to 499 30 40
*Multiply values of P w with O.SO
when the horizontal cross section is hexagonal or octagonal
and with 0.60 when the horizontal cross section is circular or elliptical.
EXAMPlE:
Find the wind pressure P w from map.
The vessel is intended to operate in Oklahoma, which is in the wind pressure map area
marked 30. In this map area the wind pressures for various height zones are:
In the height zone less than 30 ft.
25 lb. per sq. ft.
In the height zone from 30-49 ft.
30 lb. per sq. ft.
For a cylindrical tower these values sha11 be multiplied by shape factor 0.6, then the
wind pressure in different zones will be 15 and IS lb. per sq. ft. respectively
If many pieces of equipment are attached to the tower it is advisable to increase the
shape factor (according to Brownell) up to 0.S5 for a cylindrical vessel.
Users of vessels usually specify the wind pressure for manufacturers without reference to height zones or map areas. For example: 30 lb. per sq. ft. This specified pressure
shall be considered to be uniform on the whole vessel.
Relation between wind pressure and wind velocity, when the horizontal cross section
is circular, is given by the formula:
P w = 0.0025 x Vw 2
where
P w = wind pressure lb. per sq. ft.
Vw = wind velocity mph
EXAMPLE:
Wind of 100 mph velocity exerts a pressure:
P w = 0.0025 x Vw 2 = 25 lbs. per sq. ft. pressure on the projected area of a cylindrical
vessel at a height of 30 feet above ground.
The total wind pressure on a tower is the product ofthe unit pressure and the projected
area of the tower. With a good arrangement of equipment the exposed area of the wind
can be reduced considerably. For example, by locating the ladder 90 degrees from the
vapor line.
___
___
.. ___
I
110·
-----1-I
-.~-
'3·
li:
a::
~
o
Io!j
~
Z
CI
~
~
m
en
en
e
~
m
i
• • • SANTA ANA WINDS
- . - CHINOOK WINDS
AAA
COl.UMBIA RIVER GORGE WINDS
• • • WASATCH MOUNTAIN WINDS
ALLOWABLE RESULTANT
WIND PRESSURES
COMIINEO INWARD AND OUTWARD I'RESSURES
U
G:O : : : - - ,
----10".~.
:~I~:;r..EGR~ORA~U.:~C~~:: O::~~~RT
\
~~.
VI
The map based on the records of the United States Weather Bureau and developed by the National Bureau of Standards.
DESIGN
-...l
58
DESIGN OF TALL TOWERS
WIND LOAD
(Continuation)
FORMULAS
SHEAR
MOMENT
.
REQUIRED
STRI<,SS THICKNESS
t=
12M
R 2 nSE
NOTATION
H
hi
~_..L.h·~r_:~ :~
= Width of the vessel with insulation etc., ft.
D[D2
= Efficiency of the welded joints.
E
= Lever ann, ft.
h[h2
= Distance from base to section under consideration, ft.
hT
H,H[H2 = Length of vessel or vessel section, ft.
= Maximum moment (at the base) ft. lb.
M
= Moment at height hT, ft. lb.
MT
Pw
= Wind pressure, lb. per sq. ft.
R
=
S
= Stress value of material or actual stress psi.
V
t
Mean radius of vessel, in.
= Total
shear, lb.
= Required thickness, corrosion excluded, in.
EXAMPLE:
Given:
D[ = 4'-0" D2 = 3'-0" H[ = 56'-0" H2 = 44'-0"
hT = 4'-0" P w = 30 psf
Determine the wind moment
hI = HI12 = 28'-0" h2 = HI + (H212) = 78'-0"
Pw x D x H = V x h = M
Lower
30 x 4 x 56 = 6720 x 28 = 188,160
Section
Upper
Section - 30 x 3 x 44 = 3,960 x 78 = 308,880
V = 10,680
M 497,040 ft. lb.
Total
J
2
Moment at the bottom tangent line
MT = M - hT (V - 0.5 P wD j hT) =
497,040 - 4 (10,680 - 0.5 x 30 x 4
1£1
~
3' -6"
•
I;:..!...I
7t[)1
t-~/
t
,......,..
"0
"0
'"
-l
.....
o
c.
o
f-o
II
:t:
Platform
x 4) = 455,280 ft. lb.
EXAMPLE:
Given:
D j = 3 ft. 6 in. H = 100 ft. 0 in.
P w = 30 psf
Determine the wind moment
hI = HI2 = 50 ft. 0 in.
hT
=
v X hI =
PwxDjxH=
= 10,500 x 50 =
Vessel
30 x 3.5 x 100
= 2,940 = 49 =
Ladder 30 x 98 lin. ft.
=
240 x 96 =
Platform 30 x 8 lin. ft.
V
=
13,680
M =
Total
Moment at the bottom tangent line
Mr = M - hr (V - 0.5 P w D j hr ) =
692,100 - 4 (13,680 - 0.5 x 30 x 3.5 x 4) =
4 ft. 0 in.
M
525,000
144,060
23,040
692,100
ft. Ib
638,220
ft. lb.
SEE EXAMPLES FOR COMBINED LOADS ON PAGE: 69
59
DESIGN OF TALL TOWERS
WEIGHT OF THE VESSEL
The weight of the vessel results compressive stress only when eccentricity does not
exist and the resultant force coincides with the axis of the vessel. Usually the
compression due to the weight is insignificant and is not controlling.
The weight shall be calculated for the various conditions of the tower as follows:
A. Erection weight, which includes the weight of the:
Equipments:
I. shell
2.
3.
4.
5.
6.
7.
8.
9.
10.
heads
internal plate work
tray supports
insulation rings
openings
skirt
base ring
anchor ring
anchor lugs
II. miscellaneous
12. + 6% of the weight of items I through II for
overweight of the plates and weight added by
the wei dings
13.
14.
15.
16.
17.
18.
insulation
fireproofing
platform
ladder
piping
miscellaneous
Erection weight: the sum of items 1 through 18.
B. Operating weight, which includes the weight of the:
I. vessel in erection condition
2. trays
3. operating fiquid
c.
Test weight, which includes the weight of the:
I. vessel in erection condition
2. test water
The compressive stress due to the weight given by:
s=
w
et
where
S = unit stress, psi
W = weight of vessel above the section under consideration, lb.
e = circumference of shell or skirt on the mean diameter, in.
t = thickness of the shell or skirt, in.
The weight of different vessel elements are given in tables beginning on page- 374
DESIGN OF TALL TOWERS
VIBRATION
As a result of wind, tall towers develop vibration. The period of the vibration
should be limited, since large natural periods of vibration can lead to fatigue
failure. The allowable period has been computed from the maximum permissible
deflection.
The so called harmonic vibration is not discussed in this Handbook since the
trays as usually applied and their supports prevent the arising of this problem.
FORMULAS
Period of Vibration:
T sec.
T= 0.0000265
Maximum Allowable Period
of Vibration, Ta sec.
~=O.80
(-ff)2 P,
~WH
~
NOTATION
D = Outside diameter of vessel, ft.
H = Length of vessel including skirt, ft.
g
= 32.2 ft. per sec. squared, acceleration
t = Thickness of skirt at the base, in.
V = Total shear, lb. Cw, see page 61
W = Weight of tower, lb.
w =
Weight of tower per foot of height, lb.
EXAMPLE
Given:
Determine the actual and maximum allowable
period of vibration
D = 3.125 ft. 0 in.
H = 100 ft. 0 in.
= 32.2 ft/sec 2
t = 0.75 in.
V = 1440 lb.
W = 36,000 lb.
in operating condition
w = 360
g
T=0.0000265(100:?
\3.125)
..y 360x3.125
0.75
_/36000 x 100
Ta=0.80 \I 1440x32.2
= 1.05 sec.
=7.05 sec.
The actual vibration does not exceed the allowable vibration.
Reference: Freese, C. E.: Vibration of Vertical Pressure Vessel ASME Paper 1959.
61
DESIGN OF TALL TOWERS
SEISMIC LOAD (EARTHQUAKE)
The loading condition of a tower under seismic forces is similar to that of a
cantilever beam when the load increases uniformly toward the free end.
The design method below is based on Uniform Building Code, 1997 (UBC).
FORMULAS
SHEAR
F,~!
V-F,
M= {Ft X H + (V - Ft ) X (2HI3)]
Mx={FtXX] forX::S HI3
~/
Hh
I
Mx ={Ff X H + (V - Ff ) X (X-HI3)]
t JH
-LJ
(a) Seismic Loading Diagram
MOMENT
for X> HI3
Base Shear
The base shear is the total horizontal seismic shear at
the base of a tower. The triangular loading pattern and
the shape of the tower shear diagram due to that loading are shown in Fig. (a) and (b). A portion of F t of total
horizontal seismic force V is assumed to be applied at
the top of the tower. The remainder of the base shear is
distributed throughout the length of the tower, including the top.
Overturning Moment
The overturning moment at any level is the algebraic
sum of the moments of all the forces above that level.
NOTATION
-'
N
.
I
ffi'
C = umenca coe IClent = 2.355
T2i3
(need not exceed 2.75)
C = Numerical coefficient = 0.035
I.
D=Outside diameter of vessel, ft.
v
.1
(b) Seismic Shear Diagram
Base Shear
E = Efficiency ofweldedjoints
F f = Total horizontal seismic force at top ofthe vessel,
lb. determined from the following formula:
F f = 0.07 TV (Ff need not exceed 0.25 V)
=0, for T :sO. 7
H = Length of vessel including skirt, ft.
62
DESIGN OF TALL TOWERS
SEISMIC LOAD (EARTHQUAKE)
(Continuation)
NOTATION
I
= Occupancy importance coefficient (use 1.0 for
vessels)
M = Maximum moment (at the base), ft-lb.
Mx = Moment at distance X, ft-lb.
R = Mean radius of vessel, in.
Rw = Numerical coefficient (use 2.9 for vessels)
S
.. D
= Site coefficient for soil characteristics
A soil profile with either:
a) A rock-like material characterized by a shear-wave
velocity greater than 2,500 feet per second or by
other suitable means of classification. S = 1.0
I
b)Stiff or dense soil condition where the depth is
less than 200 ft. S = 1. A soil profile with dense or
stiff soil conditions, where the soil depth exceeds
200 feet. S = 1.2.
A soil profile of 40 feet or more in depth and containing more than 20 feet of soft to medium stiff
clay, but not more than 40 feet of soft clay. S =
1.5.
A soil profile containing more than 40 feet of soft
clay. S = 2.0.
= Allowable tensile stress of vessel plate material,
psi.
=
Fundamental period of vibration, seconds
=c t xH%
= Required corroded vessel thickness, in.
v
= Total seismic shear at base, lb.
W = Total weight of tower, lb.
X
= Distance from top tangent line to the level under consideration, ft.
Z
= Seismic zone factor,
0.075 for zone 1
0.15 for zone 2A
0.2 for zone 2B
0.3 for zone 3
0.4 for zone 4
(see map on the following pages for zoning).
63
DESIGN OF TALL TOWERS
SEISMIC LOAD (EARTHQUAKE)
EXAMPLE
Given:
Seismic zone: 2B
Z=O.2
D = 37.5 in. = 3.125 ft.
X= 96 ft,. 0 in.
H= 100 ft., 0 in.
W= 35,400 lb.
Determine: The overturning moment due to earthquake at the base and at a
distance X from top tangent line.
First, fundamental period of vibration shall be calculated.
T=C xHY4=0.035 x 100 314 = 1.1 sec.
t
and
1=1,
S=1.5, Rw=2.9,
C= 1.25S = 1.25 x 1.5 = 1.76<2.75
T213
1.1213
V= ZIC x W= 0.2 x 1 x 1.76 x 35,400=4,296 lb.
Rw
2.9
Ff = 0.07 TV = 0.07 x 1.1 x 4,296 = 330 lb.
M= [FfH + (V - F f ) (2HI3)] =
[330 x 100 + (4,296 - 330)(2 x 100/3)] = 294,756 ft. - lb.
X >
If-' thus
Mx = [Ff X+ (V-Ff ) (X - HI3)] =
[330 x 96 + (4,296 - 330) (100-33)] = 281,138 ft. -lb.
64
SEISMIC ZONE MAP OF THE UNITED STATES
...
...
er,
0'1
U
==
~
~
=
~
:I
f"I
a..
~
C.
C':I
.c:
'! :aU
=
~
~
c.
c.
-<
'"<Ii
~
....C':I
rJJ
~
~
"0
0
.~
•
~
.\ ·c~
~
.c:
....
~
~
:s....
'"
=
=
'"C':I
~
C':I
a..
~
65
66
DESIGN OF TALL TOWERS
ECCENTRIC LOAD
Towers and their internal equipment are usually symmetrical around the vertical
axis and thus the weight of the vessel sets up compressive stress only. Equipment
attached to the vessel on the outside can cause unsymmetrical distribution of the
loading due to the weight and result in bending stress. This unsymmetrical arrangement of small equipment, pipes and openings may be neglected, but the bending
stresses exerted by heavy equipment are additional to the bending stresses resulting
from wind or seismic load.
FORMULAS
~.
.
I
MOMENT
M= We
I
i
I
w
e
=
E
M
=
=
=
=
R
S
t
W
=
=
STRESS
REQUIRED
THICKNESS
12We
S_12We
-nR2(
(=
R 1 n SE
NOTATION
Eccentricity, the distance from the tower axis to center of
eccentric load, ft.
Efficiency of welded joints.
Moment of eccentric load, ft. lb.
Mean radius of vessel, in.
Stress value of material, or actual bending stress, psi
Thickness of vessel, excluding corrosion allowance, in.
Eccentric load, lb.
EXAMPLE
Given:
e
R
t
W
=
=
=
=
4 ft. 0 in.
15 in.
0.25 in.
1000 lb.
Determine moment, M, and stress, S.
Moment, M = We = 1000 X 4 = 4000 ft. lb.
12 X 1000 X 4
12 We
S=---=
= 272 psi
3.14 X 15 2 X 0.25
'IT R2 t
When there is more than one eccentric load, the moments shall be summarized,
taking the resultant of all eccentric loads.
67
Design of Tall Towers
ELASTIC
STABILITY
A tower under axial compression may fail in two ways because of instability:
I.
By buckling of the whole vessel (Euler buckling)
2.
By local buckling
In thin-walled vessels (when the thickness of the shell is less than one-tenth of
the inside radius) local buckling may occur at a unit load less than that required
to cause failure of the whole vessel. The out of roundness of the shell is a very
significant factor in the resulting instability. The formulas for investigation of
elastic stability are given in this Handbook, developed by Wilson and Newmark.
Elements of the vessel which are primarily used for other purposes (tray
supports, downcomer bars) may be considered also as stiffeners against buckling
if closely spaced. Longitudinal stiffeners increase the rigidity of the tower more
effectively than circumferential stiffeners. If the rings are not continuous around
the shell, its stiffening effect shall be calculated with the restrictions outlined in
the Code UG-29 (c).
FORMULAS
ALLOWABLE STRESS (S)
Without Stiffener
Ay
. Id . )
1 500 ,000 Iit (=
S =,
<"31 yte
pomt
•
dy
!
i
l
~
S
I
Ix
=
= 18 in.
= 0.25 in.
R
I
Given:
Ay
dy
=
=
y
=
t
1 sq. in.
24 in.
.~ The equivalent thickness of the shell when circumferentially
d
stiffened, in.
y
EXAMPLE
Determine the allowable compressive stress (S)
1
+ 0.04
1,500,000 x
R
I
=
1,500,000 x 0.25
20 833
18
=,
Determine the allowable compressive stress
stiffener rings
S
+ -24 =
= 0.25
+
S =
Longitudinal stiffener
is not used, then:
Ix = t = 0.25 in.
I
~ (= 1 . Id )
= 1,500,000
R
"tytx <"3 yte P•
NOTATIONS:
Cross sectional area of one logitudinal stiffener, sq. in.
Cross sectional area of one circumferential stiffener, sq. in.
Distance between logitudinal stiffeners, in.
Distance between circumferential stiffeners, in.
Mean radius of the vessel, in.
Allowable compressive stress, psi
Thickness of shell, in.
Ax The equivalent thickness of the shell when longitudinally
I +
d; stiffened, in .
Iy = t
Given:
S
=
=
=
==
=
==
=
Ax
Ay
dx
J
!
With Stiffener
=
using
1,500,000 ~ =
R
yx
1 500 000
, 1~
VO.25 x 0.29
=
(S)
.
pSI
= 22.438
PSI
0.29
Reference: Wilson, W. M., and Newmark N. M.: The Strength of Thin Cylindrical
Shells as Columns, Eng. Exp. Sta. Univ. Ill. bull. 255, 1933.
68
DESIGN OF TALL TOWERS
DEFLECTION
Towers should be designed to deflect no more than 6 inches per 100 feet of height.
The deflection due to the wind load may be calculated by using the formula for
uniformly loaded cantilever beam.
FORMULA
tlM
=
D1
E
H
I
=
=
=
R
=
=
=
t
Pw
=
NOTATIONS
Maximum deflection (at the top), in.
Width of the tower with insulation, etc. ft.
Modulus of elasticity, psi
Length of vessel, included skirt, ft.
R3 7T t, moment of inertia for thin cylindrical shell
(when R> lOt)
Mean radius of the tower, in.
Thickness of skirt, in.
Wind pressure, psf
EXAMPLE
Given:
D 1 = 2 ft., 6 in.
E
= 30,000,000
H
= 48 ft., a in.
I
= R3 7T 0.3125
P w = 30 psf
R
= 12 in.
t
= 0.3125 in.
Determine tlie maximum deflection: tlM
d
M
-
30 x 2.5 x 48 (12 x 48)3
8 x 30,000,000 X 12 3 x 3.14 x 0.3125
=
1.69 in.
The maximum allowable deflection 6 inches per 100 ft. of height:
48 x 6
for 48'-0" = - - - = 2.88 in.
100
Since the actual deflection does not exceed this limit, the designed thickness of the skirt is
satisfa(,tory.
A method for calculating deflection, when the thickness of the tower is not constant, given by S. S. Tang: "Short Cut Method for Calculating Tower Deflection".
Hydrocarbon Processing November 1968.
69
DESIGN OF TALL TOWERS
COMBINATION OF STRESSES
The stresses induced by the previously described loadings shall be investigated in
combination to establish the governing stresses.
Combination of wind load (or earthquake load), internal pressure and weight of
the vessel:
Stress Condition
At leeward
Stress due
+ Stress due
- Stress due
At windward side
+ Stress due to wind
+ Stress due to into press ..
- Stress due to weight
side
to wind
to int. press.
to weight
Combination of wind load (or earthquake load), external pressure and weight of
the vessel:
Stress Condition
At windward side
+ Stress due to wind
Stress due to ext. press.
Stress due to weight
At leeward
Stress due
Stress due
Stress due
side
to wind
to ext. press.
to weight
The positive signs denote tension and the negative signs denote compression. The
summation of the stresses indicate whether tension or compression is governing.
It is assumed that wind and earthquake loads do not occur simultaneously, thus
the tower should be designed for either wind or earthquake load whichever is
greater.
Bending stress caused by excentricity shall be summarized with the stresses
resulting from wind or earthquake load.
The stresses shall be calculated at the following locations:
1.
2.
3.
4.
At
At
At
At
the bottom of the tower
the joint of the skirt to the head
the bottom head to the shell joint
changes of diameter or thickness of the vessel
The stresses furthermore shall be examined in the following conditions:
1.
2.
3.
During erection or dismantling
During test
During operation
Under these different conditions, the weight of the vessel and consequently, the
stress conditions are also different. Besides, during erection or dismantling the
vessel is not under internal or external pressure.
For analyzing the strength of tall towers under various loadings by this
Handbook, the maximum stress theory has been applied.
70
COMBINATION OF STRESSES (cont.)
The bending moment due to wind is decreasing from the bottom to the top of the
tower, thus the plate thickness can also be decreased accordingly.
Table A and Figure B are convenient aids to find the distance down from the
top of the tower for which a certain thickness is adequate.
0.5
1.0
1.8
0.53
tjtp
m
tjtp
m
0.7
0.84
2.0
0.50
0.6
0.91
1.9
0.51
0.8
0.79
2.2
0.48
0.9
0.74
2.4
0.46
1.0
0.71
2.6
0.44
1.1
0.67
2.8
0.42
1.2
0.64
3.0
0.41
1.3
0.62
3.3
0.39
1.4
0.60
3.6
0.37
1.5
0.58
4.0
0.35
1.6
0.56
4.5
0.33
1.7
0.54
5.0
0.32
T ABLE A, VALUES OF FACTOR m
Since the longitudinal stress due to internal pressure is one half of
the circumferential stress, one half of the required wall thickness
for internal pressure is available to resist the bending force of the
wind. From Table A, using factor m can be found the distance X
down from the top tangent line within which the thickness calculated for internal pressure satisfactory also to resist the wind
pressure.
X = H x m
tp
= The required thickness for internal pressure
(Hoop Tension) in.
tw
= The required thickness for wind pressure at the bottom head
joint to shell, in.
t
X
-
=
0.233 in., tw = 0.644 in. t.Jtp = 0.644/0.233 == 2.7
100 ft.
From Table m = 0.43 and X = mH = 0.43 x 100 = 43 ft.
~
H
EXAMPLE:
0.0
=
Figure B shows the moment diagram of a tower under wind
pressure. The diagram can also be used to select the appropriate
plate thickness at various heights.
0.1 I-0.21\-
::c
Ii
~
~I-\
0.4
0.3
\
~
0
f-o O.S
~
0
f-o
::c
0.6
0
til
::c
EXAMPLE:
At the height ofO. 71 H the required thickness is 0.5
times the thickness required at the bottom.
If the required thickness is:
= 0.250 in.
for internal pressure, Ip
= 0.625 in.
for wind load, tw
at the bottom required
=0.750 in.
1/2 + tw
0.7
0.8
'-
""
0,.
"
~
at height 0.71 H;
0.5 X 0.750
thickness for internal
pressure t/2
required thickness at 0.71 H
0.9
-
1.0
0.1 0.2 0.3 0.4 O.S 0.6 0.70.8 0.9 1.0
Ratio of plate thickness required at the bottom
(t,/2 + ~) to thickness required at the considered heIght.
Fig. B
= 0.375
in.
= 0.125 in.
=
0.500 in.
71
DESIGN OF TALL TOWERS
EXAMPLE - A
Required thickness of cylindrical shell under internal pressure and wind load.
2' - 6"
~
DESIGN CONDITIONS
D
= 2 ft. 0 in. inside diameter of vessel
D J = 2 ft. 6 in. width of tower with insulation, etc.
E
= 0.85 efficiency of welded joints
H = 48 ft. 0 in. length of tower
hr = 4 ft. 0 in. distance from the base to the bottom
head to shell joint
P = 250 psi internal pressure
Pw = 30 psf wind pressure
R
= 12 in. inside radius of vessel
S
= I 5700psi stress value of SA 285 C
material at 200°F temperature
V
= Total shear lb.
o
.,.
QQ
II
.,.
:c
N
II
-
.c
No allowance for corrosion.
Minimum required thickness for internal pressure considering the strength of the long seams:
PR
250 X 12
3,000
.
t = SE _ 0.6P = 15700 X 0.85 - 0.6 X 250 = 13,195 = 0.228 m.
Minimum required thickness for internal pressure considering the strength of the girth seams:
PR
250 x 12
3,000.
t = 2SE + O.4P = 2 x 15,700 x 0.85 + 0.4 x 250 = 26,790 = 0.112 m.
Required thickness for longitudinal bending due to wind pressure. Moment at the base (M):
Pw x D J x H = V x h J = M
30 x 2.5 x 48 = 3,600 x 24 = 86,400 ft. lb.
Moment at the bottom seam (Mr)
Mr
=
=
M - hr (V - 0.5 P w D J hT ) = 86,400 - 4 (3,600 - 0.5 x 30 x 2.5 x 4)
86,400 - 13,800 = 72,600 ft. lb. = 72,600 x 12 = 871,200 in. lb.
Required thickness:
t = ~ = _ _ _ _8:..,.;.7. .;;,.1:..::,2. :,.00:.. .--_ _ _ -
R2
'TT
SE
871,200 - 0 145 in
122 x 3.14 x 15,700 x 0.85 - 6,037,135 - .
.
The required thickness calculated with the strength of the bottom girth seam:
For wind pressure
For int. pressure
TafAL
0.145 in
0.112 in.
0.254
This is greater than the thickness calculated with
the strength of the longitudinal seam therefore, this
minimum thickness 0.257 in. shall be used.
For simple vessels where the moment due to wind is small, the above calculation is satisfactory.
Vessels which are subject to larger loadings may need closer investigation with respect also to
economical viewpoints. See pages 76-84 for skirt, base and anchor bolt design.
72
DESIGN OF TALL TOWERS
EXAMPLE B
Required thickness of cylindrical shell under combined loadings of internal pressure, wind and
weight of tower.
•
3'-6"
~~
DESIGN DATA
+-E~yform
~
r--r"
D
DI
E
hT
"tl
"tl
...'"
-l
o
H
P
Co
o
f-o
Pw
II
::t::
II
=
=
=
=
=
R
=
=
S
=
V
=
Head:
.i;
-~
= 3 ft. 0 in. inside diameter
cm
=
3 ft. 6 in. width of vessel with insulation. allowance for
piping. etc.
0.85 efficiency of welded seams
4 ft. 0 in. distance from the base to the bottom head to shell
joint.
100 ft. 0 in. length of tower
150 psi internal pressure
30 psf wind pressure
18 in. inside radius of vessel
15700psi stress value of SA-285C material at 200°F
temperature
Total shear, lb.
2: I seamless elliptical
Circumference of shell on the mean diameter. in.
(corrosion allowance not required)
Minimum required thickness for internal pressure considering the strength of the longitudinal
seam of shell.
PR
t = -SE---0-.6-P =
150 x 18
15700 x 0.85 _ 0.6 x 150 = 0.204 in. Use 0.25 in. plate
Minimum required thickness for internal pressure considering the strength of the circumferential seam of shell.
PR
150 x 18
== 0.101 in.
t =
= 2------------------------2SE + 0.4P
x 15700 x 0.85 + 0.4 x 150
Minimum required thickness for head
PD
t
= -2S-E---0-.2-P- =
Wind Load
Vessel
Platform
Ladder
150 x 36
2 x 15700 x 0.85 _ 0.2 x 150 = 0.203 in.
Pw x D, x H
30 x 3.5 x 100
30 x 8 lin. ft.
30 x 98 lin. ft.
Total shear
V
X hI
10,500 x 50
240 x 96
=
2,940 x49
=
=
=
V=
13,680
M
=
M
= 525,040
=
23,040
=
144,060
= 692,100 f1. lb. moment at
base
Moment at the bottom head seam (M T)
MT
I
=M
- hT (V - 0.5 P wDlhT) =
692,100 - 4 (13680 - 0.5 x 30 x 3.5 x 4)
= ~ =
R2
1T
SE
12 x 638,220
18 2 x 3.14 x 15700 x 0.85 =
Try 0.750 in. plate for the lower courses
=
638,220 f1. lb.
7,658,640
13~583,556
For int. pressure
=
0.564
0.101
0.665 in.
73
EXAMPLE B (CONT.)
~
'0
'0
~
-
-
01)
f'4
ci I - -
I--
'0
'0
'0
(..
~
f'I
~
'0
01)
r--
ci
-
i
Q
I--
01)
~
N
.....
ci I--
--
'0
~-
~
...
Shell 40 x 97
32 x 195
24 x 294
Head top 0.3125 nom.
bot. 0.8125 nom.
Int. plate work
1ray supports
Insulation rings
Opening
+
6%
Say
The preliminary calculation of the required wall thickness shows that at the bottom approximately 0.75 in.
plate is required, to withstand the wind load and internal
pressure, while at the top the wind load is not factor
and for internal pressure (hoop tension) only 0.25 plate
is satisfactory. For economical reasons it is advisable to
use different plate thicknesses at various heights of the
tower.
The thickness required for hoop tension (0.25 in.) serves
to resist also the wind load to a certain distance down
from the top.
Find this distance (X) from table A, Page 70
tw/tp = 0.564/0.204 = 2.7 then X = 0.43 x H = 43 ft.
can be found the required
From diagram B, Page 70
thickness and length of the intennediate sheD sections.
Using 8 ft. wide plates, the vessel shall be constructed
from:
(5) 0.25 thick 8 ft. wide courses
40 ft.
(4) 0.50 thick 8 ft. wide courses
32 ft.
(3) 0.75 thick 8 ft. wide courses
24 ft.
96 ft.
Total
WEIGHT OF THE TOWER
(See tables beginning on page 374 )
3880
Skirt 4 x 195
6240
Base ring
7056
Anchor ring
160
Anchor lugs
393
800
llO
220
900
19759
1184
20943 lb.
21,000
+
6%
Say
Trays
Operating liquid
+ Erection Wt.
600
2400
3000 lb.
33,000 lb.
TOTAL OPERATING WEIGHT: 36.000 lb.
Test water
+ Erection Wt.
42,000 lb.
33,000 lb.
TOTAL TEST WEIGHT: 75,000 lb.
For weight of water content, see Page 416
260
120
1880
113
1993
2000 lb.
4600
Insulation
Platfonn
Ladder
Piping
Say
TarAL ERECTION WEIGHT: 33,000 lb.
780
720
1160
2800
1400
9960
10,000 lb.
74
EXAMPLE B (CONT.)
Checking the stresses with the preliminary calculated plate thicknesses:
Stress in ·the shell at the bottom head to shell joint:
Plate thickness 0.75 in.
PD
150 X 36.75
Stress due to internal pressure
Stress due to wind
Stress due to weight,
in erection condition
in operating condition
S
=-
= 1837 psi
4 x 0.75
12 X 638,220
- 9
.
S - ~ - R2 1T t - 18.3752 X 3.14 x 0.75 - ,632 pSI
W
31,000
S = -- =
= 358 psi
Cmt
115.5 x 0.75
S
=~ =
4t
=
Cmt
34,000
115.5 x 0.75
= 392 psi
COMBINA TION OF STRESSES
WINDWARD SIDE
LEEW ARD SIDE
IN EMPTY (ERECTION) CONDITION
Stress due to wind
Stress due to weight
+ 9,640
-
Stress due to wind
Stress due to weight
358
+ 9,282 psi
(No into pressure during erection)
Stress due to int. press.
S tress due to wind
Stress due to weight
- 9,640
358
- 9,998 psi
IN OPERATING CONDITION
+ 1,837
Stress due to wind
+ 9,640
Stress due to weight
+ 11,477
392
Stress due to int. press.
+ 11,085 psi
- 9,640
392
-~10,032
+ 1,837
- 8,195 psi
The tensile stress 11,085 psi in operating condition on the windward side governs.
The allowable stress for the plate material with 0.85 joint efficiency is 13,345 psi.
Thus the selected 0.75 in. thick plate at the bottom of the vessel is satisfactory.
Stress in the shell at 72 ft. down from the top of tower. Plate thickness 0.50 in.
-r"----~......
Stress due to wind.
U
-r-- ~
9
N
r-II
:..::
Pw x D I x X
9
0
r--
9
00
\0
x
= V x -2 = Mx
30 x 3.5 x 72 = 7,560 x 36
30 x 8 lin.-ft.
= 240 x 68
30 x 70Iin.-ft. = 2,100 x 35
Total Moment Mx
12 Mr =
12 x 361,980
s = R2 1T t
18.252 x 3.14 x 0.50
Stress due to internal pressure
(As calculated previously)
Total
Shell
Platform
Ladder
= 272,160
= 16,320
= 73,500
= 361,980 ft.-lb.
8,303 psi
1,837
10,140 psi
The calculation of stresses at the bottom head has shown that the stresses on the
windward side in operating condition govern and the effect of the weight is inSignificant. Therefore without further calculation it can be seen that the tensile stress
10,140 psi does not exceed the allowable stress 13,345 psi. Thus the selected 0.50
in. thick plate is satisfactory.
75
EXAMPLE B (CONT.)
Stress in the shell at 40 ft. down from the top of the tower. Plate thickness 0.25 in.
~
...,;--
0
~
0
0
II
00
~
I"")
><
Stress due to wind .
...
Pw
~~
0
";c
I"")
X
D}
X
X = V
X
x
2"
=
Mx
30 X 3.5 X 40 = 4,200 x 20 = 84,000
10 x 8 lin. ft. = 240 x 36 =
8,640
30 x 38 lin. ft. = 1,140 x 19 =
21,660
=
114,300 ft.-lb.
Total Moment Mx
12 Mr =
12 x 114,300
s = R2 'IT t
= 5,316 psi
18.1252 x 3.14 x 0.25
Stress due to internal pressure
(As calculated previously)
1,837 psi
Total
7,153 psi
Shell
Platform
Ladder
The 0.25 in. thick plate for shell at 40 ft. distance from top of the tower is
satisfactory. No fUrther calculation is required on the same reason mentioned above.
76
DESIGN OF SKIRT SUPPORT
A skirt is the most frequently used and the most satisfactory support for vertical
vessels. It is attached by continuous welding to the head and usually the required
size of this welding determines the thickness of the skirt.
Figures A and B show the most common type of skirt to head attachment. In the
calculation of the required weld size, the values ofjoint efficiency given by the Code
(UWI2) may be used.
FORMULA
12MI'
W
t=
+-R2 ;rrSE D ;rrSE
NOTATIONS
D= Outside diameter of skirt, in.
E = Efficiency of skirt to head joint.
(0.6 for butt weld, Fig. A, 0.45 for lap weld, Fig. B)
M= Moment at the skirt to head joint, ft. lb.
R T= Outside radius of skirt, in.
Stress value of the head or skirt material whichever
S
is smaller, psi.
Required thickness of skirt, in.
t
W= Weight of the tower above the skirt to the head
joint, in operating condition.
B
NOTE: Using extremely high skirt, the stresses at the
base may govern. To calculate the required thickness of
the skirt, in this case the above formula can be used,
considering the moment and weight at the base; E = I.
EXAMPLE
Given the same vessel considered in Example B.
D = 37.5 in.
E = 0.60 for butt joint
Mr= 638,220 ft. lb.
S = 15,700 stress value
of SA - 285 - C plate
W = 31,000Ib.
R = 18.75 in.
Determine the required skirt thickness.
Forwind:
12 MI'
12 X 638,220
t= R2 ;rrSE + 18.75 2 X3.14X 15,700XO.6
=0.736 in.
For weight:
W
t=DX3.14XSE
=0.028 in.
31,000
3.75X3.14XI5700XO.6
TOTAL
Use 13/16" thick plate for skirt.
=0.764 in.
REFERENCES: Thermal stresses are discussed in these works:
Brownell. Lloyd E .. and Young, Edwin H., "Process Equipment Design,".John Wiley and Sons, Inc., 1959. Weil,
N.A., and J. J. Murphy Design and Analysis of Welded Pressure Vessel Skirt Supports. Asme. Trans. Industrial Engineering for Industry, Vol. 82, Ser. B., Feb., 1960.
77
DESIGN OF ANCHOR BOLT
Vertical vessels, stacks and towers must be fastened to the concrete foundation,
skid or other structural frame by means of anchor bolts and the base (bearing)
ring.
The number of anchor bolts. The anchor bolts must be in multiple of four and
for tall towers it is preferred to use minimum eight bolts.
Spacing of anchor bolts. The strength of too closely spaced anchor bolts is not
fully developed in concrete foundation. It is advisable to set the anchor bolts not
closer than about 10 inches. To hold this minimum spacing, in the case of small
diameter vessel the enlarging of the bolt circle may be necessary by using conical
skirt or wider base ring with gussets.
Diameter of anchor bolts. Computing the required size of bolts the area within
the root of the threads only can be taken into consideration. The root areas of
bolts are shown below in Table A. For corrosion allowance orie eighth of an inch
should be added to the calculated diameter of anchor bolts.
For anchor bolts and base design on the following pages are described:
1.
2.
An approximate method which may be satisfactory in a number of cases.
A method which offers closer investigation when the loading conditions and
other circumstances make it necessary.
TABLE A
Bolt
Size
Y2
%
%
Ys
1
1Ys
1~
1%
1~
1%
1%
1%
2
2~
2~
2%
3
*
Bolt •
Root Area
SQ. in.
0.126
0.202
0.302
0.419
0.551
0.693
0.890
1.054
1.294
1.515
1.744
2.049
2.300
3.020
3.715
4.618
5.621
m
Dimension in.
12
13
7/8
1
1-1/8
1-1/4
1-3/8
1-1/2
1-3/4
1-7/8
2
2-1/8
2-1/4
2-3/8
2-1/2
2-3/4
3-1/16
3-3/8
3-5/8
5/8
3/4
13/16
15/16
1-1/16
1-1/8
1-1/4
1-3/8
1-1/2
1-5/8
1-3/4
1-7/8
2
2-1/4
2-3/8
2-5/8
2-7/8
For bolts with standard threads.
TABLE B
NUMBER OF ANCHOR BOLTS
Diameter of
Bolt circle in.
24
42
60
84
108
132
to
to
to
to
to
to
36
54
78
102
126
144
Minimum
Maximum
4
8
12
12·
16
20
4
8
12
16
20
24
TABLE C
MAXIMUM ALLOW ABLE STRESSES FOR
BOLTS USED AS ANCHOR BOLT
Specifica tion
Number
Diameter in.
Max. allow.
Stress psi.
SA307
SA193B 7
SA 193 B16
SA193B 7
SA 193 B16
All diameters
2 Yz and under
2 Yz and under
Over 2 Yz to 4 incl.
Over 2 Yz to 4 incl.
15,000
19,000
17,000
18,000
15,000
78
DESIGN OF ANCHOR BOLT
(Approximate Method)
A simple method for the design of anchor bolts is to assume the bolts replaced by a
continuous ring whose diameter is equal to the bolt circle.
The required area of bolts shall be calculated for empty condition of tower.
FORMULAS
Maximum
Tension Ib./lin. in.
T
Required Area of
One Bolt Sq. - in.
BA
Stress in Anchor
Bolt psi.
Ss
T- 12M _ W
- As
Cs
Ss
TC s
= BA N
NarATION
= Area within the bolt circle, sq. in.
= Circumference of bolt circle in.
= Moment at the base due to wind or earthquake, ft. lb.
= Number of anchor bolts
= Maximum allowable stress value of bolt material psi.
= Weight of the vessel during erection, lb.
AB
CB
M
N
SB
W
EXAMPLE
Given bolt circle
AB
CB
M
W
SB
N
=
30 in.; then:
Determine the size and number of required
anchor bolts.
=
707 sq. in.
94 in.
86400 ft. lb.
= 6000 lb. during erection.
= 15000 psi. the maximum
allowable stress value of
the anchor bolt material.
= 4 number of bolts.
(See Table B on the
Preceding Page)
=
=
T
=
12 x 86,400
6000
707
- ~
=
1,402 lb.llin. in.
- .
2 196 sq. In.
.
BA = 1,402 x 94 15,000 x 4
From Table A. Page 77 the root area of
2" bolt is 2.300 sq. in.
Adding 0.125 in. for corrosion, use:
(4) 2W' bolts.
Checking stress in anchor bolt:
SB
x 94 = 14324 si
2.300 x 4
'
P
= 1,402
Since the maximum allowable stress is
15,000 psi, the selected number and size
of bolts are satisfactory.
79
DESIGN OF BASE RING
(Approximate Method)
The formulas below are based on the following considerations:
1. The bearing surface of the base ring shall be large enough to distribute the load
uniformly on the concrete foundation and thus not to exceed the allowable bearing load of the foundation.
2. The thickness of the base ring shall resist the bending stress induced by wind or
earthquake.
-r-f- '."
man.
I,
3
t8
~
2
_Dj
W.fi 0l
I
1..-0 0
FORMULAS
Maximum Compression
Ib'/Iin., in.
P = 12M+lf
c
As Cs
Approximate Width of
Base Ring, in.
Approximate Thickness
of Base Ring, in.
Bearing Stress, psi
Bending Stress, psi
1- Pc
-lb
til
=0.321 1
S - PeCs
I - Au
S2
3 X SI t ~
t l/
NOTATION
AN = Area of base ring = 0.7854 (D2o - D2) sq. in.
A\" = Area within the skirt, sq. in.
C\" = Circumference on 0.0. of skirt, in.
.f, = Safe bearing load on concrete, psi. See Table E, on Page 80
II = Cantilever inside or outside, whichever is greater, in.
II I] = Dimensions, as shown on sketch above.-(Forminimum dimensions see Table
A on page 77)
M = Moment at the base due to wind or earthquake, ft. lb.
W = Weight of vessel during operation or test, lb.
Given:
M= 86,400 ft. lb.
f, = 500psi from
Table E, Page 80
Anchor bolts: (4) 2 114 in.
0.0. of skirt: 24.625 in.
ThenA,=476 sq. in.
C.\.= 77 in.
EXAMPLE
Determine the minimum width and thickness of
base ring for operating condition.
J>..
12X86,400 7,500=2275Ib/l"_'
476
+ 77
'
. m. m.
1=25~~5 =4.55 in.,
but from Table A, page 77 the
minimum dimension for I, =
2314 in. and for 13= 2 114 in.,use 6Vz in. wide base ring.
th = 0.32 X 5 = l.60 in
Checking stresses:
Use 1% in. thick baseTing
2,273 X77
305 p'si
SI
574
3 X 305 X 52 = 10,167 psi
Bearing stress
S]
Bending Stress
\.5 2
Using SA 285 C plate for base ring, 15,700 psi allowable stress can be taken. Thus the width
and thickness of the base ring are satisfactoy.
The stresses should be checked also for test condition.
80
DESIGN OF ANCHOR BOLT AND BASE RING
When a tower is under wind or earthquake load, on the windward side tensional
stress arises in the steel and on the opposite side compressive stress in the concrete
foundation. It is obvious then that the area of the bolting and the area of the base
ring are related. As the anchor bolt area increased, the base ring area can be
decreased. With the design method given here, the minimum required anchor bolt
area for a practical size of base ring can be found. The strength of the steel and
the concrete is different, therefore, the neutral axis does not coincide with the
centerline of the skirt.
Design procedure:
1. Determine the value of k
2. Calculate the required size and number of
anchor bolts. See page 77 Table B
3. Determine the inside and outside diameter of the
base ring
4. Check the stresses in the anchor bolts and
foundation
5. If the deviation between the allowable and
actual stresses are too large, repeat the
calculatidn
6. Calculate the base ring thickness
7. Use gu sset plates, anchor chairs or
compression ring if it is necessary for better
stress distribution in the base ring or skirt
D
k
0.00
.05
.10
.15
.20
.25
.30
.35
.40
.45
.50
.55
.60
.65
.70
.75
.80
.85
.90
.95
1.00
TABLE D
Values of Constants
as Functions of K
j
Cc
Ct
z
3.142
3.008
2.887
2.772
2.661
2.551
2.442
2.333
2.224
2.113
2.000
1.884
1.765
1.640
1.510
1.370
1.218
1.049
0.852
0.600
0.000
0.500
.490
.480
.469
.459
.448
.438
.427
.416
.404
.393
.381
.369
.357
.344
.331
.316
.302
.286
.270
.250
0.000
0.600
0.852
1.049
1.218
1.370
1.510
1.640
1.765
1.884
2.000
2.113
2.224
2.333
2.442
2.551
2.661
2.772
2.887
3.008
3.142
0.750
.760
.766
.771
.776
.779
.781
.783
.784
.785
.785
.785
.784
.783
.781
.779
.776
.771
.766
.760
.750
TABLE F
Bending moment per unit length of section of
a plate perpendicular to X and Y axes respeotively. Use greater value, Mx or My.
Ij{,
0.000
0.333
0.500
0.667
1.000
1.500
2.000
3.000
00
TABLE E
Properties of Concrete Four Mixtures
Ultimate 28 day
Strength psi
Allowable compr.
Strength fc psi
Safe bearing load
fb psi
Factor n
Mx
0.000
0.OO781c b2
0.0293/cb 2
0.0558/c b2
0.09721c b2
0.123 /c b2
0.131 /c b2
0.133 /c b2
0.133 Ic b2
My
-
0.5001c If
0.428/cli
0.319/c Ii
0.227/c
0.1191c It
0.1241c b2
0.1251c b2
0.125/c b2
0.1251c b2
NOTE:
See notation on facing JUl,ge.
2000
2500
3000
3750
800
1000
1200
1500
500
625
750
938
15
12
10
8
n
81
DESIGN OF ANCHOR BOLT AND BASE RING
FORMULAS
I"
Value of constant, k dimensionless
Min.
11
12
13_
tB
Total required area of anchor bolts
Bt sQ. - in.
~
Relationship between max. allowable
compressive stress at the outside edge
of base ring and at the bolt circle.
~
t
Tensile load on anchor bolts, Ft lb.
Tensile stress in anchor bolts, Sa, psi.
r-f;lr;
+.-.1 H-
b
tB
~
I
•
II
V///-
W
t
~
- 1 + (S./n/cb)
B(=2n
12M- Wzd
C,S.jd
2kd+ I
Ic =lcbTkd
2kd
/eh =ie 2kd + I
F._M-WzD
,jD
S-~
• - t,re,
Thickness of a ring which has an
area equal to the area of anchor
bolts, ts, in.
Compression load on the concrete,
Fc, lb.
'1
1
k-
t
S
= !it...
nd
Fc=F,+ W
Compressive stress in the concrete at
the bolt circle. fcb psi.
r..
Fe
. eb = (14 + nt,) rCc
Relationship between tension in steel
and compression in concrete.
S. = n/c
Base ring thickness without gusset
plate, tB, in .
Base ring thickness with gusset
plate, tB, in.
tB
=
(B=
II
J 31c/S
y6Mmax
--S-
NOTATION
b
r
=
The distance between gusset plates, measured on arc of bolt circle in.
Total area required for anchor bolt sq. in.
Constants, see Table D on the preceding page.
Diameter of anchor bolt circle, in.
Diameter of anchor bolt circle, ftCompressive stress in the concrete at the outer edge of the base ring, psi.
Compressive stress in the concrete at the bolt circle, psi.
Constant, see Table D on the preceding page.
I - t f in. = width of the base ring, in.
Moment at the base due to wind or earthquake ft. lb.
M. or M,. whichever is greater. See Table F on the preceding page.
Ratio of 'modulus of elasticity of steel and concrete Es/Ec. See Table E.
Radius of bolt circle, in.
Sa
=
Allowable tensile stress on anchor bolts, psi.
S
Maximum allowable stress value of base plate, psi.
Weight of the tower at the base, lb.
= Constant. See Table D on the preceding page.
=
=
B,
Ce,C, =
=
d
=
D
fe
feb
j
14
=
=
=
=
=
=
M
Mmax
=
n
W
z
=
=
82
DESIGN OF ANCHOR BOLT AND BASE RING
EXAMPLE
DETERMINE:
The size and number of
anchor bolts;
The width and thickness
of base ring.
DESIGN DATA:
= 5 ft., 0 in. diameter of anchor bolt circle.
= 60 in. diameter of anchor bolt circle.
n
= 10, ratio of modulus of elasticity of steel
and concrete (Table E. Page 80)
fe
= 1,200 psi allowable compr. strength of
concrete (Table E, Page 80)
S
= 15,000 psi allowable stress value of base
ring.
Sa = 18,000 psi allowable tensile stress in bolts.
W = 36,000 lb. weight of the tower.
M
= 692,100 ft. lb. moment at the base.
D
d
I
~.
1
=
+~
1
nfeb
2kd
feb = fe
t 1
2kd
=
1,200
1
+
r07ffhl
1 = 8"
t
SOLUTION:
Assume 8 in. wide base ring and a compressive stress at the bolt circle,
k =
2"
T
IBl
feb =
I
"1
1,000 psi.
Then the constants from
Table Dare:
Ce = 1.640
Cr = 2.333
= 0.783
j
= 0.427
z
1
= 0.35
18,000
lOx 1,000
2 x 0.35 x 60
= 1,008 psi
2 x 0.35 x 60 x 8
This is in sufficient agreement with the assumed
value of feb = 1,000 psi
Required area of anchor bolts
_
12M - Wzd _ 6
12 x 692,100 - 36,000 x 0.427 x 60 - 2 0
.
B-2 7T
.28
- 3.5 sq. In.
r
Cr Sa jd
2.333 x 18,000 x 0.783 x 60
Using 12 anchor bolts, the required root area for one bolt
23.50112 = 1.958 in.
From Table A 17/s in. diameter bolt would be satisfactory but adding 'Is in. for corrosion,
use (12) -2 in. diameter anchor bolts.
Tensile load on the anchor bolts
M - Wz D
692,100 - 36,000 x 0.427 x 5
Fr =
jD
=
0.783 x 5
= 157,150 lb.
Tensile stress in the anchor bolts
~
Sa
= trC
=
~
s
7T
d
=
23.50
_
.
3.14 x 60 - 0.125 tn.
14
=
+ 10
X
Compressive load on the concrete:
/.eb
.
pSI
r
s
I
157,150
0.125 x 30 x 2.333 = 17,960
=
=
(I
4
+
Fe
nl) r C = (7.875
s
e
I - Is
=
193,150
0.125) 30
8.0 - 0.125 = 7.875 in.
430
X
1.640 =
.
pSI
83
DESIGN OF ANCHOR BOLT AND BASE RING
EXAMPLE (Cont.)
Checking value of kwhich was calculated with assumed values ofiel> = 1,000 psi and
Sa= 18,000.
Then the constants from
Table Dare:
1
k=-- =
= 0.19
Cc = 1.184
1 + Sa
1 + 17,960
C I = 2.683
10 X430
nicl>
j
= 0.775
z == 0.461
F = M- WzD = 692,100-36,000 X 0.461 X 5 = 157 1921b
0.775 X 5
jD
I
_
Sa -
,.
FI _
157,192
624 .
CI - 0.125 X 30 X 2.683 - 15,
PSt
fIr
Fc= FI + W= 157,192 + 36,000 = 193,192 lb.
193,192
(7.875+ IOXO.125)30X 1.184
596 psi
Compressive stress in the anchor bolts:
Sa= nicl> = lOX 596 = 5,960 psi
Compressive stress in the concrete at the outer edge of the base ring:
2kd + I
ft· =icl> X 2kd
2 X 0.19 X 60 + 8
= 596 X 2 X 0.19 X 60
805 psi
Required thickness of base ring I} = 6 in.
{Ji
~
= I} V.:J.h l S= 6
J3X805
.
15,000 2.406 m.
To decrease the thickness of the base ring, use gusset plates.
Using (24) gusset plates, the distance between the gussets:
-785".1 1
b -- Jrd
24 - .
'b
6 - 0 764
- 7.85.
-
from Table F:
MI/IIIX= M),= 0.196ft·I/=0.196 X 805 X 62 = 5680 in. lb.
tR =
J61~,~~g
1.5076 in. Use I1h in., thick base plate.
84
ANCHOR BOLT CHAIR FOR TALL TOWERS
The chairs are designed for the maximum load which the bolt can transmit to them.
The anchor bolt size and base plate shall be calculated as described on the foregoing pages.
All contacting edges of the plates shall be welded with continuous fillet weld. The
leg size of the fillet weld shall be one half of the thinner joining plate thickness.
E
'//'
'//'
l' .(J'
........-r---+-t-D
DIMENSIONS inches
Anchor
A
B
C
D
E
1
P/4
)1 Is
PIs
2
2 1/s
3
3
3
4
4
4
112
112
112
6
6
21/2
21/2
21/2
3
3
3
3 1/2
3 1/2
3 1/2
4
4
3/4
3/4
1
1
Jl/4
Jl/4
Jl/2
)1/2
P/4
P/4
7
7
5
5
bolt diam
)114
PIs
)112
ISIs
P/4
2 3 /s
PIs
2 5 /s
2
21/4
21/2
2 3/4
3
2 3/4
3
3 1/4
3 1/2
3 3/4
21/4
21/2
5
5
5
sIs
sIs
sIs
314
314
314
1
1
)114
Jl/4
2
21/2
21/2
F
G
P/4
P/2
13 /s
ISIs
Jl/2
P/4
ISIs
PIs
2
2 1/s
13/4
PIs
2
2 1/s
21/4
21/2
2 3/4
3
3 1/4
21/4
2 3/s
21/2
2 3/4
3
3 1/4
3 1/2
The above table is taken from Scheiman A.D. Short Cuts to Anchor Bolting and
Base Ring Sizing. Petroleum Refiner, June 1963.
85
86
STRESSES IN LARGE
HORIZONTAL VESSELS
SUPPORTED BY SADDLES
The design methods of supports for horizontal vessels are based on L. P. Zick's
analysis presented in 1951. The ASME published Zick's work (pressure Vessel
and Piping Design) as recommended practice. The API Standard 2510 also refers
to the analysis of Zick. The British Standard 1515 adopted this method with
slight modification and further refinement. Zick's work has also been used in
different studies published in books and various technical periodicals.
The design method of this Handbook is based on the revised analysis mentioned
above. (Pressure Vessel and Piping; Design and Analysis, ASME, 1972)
A horizontal vessel on saddle support acts as a beam with the following deviations:
1. The loading conditions are different for a full or partially filled vessel.
2. The stresses in the vessel vary according to the angle included by the saddles.
3. The load due to the weight of the vessel is combined with other loads.
LOADINGS:
1. Reaction of the saddles.
It is a recommended practice to design the vessel
for at least a full waterload.
2. Internal Pressure. Since the longitudinal stress in the vessel is only one half of
the circumferential stress, about one half of the actually used plate thickness
is available to resist the load of the weight.
3. External pressure. If the vessel is not designed for full vacuum because vacuum
occurs incidentally only, a vacuum relief valve should be provided especially
when the vessel outlet is connected to a pump.
4. Wind load. Long vessels with very small tlr values are subject to distortion
from wind pressure. According to Zick "experience indicates that a vessel
designed to 1 psi. external pressUre can successfully resist external loads encountered in normal service."
5. Impact Loads. Experience shows, that during shipping, hardly calculable impact loads can damage the vessels. When designing the width of the saddles
and the weld sizes, this circumstance is to be considered.
87
LOCATION OF SADDLES.
The use of only two saddles is preferred both statically and economically over
the multiple support system, this is true even if the use of stiffener rings is
necessary. The location of the saddles is sometimes determined by the location
of openings, sumps, etc., in the bottom of the vessel. If this is not the case,
then the saddles can be placed at the statically optimal point. Thin walled
vessels with a large diameter are best supported near the heads, so as to utilize
the stiffening effect of the heads. Long thick walled vessels are best supported
where the maximal longitudinal bending stress at the saddles is nearly equal to the
stress at the midspan. This point varies with the contact angle of the saddles. The
distance between the head tangent line and the saddle shall in no case be more than
0.2 times the length of the vessel. (L)
Contact Angle (J
The minimum contact angle suggested by the ASME Code is 1200 , except for
very small vessels. (Code Appendix 0-6). For unstiffened cylinders under external pressure the contact angle is mandatorily limited to 120° by the ASME Code.
(U0-29).
Vessels supported by saddles are subject to:
1. Longitudinal bending stress
2. Tangential shear stress
3. Circumferential stress
88
STRESSES IN VESSELS ON TWO SADDLES
H~
'h
A •
u]~.~
L
t. -4...
Q
,
:.a~
§.~
Z
Q
z
I.i.I
=:I
..J
~
Z
Q
:l
~
i3
z
0
..J
Q
UJ
VlZ
QUJ
<u..
UJu..
:I:f:
>Vl
c:lZ
Q;:J
UJ-l
z-l
UJUJ
u..:I:
u.. Vl
-0::
t;;o
-lVl
-l'-'
UJZ
:I:VlO::
0::
0
e:
:;'<'"
~C2" "
~I\ 0
~
<
,; ~
~=
Max. Allow. Stress
FORMULAS
ut.:)
AT THE
SADDLES
(Tension at
the Top.
AR'-)
QA( l-I+
1+
Compression
at the
Bottom)
SI= +
2AL
4H
3L
*KR2 ts
·See note on facing page
AT
MIDSPAN
(Tension at
the Bottom
Compression
at the Top)
( R'U
-H'
QL 1+ 2
1 + 4H
3L
'IT R2 ts
4
S =+
I
4~
IN
SHELL
Vl
IN
SHELL
_ K3 Q
S2 -
(
RtS
L - 2A )
L + 0/3 H
SI
<: (;)(t/R)[2 - (2/3)(IOO)(t/R)]
S2 shall not exceed 0.8 times the
allowable stress value of vessel material.
NOTE: Use formula with factor K2
if ring not used or rings are adjacent
to the saddle. Use formula with factor K3 if ring used in plane of saddle.
ADDI·
TlONAL
STRESS
IN HEAD
Q
AT
BOTTOM
OF
SHELL
In compression the stress due to internal pressure minus 8 1 shall not exceed one half of the compression
yield point of the material or the
value given by:
83 plus stress due to internal pressure shall not exceed 1.25 times the
allowable tensile stress value of head
material.
S = K4Q
2
RtS
IN
HEAD
AT
HORN
OF
SADDLE
In tension S 1 plus the stress due to
internal pressure (PR/2 t s) shall not
exceed the allowable stress value of
shell material times the efficiency of
girth seam.
)
IN
SHELL
~1------1I--------------t
~
NOTATION:
All dimensions in inches
Q = Load on one saddle lbs.
R = Radius of shell
S = Stress pound per sq. inch
ts = Wall thickness of shell
th = Wall thickness of head
(Excluding corrosion allow.)
K = Constant, see page 90
() = Contact angle of saddle degree
3K6Q
4ts(b+I.5~)-~
84 shall not exceed LSO times the
allowable tensile stress value of shell
material.
85 shall not exceed 0.5 times the
compression yield point of shell material.
89
STRESSES IN VESSELS ON TWO SADDLES
NOTES:
Positive values denote tensile stresses and negative values denote compression.
E : Modulus of elasticity of shell or stiffener ring materiaI.pound per square inch.
The maximum bending stress Sl may be either tension or compression.
Computing the tension stress in the formula for S 1, for factor K the values of
K 1 shall be used.
Computing the compression stress in the formula for Sl' for factor K the values
of Kg shall be used.
When the shell is stiffened, the value of factor K = 3.14 in the formula for Sl.
The compression stress is not factor in a steel vessel where t/R ~ 0.005 and the
vessel is designed to be fully stressed under internal pressure.
Use stiffener ring if stress S 1 exceeds rhe maximum allowable stress.
If wear plate is used, in formulas for S2 for the thickness ts may be taken the
sum of the shell and wear plate thickness, provided the wear plate extends R/l 0
inches above the horn of the saddle near the head and extends between the
saddle and an adjacent stiffener ring.
In unstiffened shell the maximum shear occurs at the horn of the saddle. When
the head stiffness is utilized by locating the saddle close to the heads, the
tangential shear stress can cause an additional stress (S3) in the heads. This
stress shall be added to the stress in the heads due to internal pressure.
When stiffener rings are used, the maximum shear occurs at the equator.
If wear plate is used, in formulas for S4 for the ~ickness ts may be taken the
sum of the shell and wear plate thickness and for ts may be taken the shell thickness squared plus the wear plate thickness squared, provided the wear plate
extends R/l 0 inches above the horn of the saddle, and A""-R/2. The combined
circumferential stress at the top edge of the wear plate should also be checked.
When checking at this point: ts = shell thickness,
b = width of saddle
fJ = central angle of the wear plate but not more
than the included angle of the saddle plus 12 0
If wear plate is used, in formulas for S5 for the thickness ts may be taken the
sum of the shell and wear olate thickness, provided the width of the wear plate
equals at least b + 1.56v'"'Rt;
If the shell is not stiffened, the maximum stress occurs at the horn of the saddle.
This stress is not be to added to the internal pressure-stress.
In a stiffened shell the maximum ring-compression is at the bottom of shell.
Use stiffener ring if the circumferential bending stress exceeds the maximum
allowable stress.
90
STRESSES IN LARGE HORIZONTAL VESSELS SUPPORTED BY TWO
SADDLES
VALUES OF CONSTANT K
(Interpolate for Intermediate Values)
*K I = 3.14 if the shell is stiffened by ring or head (A
CONTACT
ANGLE
Kl*
K2
0.335
0.345
0.355
0.366
0.376
0.387
0.398
0.409
0.420
0.432
0.443
0.455
0.467
0.480
0.492
0.505
0.518
0.531
0.544
0.557
0.571
0.585
0.599
0.613
0.627
0.642
0.657
0.672
0.687
0.702
0.718
1.171
1.139
1.108
1.078
1.050
1.022
0.996
0.971
0.946
0.923
0.900
0.879
0.858
0.837
0.818
0.799
0.781
0.763
0.746
0.729
0.713
0.698
0.683
0.668
0.654
0.640
0.627
0.614
0.601
0.589
0.577
f)
120
122
124
126
128
130
132
134
136
138
140
142
144
146
148
150
152
154
156
158
160
162
164
166
168
170
172
174
176
178
180
K3
K4
0.880
0.846
0.813
0.781
0.751
0.722
0.694
0.667
0.641
0.616
0.592
0.319
- 0.569
For
0.547
Any
0.526
Con0.505
Tact
Angles 0.485
0.466
8
0.448
0.430
0.413
0.396
0.380
0.365
0.350
0.336
0.322
0.309
0.296
0.283
0.271
0.260
< R/2)
K5
0.401
0.393
0.385
0.377
0.369
0.362
0.355
0.347
0.340
0.334
0.327
0.320
0.314
0.308
0.301
0.295
0.289
0.283
0.278
0.272
0.266
0.261
0.256
0.250
0.245
0.240
0.235
0.230
0.225
0.220
0.216
K6
See
chart
on
facing
page
K7
K8
0.760
0.753
0.746
0.739
0.732
0.726
0.720
0.714
0.708
0.702
0.697
0.692
0.687
0.682
0.678
0.673
0.669
0.665
0.661
0.657
0.654
0.650
0.647
0.643
0.640
0.637
0.635
0.632
0.629
0.627
0.624
0.603
0.618
0.634
0.651
0.669
0.689
0.705
0.722
0.740
0.759
0.780
0.796
0.813
0.831
0.853
0.876
0.894
0.913
0.933
0.954
0.976
0.994
1.013
1.033
1.054
1.079
1.097
1.116
1.137
1.158
1.183
91
STRESSES IN LARGE HORIZONTAL VESSELS SUPPORTED BY TWO
SADDLES
VALUES OF CONSTANT ~
.1J~
.1
9-1 ~J
.1
' '6.~s~
I
I
II
0.05
9·.1~
I
II
lOG
004
1/
II J
11
0.04
I
I
I I
II I
1/ II
.c
~
J.
~
8
.( :03]
.14 P"
~
II
I I
8·1S0~
1111
1/11 J
1/
0.03
-
:0.032
IL
II
~
II
III I
II 1111
~
>
8.160 ,-- 0026
I I
_LI I
,I
III/ I
II II
1/
1/
0.02
11I1
1/ 1/
I
LI I
I
f I
I f
1 I
I
1/
8.?='I80'o
II
I
-.i
.1
...0.ai7
M J
II
1/
'I
V
r II/If 1/
r- 0.013
0.01
I
1
8'= bbJ-l , 6.022
J
I-
0~(jl1 ~
rill
-
O~u&,i
111/
/
""
- 0.008
I
./1
~g.~
00=9. . .0054
-~'0;0044
I 1
I I
I 1 1
0.0
0.5
~
1.0
RATIO AIR
l.S
OJ) @R
2.0
92
STRESSES IN LARGE HORIZONTAL VESSELS SUPPORTED BY NO
SADDLES
EXAMPLE CALCULATIONS
Design Data
A = 48 in. distance from tangent line
of head to the center of saddle
b = 24 in. width of saddle
H = 21 in. depth of dish of head
L = 960 in. length of vessel tanAan.
P = 250 psi. internal design pressure
Q = 300,000 lb. load on one saddle
R = 60 in. outside radius of shell
ts = 1.00 in. thickness of shell
9 = 120 deg. contact angle
Shell material: SA 515-70 plate
Allowable stress value 17,500 psi.
Yield point 38,000 psi.
Joint Efficiency: 0.85
LONGITUDINAL BENDING STRESS (S,)
Stress at the saddles
2
60 _ 212 )
1 - - 48 + ---.;~--=:;-=-300,000 x 48
-
1-
960
2x48x960
---=-.:~---.,;...:..-~.:.....--
1 + 4 x 21
(
3x 960
.
= S22 pSI.
O.33S x 60 1 x 1
Stress at midspan
QL 1 + 2 R2 [} H2 _ 4A~
4 (
1
4H
+ 3L
L
Sl=----~--rr~R~l~ts----~~
300.000 x 960
~ + 2 _60_~_-_~_P _ 4 x 48)
1 + 4 x 21
4
3.14
960
3x960
X
602
X
1
=
499
5
The sum of tensional stresses: 4959 + 7500 = 12,459 psi
It does not exceed the stress value of the girth seam: 20,000 X 0.85 = 17,000 psi
Compression stress is not a factor since fiR> 0.005; 1/60 = 0.017
.
PSI
93
STRESSES IN LARGE HORIZONTAL VESSELS SUPPORTED BY 1WO
SADDLES
EXAMPLE CALCULATIONS (cont.)
TANGENTIAL SHEAR STRESS
(S~)
Since A (48» Rl2 (6012), the applicable formula:
1.171 x 300,000 ( 960 - 2 x 48 )
60 x 1
960 + 4/3 x 21
52
=
= 5,120psi
does not exceed the stress value of shell material multiplied by 0.8; 20,000 X 0.8
16,000 psi
CIRCUMFERENTIAL STRESS
Stress at the horn of saddle (5.)
Since L (960)
> 8R(480),
5=Q
•
4Is(b+I.56..fiits) -
AIR
=48/60 = 0.8;
A(48) > RI2 (6012), the applicable formula:
JK,Q
11:
K:= 0.036 (from chart)
3 x 0.036)( 300,000
300,000
5. =-
4 x 1 (24 + 1.56 .J 60
x 1)
2t
: = 20,000 psi
S.j does not exceed the stress value of shell material multiplied by 1.5; 20,000 x 1.5
= 30,000 psi
Stress at bottom of shell
(S5)
K1 Q
Ss=--_"':"-_-'::==
Is (b + 1.56VRtsJ
Ss=
0.760 x 300,000
1 (24 + 1.56 J 60)( 1
)
6319'
=-,
PSt
does not exceed the compression yield point multiplied by 0.5; 38,000 )( 0.5
:= 19,000 psi
S5
94
STIFFENER RING
FOR LARGE HORIZONTAL VESSELS SUPPORTED BY
SADDLES
Ring
I
NOTATION.
A = Cross sectional area of ring plus the
effective area of shell, in 2
I = Moment of inertia, inj:J
K = Constant, see next page
Q = Load on one saddle, lbs.
R = Radius of shell, in.
S6 = Max. combined stress, psi.
(J = Contact angle, degree
/\
;:
))
'I
rill
IJ
II
:;
Ii
I
I
Ii
4Q
MAX. STRESS
TYPE OF RING
Max.
Allow
Stress
FORMULAS
Ring Inside.
Compression
at the Shell
Governs
B I Ir+I.SL.uyn.l.
~Rts
~
~
~
I
w
<l Saddle
~
C
>12d
i
~
and Ring
Ring Outside.
~~:l~s at the
I ·r
\ led
Ir
J
-...;:.1'
i-
<i Saddle
and Ring
~__
'===~~~
_
I
.
Ir+I.S~
I
I
D I <i Saddle
I
and Ring E1 I
Ring Outside.
Stress at the
S =_ K9 Q KJ 0 QR
Tip of the
6
A
II d
Ri
'ng
Ring Inside.
Compression
S =- K9Q_ KJ oQR
de
at the Shell
6
A
lie
Governs
~~--~~--~--------------~
Ring Out-side.
K Q K QR
~tress at the
S =-~ + -~
Shell
6
A
lie
t. -t
.J1-i»m
l-=P
'4" I
~
~
1r
I
2 (Ir+I.S6V"Rl sl
• I"
S=_K9Q+KJoQR
6
A
lie
•.
K Q
Ring Inside.
K
QR
~~~~s at the
S6 =-
Ring Inside.
Stress at the
Tip of the
Ring
S =_~9 Q _ KJ 0 QR
6
A
lid
A + -T;c
i
~
-:;;
~
]
.~
v. -
.~ ~
... ..c:
:.a
:.a]
~
-~~
;>
~ ~
C; ~
·c
.e 8aD
~ .S
...
~0
'C :::::
0~
~
]
..: .S
0 0
~ c..
;:3 "'0
~I-plr------------------+----~--------~~--------------------~ ~~
~
2(lr+I.5~)
•
~
<l
I
~ ~
• I
I
L::t
y- ~~
~ddle _P1f21·
Ring Outside.
Compression
at the Shell
Governs
S =_ K9Q _ KJ oQR
6
A
lie
~~
v.
v.
~ ~
~~
+ •.1
::§ 0
~.-pp-rI-~-S-ad-d-Ie-----j--------+-~Ri~.-n-g-l-n-sl-.d-e-.----~--------------------~ : §
and
Ring
~'"d.'".;~
~
:&1,"I
f...d
2 (Ir+l5~
Jd
I
~~~~satthe
S6=_KAQ+K1I/~R
~l
Stress at the
Tip of the
Ring
S=_K9Q_KJoQR
6
A
lid
.s.s-
,t---Ri='""'·n-g~In-s....,.id....,.e-.----+---------------------.............~ ~
95
STIFFENER RING
FOR LARGE HORIZONTAL VESSELS
SUPPORTED BY SADDLES
VALUES OF CONSTANT, K
(Interpolate for Intermediate Values)
Contact
Angle e
120°
130°
140°
150°
160°
170°
180°
.34
.33
.32
.30
.29
.27
.25
.053
.045
.037
.032
.026
.022
.017
NOTES:
1. In figures & formulas A-F positive signs denote tensile stresses and nega-
tive signs denote compression.
2.
The first part of the formulas for S6 gives the direct stress and the second
part gives the circumferential bending stress.
3.
If the governing combined stress is tensional, the stress due to internal
pressure, PR shall be added.
ts
CALCULATION OF MOMENT OF INTERIA (I)
1. Determine the width of shell that is effective to resist the circumferential bending moment. The effective width = 1.56~; 0.78~ on both sides of stiffener
ring.
2.
Divide the stiffener ring into rectangles and calculate the areas (a) of each
rectangle, including the area of shell connection within the effective width.
Add the areas (a) total area = A.
3.
Multiply the areas (a) with the distances OJ from the shell to the center of
gravity of the rectangles. Summarize the results and denote all AY
4.
Determine the neutral axis of the stiffening ring, the distance (C) from the shell
to the neutral axis C = ~y
5.
Determine the distances (h) from the neutral axis to the center of gravity of
each rectangle of the stiffener.
6.
Multiply the square of distances (h 2) by the areas (a) and summarize the
results to obtain AH2.
7.
Calculate the moment of inertia Ig of each rectangle Ig =
width and d = the depth of the rectangles.
8.
The sum of AH2 and Ilg gives the moment of intertia of the stiffener ring and
the effective area of the shell.
See example calculations on the following pages.
fl3, where b = the
96
STIFFENING RINGS
Moment ofInertia (I) - Example Calculations
(All dimensions in inches - R = 72 in. outside radius of shell)
<LSaddle
and R~in=g-~
1 = 0.78.JRd; =
0.78 -.J72 x 0.5 = 4.68
AREACDIg
b~
d3 9.86xO.5 3 =0103· 4
12
12
.
Ill.
AREAQ)lg
b J.,3
3
~ 0.5 x 6 = 9 00· 4
12
12
. Ill.
MARK
OF
AREAS
2
AREA
a
4.93
3.00
TOTAL
A=7.93
I
c
Y
axy
h
h2
a x h2
0.25
3.50
1.23
10.50
1.23
2.02
1.51
4.08
7.44
12.24
AY=I1.73
-
= AY = 11.73 = 1 48
A
7.93
.
-
.h.di
12
0.10
9.00
AH2=19.68 Jg=9.10
-
1= AJ{2 + 19 = 19.68 + 9.10 = 28.78 in.4
1 - 1.56
-fiid; =
1.56 -/72 x 0.25 = 6.618
AREACDIg
3
d !l.L.J
12 -
13.74 x 0.25 3 - 002· 4
12
- . Ill.
AREA(2)
2b2~
= 0.50 x 6 3
12
--
12
=
900·
4
.
Ill.
bet
OF AREAS
AREA
a
y
axy
h
2
h
axh2
12
CD
3.43
0.125
0.43
1.455
2.12
7.27
0.02
(2)
3.00
3.250
9.75
1.670
2.79
8.37
9.00
TOTAL
A =6.43
MARKS
-
C=AY = 10.18 = 1 58
A
6.43
.
AY= 10.18
-
-
AH2= 15.64 Jg=9.02
I=AH2 + Ig= 15.64 + 9.02 = 24.66 in.
4
97
STIFFENING RINGS
Moment of Inertia (/) - Example Calculations
(All dimensions in inches - R = 72 in. outside radius of shell)
cJ
b3 =4.00
L
--=r=----r----rr""""""'--
~~
~
-.i
AREA CD Ig
b d! 9 86 0 53
on...l......l...=.
x.
r12
12
<i S~ad:=d1e"----ii:!II"V1"
0
~
II
O""l::!
I=0.78-{RJl=
1
~ 3 /hr~t---x-----'0.78~72 x 0.5=4.68
I/G
~
~--~~--------------~
N
6
Vv
1
I~
Vv
~ ..s::
X--lf-7<t-X--
and Ring
\0
.".
~
II
'"
b2=
1=4.68IU·)1 1=4.68
on
AREA
MARK OF
a
4.93
3.00
2.00
A=9.93
AREAS
1
2
3
TOTAL
c
6
3
b 3 d'= 4 x 0.5 =004'
II
::.:
12
:;=;
~
7
""l::!
4
h2
a x h2
0.25
3.50
6.75
-
1.23
10.50
13.50
AY=25.23
2.29
0.96
4.21
5.24
0.92
17.72
25.83
2.76
35.44
AH=64.03
-
:a ~
bd-'
12
0.10
9.00
0.04
Jg=9.14
1= AJ{2 + Ig = 64.03 + 9.14 = 73.17in.4
1 - 1.56 Wid; =
~I
1.56 \172 x 0.25 = 6.618
V/ /(3)%;.z;t-·-'--::-:-Pl--r~
m.
h
02511=6.618
0
0
.
axy
= AY = 25.23 = 254
A
9.93
.
.,;"
12
Y
m----.c--r--:-J.1-~
~LQ=~3=8.00lbL~1
P2~1
\0
4
AREAQ)Ig
N
b l = 9.86
o
0 103'
.
m.
'IT' +--____::::--______________--1
~
g; 0 ~ AREAQ)Ig
SHELL~ ~
~ ~
b ct!. 0 5 63
~ '"
--.l...J...-~-900· 4
~~SV///A0::::-::::- :~
~
12 12 - . m.
I~
r- -I:--""l::! - -
o
~
~
./1
"g
i:G
r/l '"
>k
%
I
%
/..,
§ ;g
..s::A }
on
r-
AREA CD Ig
b 1d13 _ 13 •74 x.
025 3 _002'
. In. 4
12 12
-
\0
-;7; e;;-1 a-7;r"':
-'r-~--X-:%r---~ x '--,~ ~ 'IT' ~------------I
~
Shell ___.
N
"
~"'<i
..s:: r-.i II
0
~
AREAQ) Ig
b d3
3
4
22_0.50x6 _9.00in.
1212
-
on
on
N
~...; ~
I!.,
/~
//
5~~hh*
b2+1~6.868
~
b2+I~6.868
II
bl-13.74
~
bet'
AREA
a
y
axy
h
2
h
a xh2
12
1
3.43
0.125
0.43
2.59
6.72
23.09
0.02
2
3.00
3.250
9.75
0.53
0.28
0.84
9.00
3
2.00
6.375
12.75
3.66
13.40
26.80
0.01
TOTAL
A = 8.43
-
AY=22.93
MARKS
OF
AREAS
C=AY = 22.93 = 272
A
8.43
.
-
-
AH2 =50.73 Jg= 9.03
1= AH2 + Ig = 50.73 + 9.03 = 59.76 in.4
98
DESIGN OF SADDLES
WEAR
PLATE
HORN OF
SADDLE
MAX.
EFFECTIVE
AREA
1.
The saddle at the lowest section must resist the horizontal force (F). The effective
cross section of the saddle to resist this load is one third of the vessel radius (R).
F=KlIQ, Where
Q= the load on one saddle, lbs.
KII
= constant as tabulated.
The average stress shall not exceed two thirds ofthe compression yield point ofthe
material. (See example below.)
Contact Angle
.318
EXAMPLE:
Diameter of vessel = 8' - 6"
Weight of vessel = 375,000 Ibs.
Q = 187,500 Ibs.
Saddle material: SA 285 C
Web plate thickness = 0.25 in.
Contact angle = 1200
KIt = 0.204 from table above
Rl3 = 51/3 = 17 inches
Force, F = K/l X Q = 0.204 x 187,500 = 38,250 lb.
To resist this force the effective area of web plate = Rl3 x 0.25
38,250/4.25 = 9,000 Ibs. per square inch.
The allowable stress = ~ x 30,000
= 4.25 in?
= 20,000 psi.
The thickness of the web plate is satisfactory for horizontal force (F).
2. The base plate and wear plate should be thick enough to resist longitudinal bending over the web.
3. The web plate should be stiffened with ribs against the buckling.
99
EXPANSION AND CONTRACTION
OF HORIZONTAL VESSELS
I:
. Ii. SADDLES
,BOLTS
i'
i
a
.1
2
ct
BOLTS
SADDLES
t---+
+.-~
EXPANDING VESSEL
CONTRACTING VESSEL
I
For thermal expansion and contraction, one of the saddles, preferably the one
on the opposite side of the pipe connections, must be allowed to move. In this
saddle for the anchor bolts slots are to be used instead of holes. The length of
the slots shall be determined by the expected magnitude of the movement. The
coefficient of linear expansion for carbon steel per unit length and per degree
F =0.0000067. The table below shows the minimum length of the slot. Dimension "a" calculated for the linear expansion of carbon steel material between 70 0 F
and the indicated temperature. When the change in the distance between the saddles
is more than 3/8" inch long, a slide (bearing) plate should be used. When the
vessel is supported by concrete saddles, an elastic, waterproof sheet at least 1/4"
thick is to be applied between the shell and the saddle.
MINIMUM LENGTH OF SLOT (DIM. "a")
a8
'0
41
:a
"0
1i3
"0
c
'"
[/)
(:;01
'"
The width of
the slot equals
the diam. of
anchor bolt +
~".
DISTANCE
BETWEEN
SADDLES
Ft.
10
20
30
40
50
60
70
80
90
100
FOR TEMPERATURE of
-50 100 200 300
0
0
1/4
1/4
3/8
3/8
1/2
1/2
5/8
5/8
0
0
1/8
1/8
1/4
1/4
1/4
3/8
3/8
3/8
0
1/4
3/8
3/8
1/2
5/8
3/4
3/4
7/8
1
400
1/4
3/8
3/8
5/8
5/8
7/8
3/4 1-1/8
1
1-3/8
1-1/4 1-5/8
1-3/8 1-7/8
1-1/2 2-1/8
1-3/4 2-3/8
1-7/8 2-5/8
500
600
700
800
900
3/8
3/4
1-1/8
1-1/2
1-5/8
2-1/8
2-1/2
2-7/8
3-1/4
3-5/8
1/2
1
1-3/8
1-7/8
2-1/4
2-3/4
3-1/8
3-5/8
4
4-1/2
5/8
1-1/8
1-5/8
2-1/8
2-5/8
3-1/8
3-5/8
4-1/8
4-5/8
5-1/8
3/4
1-1/4
1-5/8
2-3/8
3
3-5/8
4-1/4
4-7/8
5-3/8
6
3/4
1-3/8
2
2-1/2
3-3/8
4-1/8
4-5/8
5-3/8
6
6-5/8
100
SADDLE
FOR SUPPORT OF HORIZONTAL VESSELS
,"min.
---t......-H
~~--------A--------~~
The design based on:
1. the vessel supported by two saddles
2. to resist horizontal force (F) due to the maximum operating weight ofvessel
as tabulated.
3. the maximum allowable stress is % of the compression yield point: % of
30,000 = 20,000 psi.
4. the maximum allowable load on concrete foundation SOO psi.
S. the minimum contact angle of shell and saddle 120°.
Weld: 1;4" continuous fillet weld all contacting plate edges.
Drill and tap 1;4" weep holes in wear plate.
At the sliding saddle the nuts of the anchor bolts shall be hand-tight and secured
by tack welding.
SEE FACING PAGE FOR DIMENSIONS
101
SADDLE
NOMINAL
DlAM.
OF
VESSEL
FT. - IN.
DIMENSIONS
NO.
OF
RIBS
PLATE THICKNESS
INCHES
WEB,
BASE
WEAR
FLANGE,
G
K
RIBSH
MAXIMUM
WEIGHT
ON VESSEL
A
FT.-IN.
B
FT.-IN.
C
IN.
D
IN.
E
FT.-IN.
BOLT
DlAM.
INCH
0-1O~
1-0
4
4
0-3~
~
0
Y4
Y4
-
42000
1-2
1-~
1-1
4
4
0-4
~
0
Y4
Y4
-
50000
1-4
1-2
1-2
4
4
0-5
~
0
Y4
Y4
-
56000
1-6
1-3~
1-3
4
4
0-6
~
0
62000
1-5~
1-4
4
4
0-6~
~
0
-
70000
1-10
1-7
1-5
4
0-7
~
0
76000
1-9
1-6
4
0-7~
Y2
0
Y4
';4
-
2-0
6
6
Y4
Y4
';4
-
1-8
Y4
Y4
Y4
-
84000
2-2
1-1O~
1-7
4
6
0-8
~
0
';4
90000
2-~
1-8
4
6
0-8~
~
0
~
Y4
';4
Y4
2-4
98000
2-6
2-2
1-9
4
6
0-9
~
0
~
Y4
Y4
';4
2-8
2-4
1-10
4
~
0
~
Y4
Y4
112000
2-5
1-11
6
6
11
0-9~
2-10
0-10
~
0
~
Y4
Y4
128000
3-0
2-6~
2-0
6
11
0-11
~
0
~
';4
Y4
134000
3-2
2-9
2-11
2-1
2-2
6
11
1-0
%
0
Y2
Y4
Y4
144000
6
11
1-1
%
0
~
210000
3-~
2-3
6
11
1-2
%
0
~
i
i
3
3
220000
3
252000
1-0
3-4
3-6
4-0
3-6
2-6
6
11
1-4
3
%
0
%
8"
1-6
%-
0
%
3
8"
%
I
%
%
1
%
1
%
i
i
i
4-6
3-11
3-0
6
II
5-0
4-4
3-3
6
11
5-6
4-9~
3-6
6
11
1-8
1-10
18
2-0
%
2-2
2-4
%
1
%
~
1
1
%
1
1
6-0
5-2~
3-9
9
6-6
5-8
4-0
9
18
7-0
6-1
4-3
9
18
9
18
18
2-6
1
2-8
I
18
18
2-10
1
1
2
1';4
2
7-6
6-6
8-0
6-Il~
4-6
4-9
8-6
7-4~
5-0
9
9
9-0
7-9~
5-3
9
9-6
8-3~
9
9
24
3-0
2
8"
8"
8"
104000
i
282000
3
312000
~
344000
8"
8
~
402000
3
436000
~
~
470000
%
~
502000
1
~
i
i
1
1
~
~
760000
~
~
806000
%
~
852000
8
8"
8
536000
10-0
8-8
5-6
5-9
24
3-2
3-4
lY4
2
I
1
%
~
896000
10-6
9-1~
6-0
9
24
3-6
IY4
2
1
%
~
940000
11-0
9-6~
6-3
9
24
3-8
IY4
2
1
%
~
986000
11-6
10-0
6-6
9
24
3-10
IY4
3
1
%
~
1030000
12-0
10-5
6-9
9
24
4-0
IY4
3
1
%
Y2
1076000
102
STRESSES IN VESSELS ON
LEG SUPPORT
,t\
,/ I .\
I
tff-\\
/ R!
I
VIEW
A-A
NOTATION:
W
= Weight of vessel, pounds
n
= Number oflegs
Q
= W Load on one leg, pounds
n
R
Radius of head, inch
H
Lever arm ofload, inch
Dimension of wear plate
2A.2B
S
Stress, pound per square inch
t
Wall thickness of head, inch
Factors, see charts
K
c
c
i4.B,inch
Radius of circular wear plate, inch
D
1.82 k
R
#
t
LONGITUDINAL STRESS:
CIRCUMFERENTIAL STRESS:
NOTES:
Positive values denote tensile stresses and negative values denote compression.
Computing the maximum tensile stresses, in formulas for SI' S2 and K I . K J• Kj
and K J denote negative factors and K 2• K 4• K6 and Ks denote positive factors.
Computing the maximum compression stresses in formulas for SI' S2 and K I • K 2•
K J• K 4• K j • K 6• K7 and Ks denote negative factors.
The maximum tensile stresses SI' and S2' respectively, plus the tensile stress due
to internal pressure shall not exceed the allowable tensile stress value of head
material.
The maximum compression stresses Sf. and S2' respectively, plus the tensile stress
due to internal pressure shall not exceed the allowable compression stress value of
head material.
103
STRESSES IN VESSELS ON LEG SUPPORT
0.30
\
1\
0.25
\
\
0.20
~ 0.15
.,/
......
"-
~
r-.....
-
K
"""" r-.... I--
0.05
......
o
V
"
~
~ 0.10
.,/KI
,
1\
14")
"""" .....
............ t......
~~~~~~
oooo~~
-
r---~
r--
tr:
~
o
N
D
VALUE OF K 1 , & Ks
0.35
0.30
I,Q
~
~
0.25
0.20
~
0.15
0.10
0.05
\
\
~
\
V
1\
\
K2
.,/
\;
\
v
,./"
v K6
K r-.....
\
...............
............
t-- 1-0..
~~~~~~
oooo~~
r---
tr:
~
0
N
VALUE OF K2 , & K6
D
104
STRESSES IN VESSELS ON LEG SUPPORT
0.20-1--+--1-+--+--+-+--+-_-+-_-+-_-+-_-4-_-1
~t--. 0.15
~~
I
/K3
'"
r/~~~~~~,/~~--~~---r--l
'"
0.1 0~/1-+--I-+-+-+-I--",",,~--+---+--+----1---I
0.05
"~
K7
./
/
~~~~~~
"!
0000--
-
o
o
N
M
D
0.60 -++r-+-+--+-+-It--+--+---+--I---+__--I
QQ
~
~~
0.50 +-1+-+--+--+--+-+---+----+---+---+---+---1
0.40 -It-4f--1--+-+--+--+----+---+---+--+---I----I
0.30
+t-t+l_+_~.......,.v--+-K_s+--_+_-_+_-_t_--t--_I
\\V'-
0.20 ~,~--+-_+_+-It--+--+---+--I---+__--I
\ 1\
V
0.10 -+-f->od--t"""d--t-t-::--"'+--_t_--t--_t_--t--_I
f'... ___ :: k __ r-K4
oL..+--'--'-+':~::::j;;;~=+=::;;;;;;j-=-I--+--......t
C"! ~ ~ ~ ~ C"!
0000--
"!
0
-
N
VALUE OF K4 , & KS
D
105
STRESSES IN VESSELS ON LEG SUPPORT
EXAMPLE CALCULATIONS
DESIGN DATA
W = 800,000 lb. weight ofvessel
n = 4, number of legs
W 800,000
Q = --;; = - 4 - = 200,000 lb. load on one leg
R = 100 inch, radius of head
H = 5 inch, lever arm of load
2A = 30 inch, 2B = 30 inch, dimensions of wear plate
t = 1.8 inch thickness of head
cos IX = 0.800
P = 100 psi, internal pressure
Head material: SA 515 -70
Allowable stress value: 20,000 psi
Joint Efficiency: 0.85
Yield Point: 38,000 psi
Factors K (see charts):
C = {AS = ..J 15 x 15 = 15 inch
D= 1.82
C _ fR
R "
15 _
rwo
"
1:8 =2.0-,
t = 1.82 100"
K j = 0.065,
K5 = 0.020,
K 2 = 0.030
K6= 0.010
K3= 0.065
K7= 0.022
K4 = 0.025
Ks = 0.010
LONGITUDINAL STRES:
1.) Maximum tensile stress:
Sf =
~ [cos
IX
(-K j + 6K2 ) +
Z~ ~ (-
K3 + 6K 4 ) ]
S = 200,000 [0.800 (- 0.065 + 6 x 0.030) +2.. - I 100
j
1.82
100 -" 1.8
(-0.065 x 6 x 0.025) ] =+7,634 psi
The stress due to internal pressure:
PR
100xl00
.
2t
2 x 1.8
+ 2778
PSt
The sum of tensional stresses:
7.634 + 2.778 = 10,412 psi
It does not exceed the stress value of the girth seam:
20,000 x 0.85 = 17,000
106
STRESSES IN VESSELS ON LEG SUPPORT
EXAMPLE CALCULATIONS
2.) Maximum compressional stress:
Sf
=7
[cos oc(-K,-6K2) +
~~ ~ (-KJ -6K)]
_ 200,000 [
--L_/IOO
]
1.82
0.800 (-0.065-6x 0.030) + 100 -\I IT (- 0.065-6x 0.025)
Sf -
=
-
17,044 psi
The stress due to internal pressure:
PR
Tt =
100 x 100
2 x 1.8 = + 2,778
The sum of stresses:
- 17,044 + 2,778 =
-
.
pSI
14,266 psi
It does not exceed the stress value of the girth seam:
20,000 x 0.85 = 17,000 psi
Circumferential stress:
1.) Maximum tensile stress:
_~[
I J i )]
(2
cos oc(-K j + 6Kr,) + H
R -\I _
(-K--6K
N
S2 -
S2
=
200,000 [
5 -/100
]
1.82
0.800 (-0.020 + 6x 0.010) + 100 -\I TI (- 0.022+6x 0.010)
= + 2,849 psi
The stress due to internal pressure:
PR
100x 100_
2778 .
2t = 2 x 1.8 - + ,
pSI
The sum of tensile stresses:
- 2,849 + 2,778 = - 5,627 psi
It does not exceed the stress value of the girth seam:
20,000 x 0.85 = 17,000 psi
2.) Maximum compressional stress:
S2=~ [cos cc(-K
S2=
j
-6Kr,) +
~~ ~(-K--6KN)]
200,000 [
---L_/IOO
]
1.82
0.800 (-0.020-6x 0.010) + 100-\1 T.8(-0.022-6xO.01O)
= - 5,837 psi
107
STRESSES IN VESSELS ON LEG SUPPORT
EXAMPLE CALCULATIONS
The stress due to internal pressure:
PR
100 x 100
2 778 .
2t
= 2 x l.8 = + ,
pSI
The sum of stresses:
- 5,837 + 2,778 = - 3,059 psi
It does not exceed the stress value of the girth seam:
20,000 x 0.85
=
17,000 psi
108
LEG SUPPORT
Notch out angles
to clear seam -~n
SECTION A-A
.---t
-,
VESSEL
DIA
2'-6"
3'-0"
3'-6"
4'-0"
4'-6"
5'-0"
5'-6"
6'-0"
6'-6"
7'-0"
7'-6"
1
max
VESSEL
HEIGHT MAX
ANGLE
SIZE
8'-0"
3" X 3" x 3/8"
10'-0"
3.5" X 3.5" x 3/8"
6"
14'-0"
4" X 4" X 112"
7"
16'-0"
5" X 5" X 112"
W
4"
5'-0"
10"
7'-0"
18'-0"
6" X 6" X 5/8"
1'-0"
109
STRESSES IN VESSELS DUE TO
LUG SUPPORT
~
r-Ri
Ul--r-r
r 28 "I
41""'
:J[[]
!
H ""
..!L.
~t-----+---~-
:
Q
I
Q
T
UN STIFFENED
SHELL
NOTATION:
W = Weight of vessel, lb
n = Number of lugs
W
Q = - = Load on one lug, lb
n
R = Radius of shell, in
H = Lever arm of load. in
STIFFENED
SHELL
2A, 2B = Dimensions of wear plate
S = Stress, pound per sq. in
t = Wall thickness of shell, in
C = shape factor, see table
K = Factors, see charts
D=
d
R
,,3rT
V
A
WNGITUDINAL STRESS:
S = +
1
-
QH
D R2t
NOTE: In tension S1 plus the stress due to internal pressure PRJ2t shall not exceed
the stress value of shell material times the efficiency of girth seam.
CIRCUMFERENTIAL STRESS:
S
2
=
+
-
QH
DR 2 t
NOTE: In tension S2 plus the stress due to internal pressure PRJt shall not exceed
the stress value of shell material multiplied by 1.5.
110
STRESSES IN VESSELS DUE TO LUG SUPPORT
12
r-... "'-
~
1/
~
"~
J
rl
10
~
~
,I
'-,..-
-J
f-- f -
4
i-
j
~
2
~V~1/V
Il
I
1/
II
J
o r. . .
I"
o
•
~
~
'~
-- ~~Po
f--
~~
t/'
II
........
-'-
~-
1I
-
~
t7 V-
~
,
~
---- ._- -_.
~
'\
P
~
_._-
0.10
~
~~
-
f---
..",.,..
""""
-
r\ "' \ ~
~~
~
..... r--..
r- !-
~~
t--
;:
-- f--
-- .- -
- -- -
0.15
-
--
0.20
o
VALUE OF K]
f-- f--
\.
""-" !"-
-f-
1\
\.
a.D.:
---
~
-- "" ",~
70 )
-
I--
f"'.
" r\
r\.
f-- f--
~
f---
~
~ I\.
"""....
- 1-
'1 II
1---
~
.......
,,
~
"
'" I'
~
I-- ~
0.05
I""'oi ~
I'
1/
.",
~:;'n
..
- "P
~ 'r\.
'\
~
,/
~
,,;t! --- - ;,;.- ~ ~
-j rJrJl/ v l? ~
'/
~
1\
!--
fI'
I
""
V
~
)
II [l
I--
f-- f--
II
"J
I[
,
/--II
i'-
II
~
'\
..........
V
8
6
~
1\
0.25
111
STRESSES IN VESSELS DUE TO WG SUPPORT
0.12
~~
t' ~
0.10 ~ ~
,,\ '\
'" ,
~
:~ ~
~
~ '\
~ ~l\ [\ '\
~ [\ r\ ~ 1\
\',V\'
0.08
'\,\
1\.'
' ~\ 1\ \
\
0.06
1\
~
,f\
~
\
~\
~
--
~
~
"""
\.
0.04
l\.
,~\ ~ ~ I\. f\."
,\ \ ,K\ ~ , ~r" ;
\
\
~ "-
:\
~-
'\
f---.
---
\
f---
~
~
0.02
~
--
--
f--
'\
~"'" ~
IL l' re
7
.~
~
D
~
. ~O
~
- -- -
-
----
o
._.-
0.05
--.--- ---
-
.
-
~
-. r-..
~
~ -"
~
~C
r\ ... r"- ~ ~.. r--.. ~:--... '""'"
"~ f'... ~ . ~ r-... :--... ......I--
f---
~.
~
-- . - --
o
~
-
-
.J
~
....... .......
O( .i'oo """'- ......
......
0.10
~ .......
0.15
,
to-
"
--- - ----~
..... .....
~
f-
0.20
((2 0)
VALUE OF K2
r"'-- r--.
~
0.25
112
STRESSES IN VESSELS DUE TO LUG SUPPORT
35
'-
,
1/ 1\
I
4
1\
II
30
J
\
I
rn
J
J
I
~
25
I
I
t-t--
t~I
t--
'---l-}
, -~-
II
t---
10
-llI-
j
'I
~,
li~ ,,7 /.
o
"1 'f-r 7"
1--' ~---
o
--
--
-
"'"!o
/
'f
"
~ 1-"""
'7
-- -
0.05
~
---
::J
,
.,.
\
\~
~ ':/
--
-
/
,,'~
~\,
'7
~
\
r" ~ ,\
~
-
~
~,
\
--
--
--
-- --
---
- -- -
~
7 1\ \ [\
I"'" ~
~ \ i\
rs S ~D
~ K .'\
~-
---
-
-
-- - -- --- --- r--
-
1---- '---
-----~
--- .... - - -
--
I---
~
~
" --
2 -- - ~
f-
-\'"\
\
-
I /. -1/ 7
t
rJ
5
~-
- I- t
.J
~
\'
-
I
15
--
,
\
I
J
e_
\
,
~
J
I
20
---
\
()/
~~
I
r---
,
S
-
--- ~ -.....;
--
--
~
po ~
1,.000"
r--
,....
........
~~
-5 fL-
-- t--
~~
~
~
r-
-
~
1---
-
"'"-~~~
"""r--.~ ~~ ~
- ~ ~
~~ ~~
---
----
-- I--
1----
~
~
~
r---r--.,
~
--- r-r--.
i"""" ~ ......
r--. ......
-- -
1---
-----
---~
r-I---
---r-- -- ---
--
0.10
0·15
0.20
o
VALUE OF K3
0.25
113
STRESSES IN VESSELS DUE TO LUG SUPPORT
0.08
~~
1'\ ~ ~ .....
0.06
~ ~ ~ ~.
~ ~ t\.: ~ ~
~~~~
,
\\ ,,\[\ ~
\'\ ~~\ \'\ "",
f:,(1
t-- Sl
~~i~
"
!\ " ,
~" ~- ......
0.04
~.-
.....
~
"
'("
~,
\ !\ '0,
0.02
~
-
"
.....
... ~
"-
'~.)
........ <~~
r-
o
tL ,
r--. """-
'a, '11 " r-r-
0.10
0.05
....... ............ ......
r--. .....
r"o ~ PC
v
o
~
~
~
~
--
~
r-- r--.
-- -- --- - - 1
~ ~ .....
"'U
..... .....
.....
......
r-- ~
r-- r-~ '~
'"'-
r-I-r-o
~
0.15
0.25
VALUE OF K4
BIA
112
1
2
Rlt
C}
C2
C3
C4
50
0.72
1.03
0.95
1.07
100
0.68
1.02
0.97
1.06
200
0.64
1.02
1.04
1.05
300
0.60
1.02
1.10
1.04
50
1
1
1
1
100
1
1
1
1
200
1
1
1
1
300
1
1
1
1
50
0.85
1.10
0.85
0.92
100
1.15
1.07
0.81
0.89
200
1.32
0.98
0.80
0.84
300
1.50
0.90
0.79
0.79
VALUE OF C
114
STRESSES IN VESSELS DUE TO LUG SUPPORT
EXAMPLE CALCULATIONS
DESIGN DATA
W = 1,200,000 lb. weight of vessel
n = 4 number of lugs
W
1,200,000
3 000
Q = -;; =
4
= 00,
lb. load on one lug
R = 90 in, radius of shell
= 5 in, leverarm of load
2A = 30 in, 2B = 30 in, dimensions of wear plate
t = 1.5 in, thickness of shell
p = 100 psi internal pressure
H
Shell material: SA - 515-70
Allowable stress value 20,000 psi
Yield point 38,000 psi
Joint Efficiency: 0.85
Shape factors C, (see table):
90
R/t = ~ = 60,
B/A = 15115) = 1,0
C]
=
C2
=
C3
= C4 = 1.0
The factors K, (see charts)
D =
d ~3 / ~
R
VA
K] = 2.8,
12 ~3 {fJ =
=
90
V 15
K2 = 0.025,
Q 6
.1 7,
R/t = ~
1.5
60
K4 = 0.021
K3 = 6.8
Longitudinal Stress:
s]
300,000
x 5
X
90 2
= 0.167
(
X
1
x 2.8 + 6 0.025 x 90
1 x 1.5
1.5
+ __--.:0~..!..:I6~7_ _ _ )( 90 2
2 (1.17 + 15/15)
5 x 15
)
Stress due to internal pressure:
PR
100 x 90
2t
2 x 1.5
= 3000 psi
= 11,795
+
psi
The sum of tensional stresses:
11,7:95 + 3000 = 14,795 psi
It does not exceed the stress value of the girth seam:
20,000 x 0.85 = 17,000 psi.
115
STRESSES IN VESSELS DUE TO LUG SUPPORT
Circumferential Stress:
S2
=±
Q~
DR t
( C3 K3
+6
R
)
C4 t
K4
300,000 x 5
(
S2 = 0.167 X 902 x 1.5
1 x 6.8
Stress due to internal pressure:
PR
100 X 90
6000"
=
pSI
1.5
+6
0.021 x 90 :\
1 x 1.5
-; = 10,616 psi
The sum of tensional stresses:
10,616 + 6000 = 16,6l6 psi
It does not exceed the stress value of shell material multiplied by 1.5:
20,000 X 1.5 = 30,000
116
LUG SUPPORT
FOR INSULATED VESSELS
t
,
,/
L
T
I
',.-
I,
L
l
~ ~.
~b/~
It
b
.,
TT -
--tk~
_t
LL
lMaximum Allowable
Load on One
Lug, Lbs.
600
t1--
~~
DIMENSIONS
Weight of
One Lug, Lbs.
II
b
bl
h
hI
k
IF
t
w
1,400
6Y2
5
5Y2
3%
4
%
5Y4
Y4
Y4
7
2,200
6%
5Y2
6
5
5Y4
%
5Y2
Y4
Y4
9
3,600
8Y4
6%
7 1/4
6%
7
%
6%
Y4
Y4
16
5,600
lOY4 8%
9Y4
9%
91"s
1
8Y2
Y4
Y4
24
9,000
12Y2 10% 11 Y2 14Y4 14%
1
lOY2
%
%
58
ITYs
1
11 Y2
%
%
72
1Y4
12Y2
Y2
%
126
22%
Pis
14
%
Y2
165
29
1%
16Y2
%
Y2
235
14,000
13% 11 Y2 12Y4
22,000
15Y2
36,000
17Y2 14% 15Y2
56,000
20Y2 17Y2 18Y2 28%
90,000
22% 18Y2 19Y2 31 Y2 32Y4
1%
18
%
Y2
388
140,000
25Y4 20Y2 21 Y2 34% 35%
2
20
%
Y2
482
13
17
13% 18Ys 18%
22
All dimensions are in inches
Stresses in vessel shall be checked.
Use wear plate if necessary
117
LUG SUPPORT
FOR UNINSULATED VESSELS
f
L"
,
,
"""
T
I
'F
i
r
'"
~b,~
It
b
-1kl--
-I
IT -
1-+-1
LL
Maximum Allowable
Load on One Lug,
Lbs.
600
11--
-r:-~
DIMENSIONS
Weight of
One Lug,
Lbs.
I]
b
bl
h
h]
k
If
t
w
1,400
2Yz
2
2~
4
4%
%
1~
3/16
full
1
2,200
314
2~
3
51;4
57/ 16
%
2
3h6
full
2
3,600
4
31;4
3%
6%
616/](;
%
2~
3/16
full
4
5,600
5%
5%
61;4
9%
10
1
4
1;4
1;4
9
9,000
7%
7
7%
141;4 149h6
1
5~
5/16
1;4
21
14,000
9Y2
8~
91;4
17
175/16
1
6~
5h6
1;4
28
22,000
10
9~
101;4
18
183/8
11;4
7
3fs
1;4
45
36,000
12
11~
12~
22
22~
11;4
9
~
3/16
80
56,000
15
15
16V4
28~
79 1/ H 1V4
12
9/ 16
3/ 8
148
90,000
16~
15%
17
31~
321/8 PI.!
13
5/ 8
3/ 8
218
18
17~
18%
14
5/ 8
3/ 8
260
140,000
34Yz 3Sl/8
All dimensions are in inches.
Stresses in vessel shall be checked.
Use wear plate if necessary.
2
118
LIFTING LUG
D·l
H
l"~
ex:
r
t--._._._._._._.+
VESSEL WEIGHT
(Lbs)
D
(In)
'-I--.J-.--.
T
(In)
R
(In)
H
(In)
L
(In)
12,000
1
12
112
5
10
20,000
ll/x
%
2
6
10
-::r
30,000
Pix
1
21/x
50,000
Pix
11;4
212
7
12
70,000
21/x
11;4
312
8
12
100,000
212
112
412
9
16
150,000
-''"
p~
5
WELD
(Min)
6
10
10
16
~--d
s::
..c:;:l
."t:::: 0
:::
~
-V
ca
-0::::
::::9
0) 0)
> :::
0 ......
o 0)
1-0::::
OJ)t;:::
0:)0
> s::
0)'-
.D
200,000
4
2
6
12
18
250,000
41;4
2
612
13
18
300,000
412
212
7
14
20
00
,;;;-
-x
.Dca
ga
0)
a~
Notes:
1. All dimensions are in inches.
2. The design is based on conditions:
a. ex: = 45° maximum
b. Minimum tensile strength oflug material 70,000 psi.
c. Direction of force is in the plane oflugs.
3. Use wear plate if necessary to eliminate buckling due to normal or sudden
loading.
119
LIFTING ATT ACHMENTS
•.
/*
__ ~SHACKLE
:
"
\."
~
::r:
.'
"
\
\.
I /
:!
I I
I
I
I
I
E:b~~.+=f
'.
t
-
U
V//////////~
.Jfr'
/O.~
CQ
/
<
LUG
I?';\ ."\...
'\::.~
"-
tD1
oV///////ft/////////A'
MINIMUM DIMENSIONS OF LIFTING LUGS USING SHACKLE
Load
Lbs.
Shackle
Pin
Diam.
D
710
5/16
1060
3/8
1600
7/16
2170
1/2
2820
58
34
4420
6375
78
8650
1
11300 1-1 8
13400 1-1 4
16500 1-3 8
20000 1-1/2
23750 1-5/8
32350
2
42500 2-1/4
54000 2-1/2
67600 23/4
81000
3
97000 3-1/4
Hole
Diam.
in Lug
Dl
38
7/16
1/2
5/8
3/4
7/8
1
1-1/8
1-1 4
1-3 8
1-1 2
1-5/8
1-3/4
2-1 8
2-3/8
2-5/8
2-7/8
3-1/8
3-3/8
Sheared
Edge
H
A
.50
.56
.63
.69
.94
1.13
1.19
1.31
1.50
1.63
1.75
1.88
.65
.73
.82
.90
1.22
1.47
1.55
1.70
1.95
2.12
2.28
2.45
2.25
2.56
2.81
2.94
2.93
3.33
3.66
3.82
All dimensions in inches,
I Rolled
Gascut
B
78
1-1 8
1-1 4
1-1 2
1-3 4
2
2-1 4
2-7 16
2-5 8
2-7/8
3-1 16
3-3 4
4-18
4-9/16
5
5-7/16
5-7/8
Arm of
Moment
E
.84
.97
1.16
3/4
1.44
7/8
1
1.75
2.12
1-1/8
1-1 4
2.25
1-1 2
2.59
1-5 8
2.94
1-3 4
3.06
1-7 8
3.62
4.06
2
2-3 16 4.19
2-5 8 4.75
5.25
3
3-1 4
6.00
3-9 16 7.00
3-7 8 8.61
4-1/4 9.74
120
LIFTING ATTACHMENTS (cont.)
RECOMMENDED MATERIAL: A 515-70, A 302 or equivalent. The thickness,
and length of the lifting lug shall be determined by calculation:
WELD: When fillet welds are used, it is recommended that throat areas be at
least 50 per cent greater than the cross sectional area of the lug.
To design the lugs the entire load should be assumed to act on one lug.
All possible directions of loading should be considered (during shipment, storage,
erection, handling.) When two or more lugs are used for multileg sling, the angle between each leg of the sling and the horizontal should be assumed to be 30
degrees.
EYE - BOLT
Threaded fasteners smaller
than 5/8" diameter should
not be used for lifting
because of the danger of
over torquing during assembly.
-M!IOA--~W
Commercial eyebolts are
supplied with a rated breaking strength in the X
direction.
For loadings other than along
the axis of the eyebolt, the
following ratings are recommended. These are expressed
as percentage of the rating
in the axial direction.
X = 100% Y = 33%
Z = 20% W = 10%
EXAMPLE:
An eyebolt of 1 in. diameter which is good for 4960 lb. load in tension (direction
x) can carry only 4960 x 0.33 = 1637 lb. load if it acts in direction y.
The above dimensions and recommendations are taken from C. V. Moore: Designing
Lifting Attachments, Machine Design, March 18, 1965.
•Assuming shear load only thru the minimum section, the required thickness
may be calculated by the formula:
p
t= - - - - - -
28 (R-D f2.J
1
where
t =required thickness of lug, in.
P
8
=load, lbs.
=allowable shear stress, psi.
See page 459 for design of weld and length of lug.
121
SAFE LOADS FOR ROPES AND CHAINS
The stress in ropes and chains under load is increasing with the reduction of the
angle between the sling and the horizontal. Thus the maximum allowable safe
load shall be reduced proportionally to the increased stress.
If the allowable load for a single vertical rope is divided by the cosecant of the
angle between one side of the rope and the horizontal, the result will indicate
the allowable load on one side of the inclined sling.
Example:
The allowable load for a rope in vertical position is SOOO lb. If the rope applied
to an angle of 30 degrees, in this position the allowable load on one side will be
SOOO/cosecant 30 deg. = SOOO/2 = 4000 lb. For the two-rope sling the total
allowable load 2 times 4000 = SOOO lb. The table shows the load-bearing capacity
of ropes and chains in different positions. Multiplying with the factors shown in
the table the allowable load for a certain rope or chain, the product will indicate
the allowable load in inclined position.
FACTORS TO CALCULATE SAFE LOADS FOR ROPES AND CHAINS
Angle of
Inclination
900
60 0
45 0
300
100
On One
End
1.00
0.S5
0.70
0.50
0.17
1.70
1.40
1.00
0.34
On Two
Ends
122
OPENINGS
SHAPE OF OPENINGS:
Openings in pressure vessels shall preferably be circular, elliptical or obround.
An obround opening is one which is formed by two parallel sides and semicircular ends. The opening made by a pipe or a circular nozzle, the axis of which is not
perpendicular to the vessel wall or head, may be considered an elliptical opening
for design purposes.
Openings may be of shapes other than the above. Code UG-36(a)(2)
SIZE OF OPENINGS:
Openings are not limited as to size.
The rules, construction details of this handbook conform to the Code UG-36
through UG-43 and apply to openings:
• for maximum 60 in. inside-diameter-vessel one half ofthe vessel diameter,
but maximum 20 in.
• for over 60 in. inside-diameter-vessel one third of the vessel diameter, but
maximum 40 in.
For openings exceeding these limits, supplemental rules of Code Appendix 1-7
shall be satisfied Code UG-36(b)(1)
For nozzle neck thickness see page 140.
WHERE EXTERNAL PIPING IS CONNECTED TO THE VESSEL, THE SCOPE OF
THE CODE INCLUDES:
(a) the welding end connection fQr the first circumferential joint for welded
connections,
(b) the first threaded joint for screwed connections,
(c) the face of the first flange for bolted, flanged connections,
(d) the first sealing service for proprietary connections or fittings.
Code U-I (e)(1)
123
INSPECTION OPENINGS
All pressure vessels for use with compressed air and those subject to internal
corrosion, erosion or mechanical abrasion, shall be provided with suitable
manhole, handhole, or other inspection openings for examination and cleaning.
The required inspection openings shown in the table below are selected from the
alternatives allowed by the Code, UG-46, as they are considered to be the most
economical.
INSPECTION OPENINGS ARE NOT REQUIRED:
INSIDE
DIAMETER
OF VESSEL
over 12 in.
less than 18 in.
J.D.
INSPECTION
OPENING
REQUIRED
two - l~ in.
pipe size threaded
opening
18 in.
to 36 in.
inclusive
1.0.
min. 16. in. I.D.
manhole
or
two - 2 in.
pipe size threaded
opening
over
36 in.
1.0.
min. 16 in. I.D.
manhole
or
two - 6 in.
pipe size nozzle
1. for vessels 12 in. or less inside diameter
if there are at least two minimum
in. pipe size removable connections.
2. for vessels over 12 in. but less than
16 in. inside diameter, that are to be
installed so that they must be disconnected from an assembly to permit
inspection, if there are at least two
removable connections not less than
17l in. pipe size. UG-46(e).
3. for vessels over 12 in. inside diameter
under air pressure which also contain
other substances which will prevent
corrosion, providing the vessel contains suitable openings through which
inspection can be made conveniently,
and providing such openings are equivalent in size and number to the requirement of the table. UG-46(c).
4. for vessels (not over 36 in. 1.0.) which
are provided with teltale holes (one
hole min. per 10 sq. f1.) complying
with the provisions of the Code UG-25,
which are subject only to corrosion
and are not in compressed air service.
UG-46(b).
*
The preferable location of small inspection openings is in each head or near each
head.
In place of two smaller openings a single opening may be -used, provided it is of
such size and location as to afford at least an equal view of the interior.
Compressed air as used here is not intended to include air which has had moisture
removed to the degree that it has an atmospheric dew point of ·50 F or less. The
manufacturer's Data Report shall include a statement "for non·corrosive service"
and Code paragraph number when inspection openings are not provided.
NOZZLE NECK THICKNESS
The wall thickness of a nozzle neck or other connection used as access or
inspection opening only shall not be less than the thickness computed for the
applicable loadings plus corrosion allowance.
124
OPENINGS WITHOUT REINFORCING PAD
Below the most commonly used types of welded attachments are shown. For other
types see Code, Fig. UW-16.1.
OTATIONS:
a= The angle ofbeveling shall be such as to permit
complete joint penetration and complete fusion. Depends on plate thickness, welding procedure.
t = Thickness of vessel wall less corrosion allowance, in.
til = Nominal thickness of nozzle wall less corron
A
sion allowance. in.
NOTES:
I. When complete joint penetration cannot be
verified by visual inspection or other means
permited by the Code, backing strips shall be
For detan
used with full penetration weld deposited from
lee filurea
only one side.
~j.(J~~~B
2. The purpose of weld b is to eliminate the irregularities ofthe groove weld at the root and secure
full penetration. It is urually one pass only and
NOZZLE
NOZZLE WITH
may be omitted if not needed for the above
WITH SLIP ON
WELDING NECK
FLANGE
FLANGE
purpose.
3. The weld sizes defined here are the minimum
requirements. For calculation of strength of
B
welds, see page 136.
4. Strength calculation of welds for pressure loading are not required for attachments shown in
fig. B, C, E, F, G, and for openings:
3 in. pipe size attached to vessel walls of 3/8
R-"'.......•
in. or less in thickness,
2 in. pipe size attached to vessel walls over
BACKING STRIP
3/8 in. thickness. (Code UG -36 (c) (3»
R = the lesser of \;4 t, or % in.
,= Min. weld size = tor t" or 0.375 in. whichever
is the smallest, in.
J + a] = 1114 x the smallest of t, til or I in.
J or a} = the smallest of t, til or 0.375 in.
= No minimum size requirement
tbrll H.
c
F
a
a
R
R = the lesser of \;4 t, or 3;4 in.
D
R = the lesser of \;4 t, or % in.
G
a
b
E
H
R
125
OPENINGS WITH REINFORCING PAD
Below the most commonly used types of welded attachments are shown.
For other types see Code, Fig. UW-16.1.
NOZZLE WITH
WELDING NECK
FLANGE
J
NOTATION:
Minimum weld sizes, inches. Use the
smallest values.
a = tn or te or 0.375 in.
b = No minimum size requirement.
c = 0.7t, or 0.7te, or 0.5 in.
d= 0.7!, orO.7tn, orO.7te, orO.75 in.
e = I, or tp , or 1 in.
cx;= The angle of bevel shall be such
as to permit complete joint penetration and complete fusion. Depends on plate thickness and welding techniques.
t = Thickness of vessel wall less corrosion allowance, in.
Ie = Thickness of reinforcing pad less
corrosion allowance, in.
t n = Nominal thickness of nozzle wall
less corrosion allowance, in.
tp = Thickness of pad type flange, in.
NOZZLE
WITH SLIP ON
FLANGE
t'r1i ~
~~
R
' - Backing strip
R = the lesser of 1;4 t, or 3;4 in.
SEE NOTES ON FACING PAGE.
N
K
R = the lesser of 1;4 I or 3;4 in.
L
til
-;
1/8"
Ir'
o
d
j
R
R = the lesser of 1;4 t or % in.
M
p
126
THREADED AND WELDED FITTINGS
THE FIGURES BELOW SHOW THE MOST COMMONLY USEL tYPES OF WELDED
CONNECTIONS. SEE CODE FIG. UW-16.1 FOR afHER TYPES
A
B
c
D
b
NarATION
a = t, t" or 0.375, whichever is the smallest, in.
a J + a 2 = 1-1/4 times the smallest of t, t" or 1 in.
a J or a 2 = the smallest of t, tn or 0.375 in.
b = no minimum size requirement
c = the smallest of t or 112 in.
d = the thickness of Sch 160 pipe wall, in.
e = the smallest of t or 3/4 in.
t = thickness of vessel wall, less corrosion allowance, in.
I" = nominal thickness of fitting wall less corrosion allowance, in.
The weld sizes defined here are the minimum requirements.
SEE NarES ON FACING PAGE
127
THREADED AND WELDED FITTINGS
THE FIGURES BEWW SHOW THE MOST COMMONLY USED TYPES OF WELDED
CONNECTIONS. SEE CODE FIG. UW-16.1 FOR OTHER TYPES
a
SEE NOTATION ON FACING PAGE:
G
---+c
~~~~~~~~~~
~~~~__~~~~-te
D max
=
outside diameter of pipe
+ 3/4
Max. pipe size: 3 in.
in.
FITTINGS NOT EXCEEDING 3 IN. PIPE SIZE.
In some cases the welds are exempt from size requirements, or fittings and bolting pads
may be attached to the vessels by fillet weld deposited from the outside only with certain
limitations (Code UW-16 (t) (2) and (3)) such as:
1.
The maximum vessel thickness: 3/8 in.
2.
The maximum size of the opening is limited to the outside diameter of the attached
pipe plus % in.
3.
The weld throat shall be the greater ofthe minimum nozzle neck thickness required
by the Code UG-45(a) or that necessary to satisfy the requirements ofUW 18 for
the applicable loadings ofUG 22.
4.
The welding may effect the threads of couplings. It is advisable to keep the threads
above welding with a minimum 1;4 in. or cut the threads after welding.
5.
Strength calculation of attachments is not required for attachments shown in Figs.
A, C and E, and for openings:
3 in. pipe size fittings attached to vessel walls of3/8 in. or less in thickness, 2 in.
pipe size fittings attached to vessel walls over 3/8 in. in thickness. (Code UG36(c)(3)).
128
SUGGESTED MINIMUM
EXTENSION OF OPENINGS
The tables give the approximate minimum outside projection of openings. When
insulation or thick reinforcing pad are used it may be necessary to increase these
dimensions.
OUTSIDE PROJECTION, INCHES USING WELDING NECK FLANGE
NOM.
PRESSURE RATING OF FLANGE LB
FIPE
900
150
300
600
1500 2500
SIZE
• g
\
I
!
1
Q)';::
"t:IV
'r;;.~
"0
~~;-t- . ~
SIS.
2
3
4
6
8
10
I
12
14
16
18
20
24
6
6
6
8
8
8
8
8
8
6
6
8
8
8
8
8
10
10
10
10
10
10
10
10
6
8
8
8
10
10
10
10
10
12
12
12
8
8
8
8
8
8
10
10
10
12
12
14
14
14
14
14
8
10
12
14
16
20
22
12
14
16
16
16
18
18
20
OUTSIDE PROJECTION, INCHES USING SLIP ON FLANGE
NOM.
PIPE
SIZE
I
c
0
!
1
1»:
"t:IV
'-Q)
"'.....
"0
:S ..
OQ,
~~:-r:~"~
-v
I
2
3
4
6
8
10
12
14
16
18
20
24
PRESSURE RATING OF FLANGE LB
150
300
600
900
1500
6
6
6
8
8
8
8
10
6
6
8
8
8
8
6
8
8
8
8
8
8
8
8
10
12
12
12
12
10
10
10
10
10
10
10
10
10
12
10
10
10
10
12
12
12
12
AAcA
Flush
Pipe cut to the
curvature of vessel
Set flush not cut
to the curvature
Minimum extension
for welding
10
10
12
12
12
12
12
12
12
2500
8
10
10
12
12
14
16
d~
Extension for reinforcement
or other purpose
129
REINFORCEMENTS OF OPENINGS
DESIGN FOR INTERNAL PRESSURE
Vessels shall be reinforced around the openings, except single, welded and flued
openings not subject to rapid pressure fluctuations do not require reinforcement if
not larger than:
3Y:z in. diameter in not over 3/8 in. thick vessel wall;
23/ 8 in. diameter in over 3/8 in. vessel wall.
Threaded, studded or expanded connections for which the
hole cut is not greater than 23/ 8 in. diameter.
(Code UG-36(c)(3)(a)
The design procedure described on the following pages conforms to Code UG-36 through UG-43.
For openings exceeding these limits supplemental rules of Code 1-7 shall be applied
in addition to UG-36 through UG-43.
For reinforcement of openings in flat heads see Code UG-39.
A brief outline of reinforcement design for better understanding of the procedure is
described in the following pages.
The basic requirement is that around the opening the vessel must be reinforced with
an equal amount of metal which has been cut out for the opening. The reinforcement
may be an integral part of the vessel and nozzle, or may be an additional reinforcement
pad. (Fig. A)
This simple rule, however, needs further refinements as follows:
1. It is not necessary to replace the actually removed amount of metal, but only the
amount which is required to resist the internal pressure (A). This required thickness of the vessel at the openings is usually less than at other points of the shell
or head.
2. The plate actually used and nozzle neck usually are thicker than would be required according to calculation. The excess in the vessel wall (AJ) and nozzle
wall (A.z) serve as reinforcements. Likewise the inside extension of the opening
(A 3) and the area of the weld metal (A-/) can also be taken into consideration as
reinforcement.
3. The reinforcement must be within a certain limit.
4. The area of reinforcement must be proportionally increased if its stress value is
lower than that of the vessel wall.
5. The area required for reinforcement must be satisfied for all planes through the
center of opening and normal to vessel surface.
The required cross sectional area of the reinforcement shall then be:
The required area for the shell or head to resist the internal pressure (A). From
this area subtract the excess areas within the limit (AjA2A3A-/). If the sum of the
areas available for reinforcement (Aj+A 2+A 3+A-/) is equal or greater than the area
to be replaced (A), the opening is adequately reinforced. Otherwise the difference must be supplied by reinforcing pad (A5).
Some manufacturers follow a simple practice using reinforcing pads with a crosssectional area which is equal to the metal area actually removed for the opening. This
practice results in oversized reinforcement, but with the elimination of calculations
they find it more economical.
130
REINFORCEMENT FOR OPENINGS
DESIGN FOR INTERNAL PRESSURE
(continued)
1.
B
c
D
o
E
For vessels under internal pressure the total cross-sectional
area required for reinforcement of openings shall not be
less than:
A = d Xl" where
d = the inside diameter of opening in its corroded condition,
inches.
t, = the required thickness of shell or head computed by the
applicable formulas using E = 1.0 when the opening is in
solid plate or in a category B joint. When opening passes
through any other welded joint, E = the efficiency of that
joint. When the opening is in a vessel which is radiographically not examined, E = 0.85 for type No.1 joint
and E = 0.80 for type No.2 joint.
When the opening and its reinforcement are entirely
within the spherical portion of a flanged and dished head,
t, is the thickness required by the applicable formulas
using M= 1.
When the opening is in a cone, t, is the thickness required
for a seamless cone of diameter, D measured where the
nozzle axis intersects with the wall of the cone.
When the opening and its reinforcement are in a 2: I ellipsoidal head and are located entirely within a circle the
center of which coincides with the center of the head and
the diameter of which is equal to 0.8 times the head
diameter, t, is the thickness required for seamless sphere
of radius 0.9 times the diameter of the head.
If the stress value of the opening's material is less than
that of the vessel material, the required area A shall be
increased. (See next page for examples.)
2.
F
h
AREA OF REINFORCEMENT
A VAILABLE AREAS OF REINFORCEMENT
AJ= Area of excess thickness in the vessel wall (t-t,) d or
(t-t,) (t" + t)2 use the larger value, square inches.
If the stress value of the opening's material is less than
that of the vessel material, area Al shall be decreased.
(See next page for examples.)
A 2= Area of excess thickness in the nozzle wall (t,,- trn) 5t or
(t,,-t,,) 5t" use - the smaller value, square inches.
A3= Area ofinside extension ofnozzle square inches (t,,-c)2h.
A4= Area of welds, square inches.
If the sum of A, A2 A3 andA-I is less than the area for reinforcement required, A the difference must be supplied by
reinforcing pad.
131
REINFORCEMENT FOR OPENINGS
DESIGN FOR INTERNAL PRESSURE
(continued)
G
3.
LIMITS OF REINFORCEMENT
The metal used as reinforcement must be located within the
limits.
The limit measured parallel to the vessel wall X = d or Rn +
tn + t, use larger value.
The limit measured parallel to the nozzle wall Y = 2.5 tor2.5t/1'
use smaller value.
When additional reinforcing pad is used, the limit, Y to be
measured from the outside surface of the reinforcing pad.
- - - - - - - - - - 1 Rn= inside radius of nozzle in corroded condition, inches.
NOTATION:
For other notations, see the preceding page.
r = thickness of the
vessel wall less cor- 4. STRENGTH OF REINFORCEMENT
rosion allowance,
I-------------------------l
If the strength of materials in AI A2 A3 A./ and A5 or the
inches.
material
of the reinforcing pad are lower than that of the
Ir = see preceeding page
vessel material, their area considered as reinforcement shall
In= nominal thickness
be proportionately decreased and the required area, A in
of nozzle wall irrespective of product inverse proportion increased. The strength ofthe deposited
form. less corrosion weld metal shall be considered as equivalent to the weaker
material of the joint.
allowance. inches.
Irn=required thickness
of seamless nozzle
wall. inches.
h = distance nozzle
projects beyond the
inner surface of the
vessel wall less corrosion allowance.
inches.
c = corrosion allowance,
inches.
d = see preceding page.
It is advisable to use for reinforcing pad material identical
with the vessel material.
No credit shall be takenJor additional strength of reinforcement having higher stress value than that of the vessel wall.
EXAMPLES:
1.
a. The stress value of nozzle material: 17,100 psi.
The stress value of shell material: 20,000 psi.
Ratio 17,100/20,000=0.855
To the required area, A shall be added:
+2t/1 tr(1-0.855)
b. From the area AI shall be subtracted:
-2t/1X (t-t r) (1-0.855)
2.
Using identical material for the vessel and reinforcing
pad, the required area for reinforcement is 12 square
inches.
If the stress value of vessel material = 20,000 psi.,
the stress value of the nozzle material = 17,100 psi.,
ratio 20,000117, 100 = 1.17
In this proportion shall be increased the area ofreinforcing pad:
12 X 1.17 = 14.04 square inches.
132
REINFORCEMENT FOR OPENINGS
DESIGN FOR INTERNAL PRESSURE
( continued)
100
5. REINFORCEMENT IN DIFFERENT
PLANES FOR INTERNAL PRESSURE
\
0.95
0.90
1
Since the circumferential stress in cylindrical shells and cones is two times greater
than the longitudinal stress, at the opening the plane containing the axis of the
shell is the plane of the greatest unit loading due to pressure. On the plane perpendicular to the vessel axis the unit loading
is one half of this.
\
0.85
0.80
~
...0
Chart shows the variation of the stresses
on different planes. (Factor F)
0.75 ~
...
;:J
~
When the long dimension of an elliptical
or obround opening exceeds twice the
short dimensions, the reinforcement
across the short dimensions shall be increased as necessary to provide against
excessive distortion due to twisting moment. Code UG-36(a)(l).
0.70
0.65
0.60
0.551-+-+-++-+-~-+-++-+-+-I~~-+-~
1"'-.
Factor F shall not be less than 1.0, except
for integrally reinforced openings in cylindrical shells and cones it may be less.
O. 50 L...L---L.....L......L.....I...-.L......I---L......J.......L...J..-..r........J'--I.--l.......L.....L--'=
0"
10"
20"
30"
40"
50"
60° 70°
80° 90'
Angle
e
of Plane with Longitudinal Axis
Factor F - Fig. UG-37
4T ? PI..,45}
-(f *-*
PI,.,
F= 1.00"
Longitudinal
axis of shell
The total cross-sectional area of reinforcement in any planes shall
be:
A = dx trx F
F= 0.5
F= 0.75
Longitudinal
axis of shell
(Notations on preceeding pages.)
DESIGN FOR EXTERNAL PRESSURE
The reinforcement required for openings in a single-walled vessel subject to external
pressure need be only 50 percent of that required for internal pressure where tr is the
wall thickness required by the rules for vessels under external pressure. Code UG37(d)(l).
A = dx trx F
2
(See Notations on preceeding pages.)
133
REINFORCEMENT OF OPENINGS
EXAMPLES
EXAMPLE 1.
tn
tm
Rn
I
~ ~ f-'"'-r--
I
tr
h
-,.
I
I
I
t
I,"
~
3*
DESIGN DATA:
Inside diameter of shell: 48 in.
Design pressure: 250 psi at 200 0 F
Shell material: SA-285-C
S=15,700 psi t = 0.625 in.
The vessel is spot radiographed.
No allowance for corrosion.
Nozzzle material: SA-53-B
S = 17,100 psi, tn = 0.432 in.
Nozzle nom. size: 6 in.
Extension of nozzle inside the vessel: 1.5 in.
h=2.5.tn=2.5 x 0.432=1.08 in.
The nozzle does not pass through seams.
Fillet weld size: 0.375 in.
Wall thickness required:
PR
250x24
for shell: tr = - - - - = - - - - - - - - = 0 . 3 8 6 i n .
8E-0.6 15,700x1.0-0.6x250
for nozzle: t
=
m
PRn
8E-0.6P
250x2.88
--------=0.043in.
17,100x 1.0- 0.6x 250
AREA OF REINFORCEMENT REQUIRED
A = dtr = 5.761 x 0.386 =
AREA OF REINFORCEMENT AVAILABLE
Al = (Excess in shell.) Larger of the following:
(t-tr ) d = (0.625-0.386) x 5.761 = 1.377 sq. in. or
(t-t r) (tn + t) 2 = (0.625 - 0.386) x (0.432 + 0.625) x 2 =
0.505 sq. in.
A2 = (Excess in nozzle neck.) Smaller of the followmg:
(tn-tm ) 5t = (0.432-0.043) x 5 x 0.625 = 1.216 sq. in.
(tn-tm ) 51n = (0.432-0.043) x 5 x 0.432 =
(No credit for additional strength of nozzle material having
higher stress value that of the vessel wall.)
2.224 in.
1.377 sq. in.
0.843 sq. in.
A3 = (Inside projection.) tn x 2h = 0.432 x 2 x 1.08 =
0.933 sq. in.
A4 = (Area of fillet weld) 0.375 2
As = (Area of fillet weld inside) 0.375 2
0.140 sq. in.
0.140 sq. in.
TOTAL AREA AVAILABLE
Since this area is greater than the area required for
reinforcement, additional reinforcement is not needed.
3.433 sq. in.
134
REINFORCEMENT OF OPENINGS
EXAMPLES
EXAMPLE 2.
In (I - Ir)
d
h
DESIGN DATA:
Inside radius of shell: R = 24 in.
Design pressure: P = 300 psi at 200 0 F.
Shell material: t = 0.500 in. SA-516-70 plate,
S = 20,000 psi
The vessel is spot examined
There is no allowance for corrosion
Nozzle nominal size: 6 in.
Nozzle material: SA-53 B
S=17,100psi.
t n =0.432 in.
Extension of nozzle inside the vessel: 1.5 in.
Fillet weld size inside: 0.500 in.;
Fillet weld size outside: 0.625 in.
Ratio of stress values: 17,100/20,000 = 0.855
Wall thickness required:
PR
Shell, tr = -S-E---0-.6-P-
PR
SE -0.6P
Nozzle, tm = - - - "n- -
300x24
20,000xl-0.6x300
0.364in.
300x2.88
17.1 00 x 1.0 - 0.6 x 300
0.05Iin.
Since the strength of the nozzle material is lower than that of the vessel material, the required area for
reinforcement shall be proportionally increased and the areas available for reinforcement proportionally
reduced.
AREA OF REINFORCEMENT REQUIRED
A = dtr 5.761 x 0.364 =
2.097 sq. in.
Area increased: + 2tn x tr (1-17,100/20,000) = 2·x 0.432 x 0.364 x (1-0.855) = 0.046 sq. in.
2.143 sq. in.
AREA OF REINFORCEMENT AVAILABLE
AI = (Excess in shell.) Larger of the following:
(t - t r ) d = (0.500 - 0.364) x 5.761 = 0.784 sq. in. or
(t - tr) (tn + t) 2 = (0.500 - 0.364) x (0.432 + 0.500) x 2 = 0.254 sq. in.
Area reduced: -2 x tn (t -tr ) (1 -- 0.855) =
-2 x 0.432 x (0.500 - 0.364) (l - 0.855) = -0.017 sq. in.
0.767 sq. in.
A2 = (Excess in nozzle neck.) Smaller of following:
(tn - t rn ) 5t = (0.432 - 0.051) 5 x 0.500 = 0.953
(tn - trn) 5tn = (0.432 - 0.051) 5 x 0.432 = 0.823
Area reduced: 0.855 x 0.823 = 0.704 sq. in.
Since the strength of the nozzle is lower than that of the shell,
a decreased area shall be taken into consideration.
17,100/20,000 = 0.855,
0.855 x 0.823 =
0.704 sq. in.
A3 = (Inside projection.) tn x 2h = 0.432 x 2 x 1.08 = 0.933
Area decreased 0.933 x 0.855 =
0.797 sq. in.
A4 = (Area of fillet weld) 2 x 0.5 x 0.625 2 x 0.855 =
0.334 sq. in.
As = (Area of fillet weld inside) 2 x 0.5 x 5002 x 0.855 =
0.214 sq. in.
TOTAL AREA AVAILABLE
2.816 sq. in.
Additional reinforcement not required.
135
REINFORCEMENT OF OPENINGS
EXAMPLES
EXAMPLE 3.
DESIGN DATA:
Inside diameter of shell: 48 in.
Design pressure: 300 psi at 200 F.
Shell material: 0.500 in. SA-516-60 plate,
The vessel fully radiographed, E = I
There is no allowance for corrosion
Nozzle nominal size: 8 in.
Nozzle material: SA-53 B, 0.500 in. wall
Extension of nozzle inside the vessel: 0.5 in.
The nozzle does not pass through the main
seams.
Size of fillet welds 0.375 in.
(Reinforcement pad to nozzle neck.)
::,1
I,
0
~I I
-f--4F"1r-- I
~
Wall thickness required:
Shell
tr =
Nozzle
PR
SE-0.6P
t
,
rn
=
300x24
17,100x1-0.6x300
PR
n
SE-0.6P
=
0.426 in.
300x3.8125
17,100xl-0.6x300
AREA OF REINFORCEMENT REQUIRED
A = d x tr = 7.625 x 0.426 =
0.068 in.
3.249 sq. in.
AREA OF REINFORCEMENT AVAILABLE
Al = (Excess in shell.) Larger of the following:
(t - tr) d = (0.500 - 0.426) 7.625 = 0.564
0.564 sq. in.
or (t - tr ) (tn + t) 2 = (0.500 - 0.426) ( 0.500 + 0.500) 2 = 0.148 sq. in.
A2 = (Excess in nozzle neck.) Smaller of following:
(tn - trn) 5t = (0.500 - 0.068) 5 x 0.5 = 1.08 or
1.08 sq. in.
(t n - trn) 5tn = (0.500 - 0.068)5 x 0.5 = 1.08
0.500 sq. in.
A3 = (Inside projection.) tn x 2h = 0.500 x 2 x 0.5 =
2
0.141 sq. in.
A4 = (Area of fillet weld) 0.375
. (The area of pad to shell weld disregarded)
2.285 sq. in.
TOTAL AREA AVAILABLE
This area is less than the required area, therefore the difference shall be provided
by reinforcing element. It may be heavier nozzle neck, larger extension of the
nozzle inside of the vessel or reinforcing pad. Using reinforcing pad, the required
area of pad: 3.249 - 2.285 = 0.964 sq. in. Using 0.375 in. SA-516-60 plate for
reinforcing pad the width of the pad 0.964/0.375 = 2.571
The outside diameter of reinforcing pad: Outside diameter of pipe: 8.625
width of reinforcing pad:
2.571
11.196 in.
136
STRENGTH OF ATTACHMENTS
JOINING OPENINGS TO VESSEL
A
At the attachments, joining openings to the vessel, failure may
occur through the welds or nozzle neck in the combinations
shown in figures A and B.
The strength of the welds and the nozzle neck in those combinations shall be at least equal to the smaller of:
I. The stength in tension of the cross-sectional area of the element of reinforcement being considered, or
Possible paths of failure:
1. Through <D - <D
2. Through ~ - ~
2. The strength in tension of area a (A = d x tr ) less the strength
in tension of the excess in the vessel wall (A I).
B
The allowable stress value of the welds is the stress value of the
weaker material connected by the welds multiplied by the following factors:
Groove-weld tension
Groove-weld shear
Fillet-weld shear
3 2
Possible paths of failure:
1. Through <D - <D
2. Through ~ - ~
3. Through Q) - Q)
0.74
0.60
0.49
The allowable stress value of nozzle neck in shear is 0.70 times
the allowable stress value of nozzle material.
EXAMPLE 4.
A = 2.397 sq. in. Al = 0.484 sq. in.
do = 6.625 in., outside diameter of nozzle
dm = 6.193 in., mean diameter of nozzle
S = 20,000 psi allowable stress value of vessel material
Sn = 17, 100 psi allowable stress value of nozzle material
tn = 0.432 in. wall thickness of nozzle.
t = 0.500 in. wall thickness of vessel'
0.375 in. fillet weld leg.
Check the strength of attachment of nozzle load to be carried by welds.
Load to be carried by welds (A - A I) S = (2.397 - 0.484) x 20,000 = 38,260 lb.
STRESS VALUE OF WELDS:
Fillet-weld shear
0.49 x 20,000 = 9,800 psi.
Groove-weld tension
0.74 x 20,00 = 14.800 psi.
Stess value of nozzle wall shear
0.70 x 17,100 =11,970 psi.
STRENGTH OF WELDS AND NOZZLE NECK:
a. Fillet-weld shear ~L x weld leg x 9,800 = 10.4065 x 0.375 x 9,800 = 38.243 lb.
2
b. Nozzle-wall shear 1Cd., x tn x 11,970 = 9.72 x 0.432 x 11,970 = 50,262 lb.
2
c. Groove-weld tension 1Cdo x t x 14,800 = 10.4065 x 0.500 x 14,800 = 77 ,008 lb.
2
POSSIBLE PATH OF FAILURES:
1. Through a. and b. 38,243 + 50,262 = 88,505 lb.
2. Throgh a. and c. 38,243 + 77,008 = 115,251 lb.
Both paths are stronger than the required strength 38,260 lb.
137
STRENGTH OF ATTACHMENTS
JOINING OPENINGS TO VESSEL
EXAMPLE 5.
DESIGN DATA
A = 3.172 sq. in., Al = 0.641 sq. in., A2 = 0.907 sq. in.
dp = 12.845 in. outside diameter of reinforcing pad.
do = 8.625 in. outside diameter of nozzle.
dm = 8.125 in. mean diameter of nozzle.
S = 20,000 psi allowable stress value of vessel material
Sn = 17,100 psi allowable stress value of nozzle material
t = 0.5000 in. thickness of vessel wall.
0.375 in. leg of fillet - eeld a
0.250 in. leg of fillet - weld d
te = 0.250 in. thickness of reinforcing pad.
Check the strength of attachment of nozzle.
LOAD TO BE CARRRIED BY WELDS:
(A - A I)S = (3.172 - 0.641) x 20,000 = 50,620 lb.
LOAD TO BE CARRIED BY WLDS a, c, e:
(A2 + 2 tnt)S = (0.907 + 2 x 0.500 x 0.500) x 17,100 lb. = 24,059
STRESS VALUE OF WELDS:
Fillet - weld shear
0.49 x 20,000 = 9,800 psi
Groove - weld tension 0.74 x 20,000 = 14,800 psi
STRESS VALUE OF NOZZLE WALL SHEAR:
0.70 x 17,100 = 11,970 psi
STRENGTH OF WELDS AND NOZZLE NECK:.
a. Fillet weld shear
redo
x weld leg x 9,800
2
red
b. Nozzle wall shear ----I!!.x tn x 11,970
2
= 13.55
= 12.76 x
x 0.375 x 9,800
0.500 x 11,970
= 49,796 lb.
= 76,368
c. Groove weld tension ;rdo x weld leg x 14,800 = 13.55 x 0.500 x 14.800
2
lb.
= 100,270 lb.
;rd
d. Filet weld shear _P_x weld leg x 9,800 = 20.18 x 0.25 x 9.800 = 49,433 lb.
2
e. Groove weld tension
redo weld leg x 14,800 = 13.55 x 0.25 x 14,800 = 50,128 lb.
2
POSSIBLE PATH OF FAILURE:
1. Through band d
76,368 + 49,433
= 125,801 lb.
2. Through C and d
100,270 + 49,433
= 149,703 lb.
3. Through a,c and e 49,796 + 100,270 + 50,128 = 200,194 lb.
Paths 1. and 2. are stronger than the total strength of 50,620 lb.
Path 3. is stronger than the strength of 24,059 lb.
The outer fillet weld d strength 49,433 lb. is greater than the reinforcing pad strength of
(dp - dcJt e x S = (12,845 - 8,625) x 0.25 x 20,000 =
21,100 lb.
138
LENGTH OF COUPLINGS AND PIPE FOR OPENINGS
NOZZLE IN SPHERE OR CYLINDER
C
=
R,-vR/ r2
EXAMPLE:
Given: Ri = 15 in., r = 8 in.
u
Find: C = 15--J15 2-8 2
=
15-"'225 - 4 = 15-12.6886
=
2.3114 in.
NOZZLE IN SPHERE OR CYLINDER
X= G-Y
Y= -JR/-(F + rj2
~
EXAMPLE:
Given: Ri = 15 in.,
G = 24 in.,
F = 6 in.
r = 4.3125 in.
Find: X
Y = ...;rI5'-2--{-6-+-4-.3-12-5-Y = -J225-1 06 = W9
Y= 10.9
X= 24-10.9 = 13.1 in.
COUPLING IN SPHERE OR CYLINDER
X= V-Y
EXAMPLE:
Given: Ri = 15 in., Ro = 16 in., F = 6 in., r = 1.25 in.
V = "'16 2-{6-1.25)2 = -J256-22.56 = 15.30 in.
Y= -J15 2-{6 + 1.25)2 = "'225-52.56 = 13.12 in.
X = 15.30-13.12 = 2.18 in.
COUPLING IN SPHERE OR CYLINDER
X= V-Y, Sin/3=AIRo ,
r=a+/3
F =Sin xRo
r
EXAMPLE:
Given: Ro = 12 in., a= 15°, A = 6 in.
Find: F
Sin /3= 6/12 = 0.500 = 30° r= 30°+15° = 45°
F= Sin 45° x 6 = 0.7071 x 6 = 4.243 in.
When F is known, Find X as in Example C above.
NOZZLE IN 2: 1 ELLIPSOIDAL HEAD
X=G-Y-SF
Y= VR/-(F+r)2
2
~I
I
EXAMPLE:
Given: Ri = 24 in., F= 12 in., r= 8 in., SF= 2 in.
G=20 in.
Find: X
Y = Y~24-:2-=-(--:-:-12-:-+---:8-'-)2' = -J576-400 = 6.3 in.
2
X
=
20---6.63-2
2
=
11.37 in.
139
LENGTH OF COUPLING AND PIPE FOR OPENINGS
~
COUPLING IN 2: 1 ELLIPSOIDAL HEAD
I-f+~
L~~~+-.j~
SEAN
i
R;
~
-V
>C
:>
>-
~
R.
NOZZLE IN FLANGED & DISHED HEAD
Flrl
T
V
I
I
I.I~
!:!
l(
-"'"
.,r
~
~
10
b..
~ll~
tIN~/N:E!.h
.
~
~
-=--
+ r)2
X = V-V, V =VR;- (F_r)2, Y =V R?-(F
I
EXAMPLE
Ri = 24 in., Ro = 25 in., F = 8 in., r = 1 in.
Given:
Find: X
V =,.,/25 2- (8 _1)2 =V625 ·49 = 24 in.
~~
r;~
~~. ~-2 t~ ~:-
~~
SEAN'
~
V-
6
.J
X
,
J
I
'~-=:A,
~~
I
VESSEL
R{
Y =-V242- (8 + 1)2 ='V576-81 = 22.25 in.
X=
y
f
:>
>.
~~
I
X=G-Y-SF, Y = ID-C, C = R i · Ri2 - (F + r) 2
EXAMPLE
Given:
Inside depth of dish, ID = 8 in.
Ri = 48 in., Ro = 49 in., F = 24 in., r = 2 in., G = 18 in.,
SF = 2 in.
Find: X
C = 48-""; 48 2 - (24 + 2)2 = 7.70 in.
X= 18-7.70-2 = 8.30 in.
COUPLING IN FLANGED & DISHED HEAD
,rr
L.IN
,j
R? _ (F + r) 2
R i-(F-r)2,
= v- Y, v
Y
2
2
EXAMPLE
Given:
Ri = 29 in .• Ro = 30 in., F = 18 in., r = 1 in.
Find: X
2
-V30 -(18-1)2 =-'/900-289 = 12.36 in.
V
2
2
-V29 2 - (18 + 1)2 ";841-361 = 10.95 in.
Y
2
2
X= 12.36-10.95 = 1.41 in.
x
24-22.25 = 1.75 in.
NOZZLE IN CONE
When ex is less than 45 0
X=G-Y, Y=Ri-[tanex x(F+r)]
EXAMPLE
Ri = 24 in., G = 30 in .• F = 12 in., r = 2 in.,
Given:
0: = 30 0
Find: X
Y = 24- [tan 30 0 (12 + 2)] = 24-8.08 = 15.92 in.
X = 30· 15.92 = 14.08 in.
I
d ~x
'~1hA
I
l
~~J).
[\
COUPLING IN CONE
X=V+2Y, V=
: I ...
~ I ...
~~
Jy.~
V Y
I
•
...i
cos ex
Y = tan ex x r
EXAMPLE
tc = 2 in., r = 1 in., a = 30 0
Given:
Find: X
2
V = - - = 2.31 Y = 0.5774 x 1 = 0.5774
0.866
X = 2.31 + 2 x 0.5774 = 3.46 in.
140
NOZZLE NECK THICKNESS
CodeUG-45
1.
for Access Openings, Openings for Inspection only the minimum wall thickness of necks shall not be less than the thickness computed from the applicable loadings in UG-22 such as internal or external pressure, stattic, cyclic,
dynamic, seismic, impact reactions, etc.
2.
for Nozzles and other openings (except access and inspection openings) the
minimum wall thickness of necks shall be the larger of he chickness computed from the applicable loadings in UG-22 or the smaller of wall thickness
determined in 3, 4, 5, 6 below.
3.
In vessels under internal pressure thicknes of the shell or head required for
internal pressure only, assuming £ = 1.0.
4.
In vessels under external pressure thickness of the shell or head for internal
pressure using it as an equivalent value for external pressure, assuming £=1.0.
5.
In vessels under internal or external pressure the greater of the thickness
determined in 3 and 4.
6.
The minimum wall thickness of standard wall pipe.
7.
The wall thickness of necks in no case shall be less than the minimum thickness specified in UG-16(b) for:
Shells and heads:
0.0625 in.
Unfired steam boilers:
0.2500 in.
In compressed air service:
0.0918 in.
8.
Allowance for corrosion and threading - when required - shall be added to
the thicknesses determined in 1. through 7. above.
Using pipe listed in Table of Std. ANSI 836.10, the minimum wall thickness
equals 0.875 times the nominal wall thickness.
See Code UG-45 footnote No. 27 using pipe sizes 22, 26 and 30 inches.
For selection of required pipe under internal pressure, see table "Maximum
Allowable Internal Working Pressure for Pipes" on the following pages.
EXAMPLES for using the table:
Internal Design Pressure:
Corrosion Allowance
The Required Pipe for Manway:
The Required Pipe for Nozzle:
18"
800 psig
0.125"
Sch.60
Sch.60
0.750" Wall
0.750" Wall
2. Opening Diameter:
Internal Design Pressure:
Corrosion Allowance
The Vessel Wall Thickness
The Required Pipe for Manway:
The Required Pipe for Nozzle:
18"
150 psig
0.125"
0.3125"
Sch.l0
Std. Wt
0.250" Wall
0.375" Wall
1. Opening Diameter:
141
NOZZLE NECK THICKNESS
CodeUG-45
(Continued)
3. Opening Diameter:
18"
Internal Design Pressure:
140 psig
Corrosion Allowance
0.125"
The Vessel Wall Thickness
0.750"
The Required Pipe for Manway:
Sch. 10
The Required Pipe for Nozzle:
Sch.40
Std. Wt. 0.328" + 0.125" Corr. Allow.
4. External Design Pressure:
Material SA 516-60;
Outside diameter of cylindrical shell:
Shell thickness:
The required thickness for 14 in. 0.0.,
0.250" Wall
0.453" Wall (min.)
P = 35 psi
S= 17,100
D{) = 96 in.
t = 1 in.
12 in. long nozzle neck:
1. To withstand 35 psi external pressure approximately 0.05 in. wall re-
quired, but the thickness shall not be less than the smaller of:
2. The thickness required for the shell under 35 psi internal pressure (as
equivalent external pressure)
PR
35 X 47
.
t SE _ 0.6P
17,100 _ 32 = 0.097 In.
3. The minimum thickness of standard wall pipe: 0.328 in. (0.375 in. nom.)
The smaller of2. and 3. 0.097 for wall thickness of nozzle neck is
satisfactory.
5. External Design Pressure:
P = 15 psi
Material SA 516-60;
S= 17,100
Outside diameter of cylindrical shell: D{) = 36 in.
t=0.3125 in.
Shell thickness:
The required thickness for 14 in. 0.0.,-12 in. long nozzle neck:
1.
To withstand 15 psi external pressure approximately 0.02 in. wall required, but the thickness shall not be less than the smaller of the
following:
2.
The th ickness required for the shell under 15 psi internal pressure
t
3.
PR
15X17.6875
SE-0.6P
17,100-9
0016·
.
In.
The minimum thickness of standard wall pipe: 0.328 in. (0.375 in. nom.)
The smaller of2. and 3. is 0.016 in., butthe thickness of the nozzle
neck shall be in no case less than 0.0625 in. UG-45(a)(2).
142
MAXIMUM ALLOWABLE
INTERNAL WORKING PRESSURE FOR PIPES
The Calculations Based on the Formula:
p=
2 SEt
D+ 1.2t'
where
P = The max. allowable working pressure, psig.
S = 17,100 psig. the stress value of the most commonly used materials for pipe
(A53B, AI06B) at temperature - 20 to 650 OF. For higher temperature see notes
at the end of the tables.
E = 1.0 joint efficiency of seamless pipe
D = Inside diameter of pipe, in.
t = Minimum pipe wall thickness, in. (.875 times the nominal thickness).
Nom.
pIpe
SIze
112
3/4
1
1-114
1-112
2
Designation
STD.
X-STG.
SCH.160
XX-STG.
STD.
X-STG.
SCH.160
XX-STG.
STD.
X-STG.
SCH.160
XX-STG.
STD.
X-STG.
SCH.160
XX-STG.
STD.
X-STG.
SCH.160
XX-STG.
STD.
X-STG.
SCH.160
XX-STG.
Pipe wall
thickness
.Min.
Nom.
0.109
0.095
0.147
0.129
0.164
0.187
0.294
0.257
0.099
0.113
0.154
0.135
0.218
0.191
0.308
0.270
0.133
0.116
0.154
0.179
0.219
0.250
0.313
0.358
0.140
0.123
0.191
0.167
0.250
0.219
0.334
0.382
0.145
0.127
0.200
0.175
0.281
0.246
0.400
0.350
0.154
0.135
0.191
0.218
0.343
0.300
0.382
0.436
Corrosion allowance in.
0
1116
118
3/16
Max. Allow. Pressure psig.
4,252 1,365
5,987 2,888
163
7,912 4,575
1,649
13,854 9,719 6,146 3,030
3,487 1,222
4,900 2,498
328
7,280 4,638 2,263
114
11,071 8,026 5,308 2,867
3,245 1,437
4,513 2,607
848
6,570 4,498 2,592
834
10,054 8,462 5,519 3,532
2,692 1,283
3,741 2,266
882
5,043 3,487 2,028
658
8,201 6,435 4,788 3,246
2,414 1,192
35
3,399 2,124
918
4,939 3,578 2,294 1,079
7,388 5,886 4,473 3,139
2,036 1,069
143
2,938 1,933
971
50
4,805 3,716 2,676 1,683
6,312 5,155 4,050 2,997
114
287
661
1,703
1,803
1,878
731
1,988
143
MAXIMUM ALLOWABLE WORKING PRESSURE (cont)
I
Nom.
pIpe
SIze
2~
3
31;2
4
5
6
8
Designation
STD.
X-STG.
SCH-160
XX-STG.
STD.
X-STG.
SCH.160
XX-STG.
STD.
X-STG.
XX-STG.
STD.
X-STG.
SCH.120
SCH.160
XX-STG.
STD.
X-STG.
SCH.120
SCH.160
XX-STG.
STD.
X-STG.
SCH.120
SCH.160
XX-STG.
SCH.20
SCH.30
STD.
SCH.60
X-STG.
SCH.I00
SCH.120
Pipe wall
thickness
Nom. Min.
0.203 0.178
0.276 0.242
0.375 0.328
0.552 0.483
0.216 0.186
0.300 0.263
0.438 0.383
0.600 0.525
0.226 0.198
0.318 0.278
0.636 0.557
0.237 0.208
0.337 0.295
0.438 0.383
0.531 0.465
0.674 0.590
0.258 0.226
0.375 0.328
0.500 0.438
0.625 0.547
0.750 0.656
0.280 0.245
0.432 0.378
0.562 0.492
0.718 0.628
0.864 0.756
0.250 0.219
0277 0.242
0.322 0.282
0.406 0.355
0.500 0.438
0.593 0.519
0.718 0.628
Corrosion allowance in.
1/4
1/16
1/8
3/16
Max. Allow. Pressure Psig.
639
2,227 1,419
657
3,085 2,246 1,437
947
4,293 3,409 2,559 1,738
6,637 5,664 4,728 3,829 2,962
13
633
1,930 1,272
126
750
2,793 2,053 1,391
4,100 3,378 2,679 1,999 1,339
5,874 5,052 4,301 3,572 2,867
88
632
1,762 1,190
240
787
2,515 1,925 1,348
5,359 4,691 4,042 3,410 2,208
156
639
1,640 1,134
319
832
2,365 1,842 1,331
3,122 2,582 2,054 1,539 1,035
3,852 3,294 2,749 2,218 1,698
5,009 4,423 3,852 3,294 2,749
237
629
1,435 1,028
484
2,115- 1,696 1,284
881
2,872 2,439 2,014 1,597 1,187
3,649 3,201 2,761 2,330 1,907
4,452 3,988 3,534 3,088 2,650
628
298
963
1,303
670
2,044 1,692 1,346 1,005
2,699 2,338 1,981 1,631 1,285
3,507 3,132 2,764 2,400 2,044
4,294 3,906 3,526 3,150 2,781
128
375
629
885
468
216
722
981
126
631
377
888
1,147
419
931
673
1,454 1,191
758
1,809 1,542 1,277 1,016
2,161 1,890 1,621 1,355 1,093
2,643 2,365 2,091 1,820 1,552
0
144
MAXIMUM ALLOWABLE WORKING PRESSURE (cont)
Nom.
pIpe
SIze
8
10
12
14
Designation
SCH.140
SCH.160
XX-STG.
SCH.20
SCH.30
STD.
X-STG.
SCH.80
SCH.I00
SCH.120
SCH.140
SCH.160
SCH.20
SCH.30
STD.
SCHAO
X-STG.
SCH.60
SCH.80
SCH.100
SCH.120
SCH.140
SCH.160
SCH.I0
SCH.20
STD.
SCHAO
X-STG.
SCH.60
SCH.80
SCH.I00
SCH.120
SCH.140
Pipe wall
thickness
Nom. Min.
0.812 0.711
0.906 0.793
0.875 0.766
0.250 0.219
0.307 0.269
0.365 0.319
0.500 OA38
0.593 0.519
0.718 0.628
0.843 0.738
1.000 0.875
1.125 0.984
0.250 0.219
0.330 0.289
0.375 0.328
OA06 0.355
0.500 OA38
0.562 OA92
0.687 0.601
0.843 0.738
1.000 0.875
1.125 0.984
1.312 1.148
0.250 0.219
0.312 0.273
0.375 0.328
OA38 0.383
0.500 OA38
0.593 0.519
0.750 0.656
0.937 0.820
1.093 0.956
1.250 1.094
0
3,017
3,393
3,269
707
873
1,038
1,439
1,716
2,095
2,484
2,976
3,377
595
788
897
973
1,207
1,361
1,674
2,074
2,482
2,812
3,317
541
677
816
956
1,096
1,306
1,664
2,101
2,469
2,850
Corrosion allowance in.
114
1/16
118
3/16
Max. Allow Pressure Psig.
2,736 2,456 2,180 1,909
3,106 2,822 2,543 2,266
2,983 2,701 2,423 2,148
102
300
502
462
259
57
666
220
421
831
625
606
1,228 1,019
811
873
1,502 1,290 1,080
1,877 1,662 1,447 1,236
2,261 2,248 1,825 1,610
2,750 2,526 2,264 2,085
3,146 2,918 2,692 2,469
86
253
422
103
273
615
443
209
379
550
723
282
453
625
799
681
554
856
1,030
658
832
1,183 1,006
962
1,494 1,315 1,137
1,891 1,710 1,528 1,349
2,295 2,110 1,926 1,744
2,623 2,435 2,248 2,063
3,123 2,932 2,740 2,552
78
385
230
209
55
363
519
190
345
657
501
482
327
639
796
463
620
774
937
825
666
1,144
983
1,500 1,337 1,175 1,014
1,933 1,767 1,602 1,438
2,299 2,130 1,963 1,796
2,676 2,505 2,334 2,166
I
145
MAXIMUM ALLOWABLE WORKING PRESSURE (cont)
Nom.
DesigpIpe
nation
SIze
14 SCH.160
SCH.10
SCH.20
SCH.30.STD.
SCHAOX-STG.
16 SCH.60
SCH.80
SCH.100
SCH.120
SCH.140
SCH.160
SCH.lO
SCH.20
STD.
SCH.30
X-STG.
18 SCHAO
SCH.60
SCH.80
SCH.100
SCH.120
SCH.140
SCH.160
SCH.10
SCH.20 STD.
SCH.30 X-STG.
SCHAO
20 SCH.60
SCH.80
SCH.100
SCH.120
SCH.140
SCH.160
Pipe wall
thickness
Nom. Min.
10406 1.230
0.250 0.219
0.312 0.273
0.375 0.328
0.500 00438
0.656 0.574
0.843 0.738
1.031 0.902
1.218 1.066
10438 1.258
1.593 1.394
0.250 0.219
0.312 0.273
0.375 0.328
00438 0.383
0.500 00438
0.562 00492
0.750 0.656
0.937 0.820
1.156 1.012
1.375 1.203
1.562 1.367
1.781 1.558
0.250 0.219
0.375 0.328
0.500 00438
0.593 0.519
0.812 0.711
1.031 0.902
1.281 1.121
1.500 1.313
1.750 1.531
1.968 1.722
Corrosion allowance in.
0 1116
1/8
3/16
114
Max. Allow Pressure Psig.
3,230 3,055 2,880 2,707 2,535
189
64
473 336
318
183
49
590 453
437
302
166
712 574
541
404
956 817
679
981
841
703
1,263 1,121
1,637 1,493 1,350 1,209 1,068
2,018 1,873 1,727 1,583 1,439
2,406 2,257 2,110 1,963 1,818
2,869 2,717 2,566 2,416 2,268
3,202 3,048 2,895 2,743 2,593
178
61
419 298
43
282
163
524 403
148
267
631 509
388
253
494
373
739 616
359
481
848 725
603
463
585
955 831
707
785
908
1,287 1,157 1,032
1,616 1,488 1,362 1,235 1,110
2,013 1,883 1,754 1,625 1,497
2,414 2,282 2,151 2,020 1,890
2,764 2,631 2,496 2,364 2,232
3,179 3,042 2,907 2,772 2,637
54
160
377 263
133
240
567 458
348
432
323
761 650
541
463
684
573
906 794
914
802
1,250 1,137 1,026
1,599 1,485 1,370 1,257 1,144
2,006 1,888 1,772 1,657 1,542
2,368 2,250 2,131 2,014 1,898
2,788 2,667 2,546 2,427 2,308
3,162 3,039 2,916 2,795 2,674
146
MAXIMUM ALLOWABLE WORKING PRESSURE (cont)
Nom.
pIpe
SIze
Designation
22
SCH.10
SCH.20 STD.
X-STG.
SCH.30
SCH.40
24 SCH.60
SCH.80
SCH.IOO
SCH.120
SCH.140
SCH.160
26
30
Pipe wall
thickness
Nom. Min.
0.250 0.219
0.312 0.273
0.375 0.328
0.437 0.382
0.500 0.438
0.562 0.492
0.625 0.547
0.688 0.602
0.750 0.656
0.250 0.219
0.375 0.328
0.500 0.438
0.562 0.492
0.687 0.601
0.968 0.847
1.218 1.066
1.531 1.340
1.812 1.586
2.062 1.804
2.343 2.050
0.250 0.219
0.312 0.273
0.375 0.328
0.437 0.382
0.500 0.438
0.562 0.492
0.625 0.547
0.688 0.602
0.750 0.656
0.312 0.273
0.375 0.328
0.500 0.438
Corrosion allowance in.
1/4
0 1/16
3/16
1/8
Max. Allow. Pressure Psig.
50
343 243
145
132
35
230
428 329
218
120
316
515 416
155
402
304
601 501
294
491
392
690 591
477
378
677
577
776
565
466
665
867 766
554
753
653
956 855
639
739
1,044 942
841
45
133
313 223
200
290
110
471 380
269
359
632 541
450
346
437
528
712 620
505
597
688
873 780
861
959
1,241 1,146 1,053
1,574 1,478 1,383 1,289 1,194
1,998 1,900 1,803 1,707 1,610
2,386 2,286 2,187 2,089 1,991
2,734 2,634 2,534 2,433 2,334
3,135 3,032 2,930 2,829 2,728
42
123
289 206
29
111
194
361 278
102
184
267
435 351
173
256
339
508 424
248
331
414
583 499
320
403
487
656 572
393
477
562
730 646
467
551
636
805 721
624
540
794
709
880
26
96
168
313 240
88
160
232
376 304
214
287
359
505 432
147
NOTE: IF THE STRESS VALUE OF PIPE LESS THAN 17100 PSIG.
DUE TO HIGHER TEMPERATURE, MULTIPLY THE MAX.
ALLOWABLE PRESSURE GIVEN IN THE TABLES BY THE
FACTORS IN THIS TABLE:
A53B
AI06B
TEMPERATURE NOT EXCEEDING DEGREE OF
650
700
750
800
850
900
950
1 000
17,100 15,600 13,OOC 10,800 8,700 5,900
-
stress
values
pSlg 17,100 15,600 13,OOC 10,800 8,700 5,900 4,000 2,500
Factor
1.000
0.9123 0.7602 0.6316 0.4971 0.3450 0.2339 0.1462
Example:
The Maximum Allowance Pressure for 6" x Stg. Pipe With a Corrosion
Allowance of 118" From Table = 1,346 psi. - at Temperature 800 OF
The Max. Allow. Press. 1,346 x 0.6316 = 850 psig.
Example to find max. allow. pressure for any stress values:
The Max. Allow. Press. 1,346 Psig. From Tables
The Stress Value 13,000 psi.
13 000
For This Pipe The Max. Allow. Pressure
'
x 1,346 = 1,023 psi.
. 17,100
148
REQUIRED WALL THICKNESS FOR PIPES
UNDER INTERNAL PRESSURE
The required wall thickness for pipes, tabulated on the following pages, has been
computed with the following formula:
PR
t= SE-O.6P
, where
t = the required minimum wall thickness of pipe, in.
P = internal pressure, psig.
S = 17,100 psig. the stress value of the most commonly used materials for pipe.
A 53 B and A 106 B @ temp~rature -20 to 650°F.
E = Joint efficiency of seamless pipe
R = inside radius of the pipe, in.
For the inside diameter of the pipe round figures are shown. With interpolation
the required thickness can be determined with satisfactory accuracy.
The thicknesses given in the tables do not include allowance for corrosion.
For the determination of the required pipe wall thickness in piping systems the
various piping codes shall be applied.
Selecting pipe, the 12.5% tolerance in wall thickness shall be taken into consideration. The minimum thickness of the pipe wall equals the nominal thickness
times .875.
149
REQUIRED PIPE WALL THICKNESS
FOR INTERNAL PRESSURE
I.S.
DIAM
1
2
3
4
5
50
0.002
0.003
0.005
0.006
0.008
100
0.003
0.006
0.009
0.012
0.015
150
0.005
0.009
0.014
0.018
0.022
PRESSURE PSIG.
250
300
200
350
0.009
0.006 0.008
0.011
0.012 0.015 0.018 0.021
0.018 0.022 0.027 0.031
0.024 0.030 0.036 0.042
0.030 0.037 0.045 0.052
6
7
8
9
10
0.009
0.011
0.012
0.013
0.015
0.018
0.021
0.024
0.027
0.030
0.027
0.031
0.036
0.040
0.044
0.036
0.042
0.047
0.053
0.059
0.045
0.052
0.059
0.065
0.074
0.054
0.062
0.071
0.080
0.089
11
12
13
14
15
0.016
0.018
0.019
0.021
0.022
0.033
0.036
0.038
0.041
0.044
0.049
0.053
0.058
0.062
0.066
0.065
0.071
0.077
0.083
0.089
0.081
0.089
0.096
0.104
0.111
16
17
18
19
20
0.024
0.025
0.027
0.028
0.030
0.047
0.050
0.053
0.056
0.059
0.071
0.075
0.080
0.084
0.089
0.095
0.100
0.106
0.112
0.118
21
22
23
24
25
0.031
0.033
0.034
0.035
0.037
0.062
0.065
0.068
0.071
0.074
0.093
0.097
0.102
0,106
0.111
26
27
28
29
30
0.038
0.040
0.041
0.043
0.044
0.077
0.080
0.083
0.085
0.088
0.115
0.119
0.124
0.128
0.133
400
0.012
0.024
0.037
0.048
0.060
450
0.014
0.027
0.040
0.054
0.067
500
0.015
0.030
0.045
0.060
0.075
0.063
0.073
0.083
0.094
0.104
0.072
0.083
0.095
0.107
0.112
0.081
0.094
0.107
0.121
0.134
0.090
0.105
0.119
0.134
0.149
0.098
0.107
0.116
0.124
0.133
0.114
0.125
0.135
0.145
0.156
0.131
0.143
0.155
0.166
0.178
0.147
0.161
0.174
0.188
0.201
0.164
0.179
0.194
0.209
0.224
0.118
0.126
0.133
0.140
0.148
0.142
0.151
0.160
0.169
0.178
0.166
0.176
0.187
0.197
0.208
0.190
0.202
0.214
0.226
0.238
0.214
0.228
0.241
0.254
0.268
0.238
0.253
0.268
0.283
0.298
0.124
0.130
0.136
0.142
0,148
0.155
0.163
0.170
0.177
0.185
0.187
0.195
0.204
0.213
0.222
0.218
0.228
0.239
0.249
0.259
0.249
0.261
0.273
0.285
0.297
0.281
0.294
0.308
0.321
0.335
0.313
0.328
0.343
0.357
0.372
0.153
0.159
0.165
0.171
0.177
0.192
0.199
0.207
0.214
0.222
0.231
0.240
0.249
0.257
0.266
0.270
0.280
0.290
0.301
0.311
0.309
0.321
0.332
0.344
0.356
0.348
0.361
0.375
0.388
0.401
0.387
0.402
0.417
0.432
0.447
150
REQUIRED PIPE WALL THICKNESS
FOR INTERNAL PRESSURE (cont.)
I.S.
DIAM
1
2
3
4
5
550
0.017
0.033
0.050
0.066
0.082
600
0.018
0.036
0.054
0.072
0.090
650
0.020
0.039
0.059
0.078
0.098
PRESSURE PSIG.
700
800
750
850
0.021 0.023 0.024 0.026
0.042 0.045 0.048 0.052
0.063 0.068 0.073 0.077
0.084 0.090 0.097 0.103
0.105 0.113 0.121 0.128
900
0.028
0.055
0.082
0.109
0.136
950
0.029
0.058
0.087
0.115
0.144
1,000
0.031
0.061
0.091
0.122
0.152
6
7
8
9
10
0.099
0.115
0.132
0.148
0.164
0.108
0.126
0.144
0.162
0.180
0.117
0.136
0.156
0.175
0.195
0.126
0.147
0.168
0.189
0.210
0.135
0.158
0.181
0.203
0.226
0.l45
0.l69
0.193
0.217
0.241
0.154
0.180
0.205
0.231
0.257
0.l63
0.191
0.218
0.245
0.272
0.173
0.201
0.230
0.259
0.288
0.182
0.212
0.243
0.273
0.303
11
12
13
14
15
0.181
0.197
0.214
0.230
0.246
0.197
0.215
0.233
0.251
0.269
0.214
0.234
0.253
0.273
0.292
0.231
0.252
0.273
0.294
0.315
0.248
0.271
0.293
0.316
0.338
0.265
0.289
0.313
0.337
0.361
0.282
0.301
0.333
0.359
0.385
0.299
0.326
0.354
0.381
0.408
0.316
0.345
0.374
0.403
'0.431
0.334
0.364
0.394
0.425
0.455
16
17
18
19
20
0.263
0.279
0.296
0.312
0.328
0.287
0.305
0.323
0.341
0.359
0.312
0.331
0.350
0.370
0.389
0.336
0.357
0.378
0.399
0.420
0.361
0.383
0.406
0.428
0.451
0.385
0.409
0.434
0.458
0.482
0.401
0.436
0.461
0.487
0.513
0.435
0.462
0.489
0.517
0.544
0.460
0.489
0.518
0.546
0.575
0.485
0.516
0.546
0.576
0.606
21
22
23
24
25
0.345
0.361
0.378
0.394
0.410
0,377
0.395
0.413
0.430
0.448
0.409
0.428
0.448
0.467
0.487
0.441
0.462
0.483
0.504
0.525
0.473
0.496
0.518
0.541
0.564
0.506
0.530
0.554
0.578
0.602
0.538
0.564
0.590
0.615
0.641
0.571
0.598
0.625
0.653
0.680
0.604
0.633
0.661
0.690
0.719
0.637
0.667
0.697
0.728
0.758
26
27
28
29
30
0.427
0.443
0.460
0.476
0.492
0.460
0.484
0.502
0.520
0.538
0.506
0.525
0.545
0.564
0.584
0.546
0.567
0.588
0.609
0.630
0.586
0.608
0.631
0.654
0.676
0.626
0.650
0.674
0.698
0.722
0.666
0.692
0.718
0.743
0.769
0.707
0.734
0.761
0.788
0.816
0.747
0.776
0.805
0.834
0.862
0.788
0.819
0.849
0.879
0.909
151
REQUIRED PIPE WALL THICKNESS
FOR INTERNAL PRESSURE (cont.)
I.S.
DIAM .
1
2
3
4
5
1,100
0.034
0.067
0.101
0.139
0.168
1,200
0.037
0.074
0.110
0.147
0.184
1,300
0.040
0.078
0.120
0.160
0.199
PRESSURE PSIG.
1,400 1,500 1,600 1,700
0.043 0.047 0.050 0.053
0.086 0.093 0.099 0.106
0.130 0.139 0.149 0.159
0.173 0.183 0.199 0.212
0.216 0.232 0.248 0.265
6
7
8
9
10
0.201
0.235
0.268
0.301
0.335
0.220
0.257
0.293
0.330
0.367
0.239
0.279
0.319
0.359
0.399
0.259
0.301
0.345
0.388
0.431
0.278
0.324
0.371
0.417
0.463
0.298
0.347
0.397
0.446
0.496
11
12
13
14
15
0.368
0.402
0.435
0.469
0.502
0.403
0.440
0.477
0.513
0.550
0.438
0.478
0.518
0.558
0.598
0.474
0.517
0.560
0.603
0.646
0.510
0.556
0.602
0.648
0.695
16
17
18
19
20
0.536
0.569
0.603
0.636
0.669
0.586
0.623
0.660
0.696
0.733
0.638
0.677
0.717
0.757
0.797
0.689
0.732
0.775
0.818
0.861
21
22
23
24
25
0.703
0.736
0.770
0.803
0.837
0.770
0.806
0.843
0.879
0.916
0.837
0.877
0.916
0.956
0.996
26
27
28
29
30
0.870
0.904
0.937
0.971
1.004
0.953
0.989
1.026
1.063
1.099
1.036
1.076
1.116
1.155
1.195
1,800
0.057
0.113
0.169
0.225
0.281
1,900
0.060
0.119
0.179
0.238
0.298
2,000
0.063
0.126
0.189
0.252
0.315
0.318
0.370
0.423
0.476
0.529
0.337
0.394
0.450
0.506
0.562
0.357
0.417
0.477
0.536
0.596
0.378
0.441
0.503
0.566
0.629
0.546
0.595
0.645
0.694
0.744
0.582
0.635
0.688
0.740
0.793
0.618
0.675
0.731
0.787
0.843
0.665
0.715
0.774
0.834
0.893
0.692
0.755
0.818
0.881
0.944
0.741
0.787
0.834
0.880
0.926
0.793
0.843
0.893
0.942
0.992
0.846
0.899
0.952
1.005
1.058
0.899
0.955
1.012
1.068
1.137
0.953
1.012
1.072
1.131
1.191
1.007
1.070
1.132
1.195
1.258
0.904
0.947
0.991
1.034
1.077
0.973
1.019
1.065
1.111
1.158
1.041
1.091
1.140
1.190
1.240
1.110
1.163
1.216
1.269
1.322
1.180
1.236
1.292
1.349
1.405
1.250
1.310
1.369
1.429
1.488
1.321
1.384
1.447
1.510
1.573
1.120
1.163
1.206
1.249
1.292
1.204
1.250
1.297
1.343
1.389
1.289
1.339
1.388
1.438
1.487
1.375
1.428
1.480
1.533
1.586
1.461
1.517
1.573
1.630
1.686
1.548
1.607
1.667
1.727
1.786
1.636
1.698
1.761
1.824
1.887
152
REQUIRED PIPE WALL THICKNESS
FOR INTERNAL PRESSURE (cont.)
LS.
PRESSURE PSIG.
DIAM 2,100 2,200 2,300 2,400 2,500 2,600 2,700 2,800 2,900 3,000
1
2
3
4
5
0.067
0.133
0.199
0.266
0.332
0.070
0.140
0.209
0.279
0.349
0.074
0.147
0.220
0.293
0.366
0.077
0.154
0.230
0.307
0.383
0.080
0.161
0.241
0.321
0.401
0.084
0.168
0.251
0.335
0.419
0.088
0.175
0.262
0.349
0.436
0.091
0.182
0.273
0.364
0.454
0.095
0.189
0.284
0.378
0.472
0.098
0.196
0.294
0.393
0.491
6
7
8
9
10
0.398
0.464
0.531
0.597
0.663
0.419
0.488
0.558
0.628
0.697
0.439
0.512
0.586
0.659
0.732
0.460
0.537
0.613
0.690
0.767
0.481
0.561
0.641
0.722
0.802
0.502
0.586
0.670
0.753
0.834
0.524
0.611
0.700
0.785
0.872
0.545
0.636
0.727
0.818
0.908
0.567
0.661
0.756
0.850
0.944
0.589
0.687
0.785
0.883
0.981
11
12
13
14
15
0.730
0.796
0.862
0.928
0.995
0.767
0.837
0.907
0.976
1.046
0.805
0.878
0.951
1.025
1.098
0.843
0.920
0.997
1.073
1.145
0.882
0.962
1.042
1.112
1.202
0.921
1.004
1.088
1.172
1.255
0.960
1.047
1.134
1.221
1.308
0.999
1.090
1.181
1.271
1.362
1.039
1.133
1.228
1.322
1.416
1.079
1.177
1.275
1.373
1.471
16
17
18
19
20
1.061
1.127
1.194
1.260
1.326
1.116
1.185
1.255
1.325
1.395
1.171
1.244
1.317
1.390
1.463
1.226
1.303
1.380
1.456
1.533
1.282
1.363
1.443
1.523
1.603
1.339
1.421
1.506
1.590
1.673
1.396
1.483
1.570
1.657
1.745
1.453
1.544
1.635
1.725
1.816
1.511
1.605
1.700
1.794
1.888
1.569
1.667
1.765
1.863
1.961
21
22
23
24
25
1.392
1.459
1.525
1.591
1.658
1.464
1.534
1.604
1.673
1.743
1.537
1.610
1.683
1.756
1.829
1.610
1.686
1.763
1.839
1.916
1.683
1.763
1.843
1.923
2.004
1.757
1.841
1.924
2.008
2.092
1.832
1.919
2.006
2.093
2.181
1.907
1.998
2.089
2.179
2.270
1.983
2.077
2.172
2.266
2.360
2.059
2.157
2.255
2.353
2.451
26
27
28
29
30
1.724
1.790
1.856
1.924
1.989
1.813
1.883
1.952
2.022
2.092
1.902
1.976
2.049
2.122
2.195
1.994
2.069
2.146
2.223
2.299
2.084
2.164
2.244
2.324
2.404
2.175
2.259
2.343
2.426
2.510
2.268
2.355
2.442
2.529
2.617
2.361
2.452
2.543
2.633
2.724
2.455
2.549
2.644
2.738
2.832
2.549
2.647
2.745
2.843
2.942
153
NOZZLE EXTERNAL FORCES AND MOMENTS IN
CYLINDRICAL VESSELS
Piping by the adjoining nozzles exert local stress in the vessel. The method, below, to determine
the nozzle loads is based in part on the Bulletin 107 of Welding Research Council and represents
a simplification of it. The vessels are not intended to serve as anchor points for the piping. To
avoid excessive loading in the vessel, the piping shall be adequately supported.
External Forces & Moments
To calculate the maximum force and moment, first evaluate p and y. Then determine
a, I, and L1 from Figures I, 2 and 3, for the specified p and y, substitute into the
equations below, and calculate F RRF, MRCM and MRLM.
P =.875 (~:)
y= Rm
T
Determine a, I and L1 from Figures I, 2 and 3.
Calculate Pressure Stress (oj.
If O'is greater than So, then use So as the stress due to design pressure.
M
III.M =
FRF
~
O~
__________
R,/r,,(.S
--..1-
Plot the value of F RRFas F RF and the smaller of MRCM and MRLM
as M RM. The allowable nozzle loads are bounded by the area
of F RF, 0, M RM.
~~
MRJo/
EXAMPLE: Determine Resultant Force and Moment
Rm=37.5
ro=15"
p=
T=.75"
P=150psi
.875E~:) = .875 b~~5)= .35
From Figure I, a. = 440
y- 0')
From Figure 2, I = 1,070
Sv=31,500psi@460°
S,,=20,000psi
y=
(Ri~ = 3.~; = 50
From Figure J, ..1 = 340
154
NOZZLE EXTERNAL FORCES AND MOMENTS
IN CYLINDRICAL VESSELS (continued)
Calculate Pressure Stress
f2}L 2C.1 50) (37.5
".,. = 2P(1)m--2
- .7 5)= 14850
,
pSI. < Sa = 20,000 psi.
r
75 ~
2
r
u
Use a = 14,850 in the equations for calculating FRRF and
Calculate Allowable Forces and Moments
_ R/I?
_ (3.75)2 "
_
FRRF--a (5v-0-)- 440
(-,1,500-14,850)-53,214Ib.
MRLM
37.5 2 (I5) (31,500)
1,070
620,984 in.-Ib.
0&
MRJ,(
= 620, 984 in-lb.
Plot for the value of FRRF' as FRF and the smaller of
M RCM and MRLM as M RM• The allowable nozzle loads
are bounded by the area of FRF , 0, M RM .
Therefore, a nozzle reaction of F = 20,000 lbs. and
M = 100,000 in. lbs. would be allowable (point A)
but a nozzle reaction of F = 5,000 Ibs. and M =
620,000* in. Ibs. would not be allowable (point B).
*Note: Use absolute values in the graph.
NOTATION:
P
=
ro
= Nozzle Outside Radius, inches
Rm
T
Sy
=
Mean Radius of Shell, inches
=
Shell Thickness, inches
=
Yield Strength of Material at Design
Temperature, pounds per square inch
MRCAF Maximum Resultant Circumferential
0'
=
Stress Due to Design Pressure, pounds
per square inch
MP.LJ..F Maximum Resultant Longitudinal Mo-
Sa
=
Stress Value of Shell Material, pounds
per square inch.
fJ
r
a
Design Pressure, pounds per sq. in.
=
Dimensionless Numbers
=
Dimensionless Numbers
I
=
L.1
= Dimensionless Numbers
FRRF
= Maximum Resultant Radial Force,
Dimensionless Numbers
pounds·
Momentm , inch-pounds*
ment, inch-pounds·
FRF
= Maximum Resultant Force, pounds·
FRM
=
Maximum Resultant Moment, inchpounds*
·Use absolute values.
= Dimensionless Numbers
REFERENCES:
Local Stresses in Spherical and Cylindrical Shells due to External Loadings, K. R.
Wichman, A. G. Hopper and 1. L. Mershon - Welding Research Council. Bulletin
107/August 1965 - Revised Printing - December 1968.
Standards for Closed Feedwater Heaters, Heat Exchange Institute, Inc., 1969.
155
NOZZLE LOADS
Fig.!
-
-
2
=l'Y=
I '''-,-,- 1-
"""-.,,, .~
k
,-~+
__ •
'0--'-
, I
2
- 'c'
·--t--H
f,+-
I-
.
:
".;:.'-'--'
N-
--:.: fT-T ,
c;~.
r---- f--'
' ,
10
0
.05
,I
.15
.2
.25
.3
.35
.4
.45
. 'Y I '
'
.5
,
I
156
NOZZLE LOADS
Fig 2
1
'1 • • • • • • • • •
2
4
2
!_-----
103
9
2
2
10
o
.05
.1
.15
.2
.25
.3
.35
.4
.45
.5
157
NOZZLE LOADS
Fig. 3
3
2
104
9
8
7
6
S
4
3
2
10]
9
lllllllllllllllllllllllllllllllllllllllllllll~!!~lIliiilii
2
102
9
8
7
6
3
2
10
o
.OS
.1
.IS
.2
.25
.3
.35
.4
{3
.45
.S
158
NOTES
159
REINFORCEMENT
AT THE JUNTION OF CONE TO CYLINDER
UNDER INTERNAL PRESSURE
At the junction of cone or conical section to cylinder (Fig. C and D) due
to bending and shear, discontinuity stresses are induced which are with
reinforcement to be compensated.
DESIGN PROCEDURE (The half apex angle
a 5'30 deg.)
1. Determine PISsEI and read the value of L1 from tables A and B.
2. Determine factor y, For reinforcing ring on shell, y = SsEs
For reinforcing ring on cone, y I Sc Ec
TABLE A - VALVES OF d FOR JUNCTIONS AT THE LARGE END
PISs, Ell 0.001 I 0.002 I 0.003 I 0.004 10.005 I 0.006 I 0.007 I 0.008 J 0.009*
d, deg., 11 I 15 I 18 I 21 I 23 I 25 I 27 I 28.5 I 30
TABLE B - VALVES OF d FOR JUNCTIONS AT THE LARGE END
PISs, EI /
/ 0.002 / 0.005 / 0.010 / 0.020 / 0.040 / 0.080 / 0.100 I 0.125*
d, deg.J
I 4 , 6 I 9 I 12.5 I 17.5 I 24 I 27 I 30
* /). = 30 deg. for greater value of PISs E/
When the value of Ll is less than a, reinforcement shall be provided.
3. Determine factor k = y I Sr Er (Use minimum 1.0 for k in formula).
4. Design size and location of reinforcing ring (see next page).
NOTATION
E = with subscripts s, c or r modulus of
elasticity of she 11, cone or reinforcing
ring material respectively, psi.
See charts beginning on page 43 for
modulus of elasticity.
E= with subscripts lor 2 efficiency of
welded joints in shell or cone
respectively.
For compression E=1.0 for butt
welds.
fi = axial load at large end due to wind,
dead load, etc. excluding pressure,
lb/in.
ji= axial load at small end due to wind,
dead load, etc. excluding pressure,
lb/in.
P= Design pressure, psi
QI=algebraic sum of PRL I2 andfi Ib/in.
Qs= algebraic sum of PRs/2 andji lb/in.
RL ~inside radius of large cylinder at large
end of cone, in.
Rs=inside radius of small cylinder at small
end of cone, in.
S= with subscripts s, cor r allowable stress
of shell, cone or reinforcing material,
psi.
t= minimum required thickness of cylinder at the junction, in.
ts= actual thickness of cylinder at the junction, in.
t7= minimum required thickness of cone
at the junction, in.
tc= actual thickness of cone at the junction,
in.
a,= half apex angle of cone or conical section, deg.
d= angle from table A or B, deg.
y = factor: Ss Es or Sc Ec
160
REINFORCEMENT
AT THE JUNCTION OF CONE TO CYLINDER
r::-r
FORMULAS
a
Max.
l~ ..... ~;
30°
JUNCTION AT THE LARGE END
Required area of reinforcement, A sq. in. when tension governs
(see notes)
e~
A
~
FIG. C
-
AeL
·· ,
\ -L I')
y,
=
(Is-I)
&;;; + (te-Ir) VRLte /
cos a
The distance from the junction within which the additional reinforcement shall be situated, in.
~
a
Max.
30°
FIG. 0
(l-~)tana
kQIfiL
SsE]
Area of excess metal for reinforcement, sq. in.
~
·
rL -
The distance from the junction within which the centroid of the
reinforcement shall be situated, in.
0.25 x .,JRLfs
JUNCTION AT THE SMALL END
Required area of reinforcement A sq. in. when tension governs (see notes)
Ars
=
~~~)
SsE! 1 a" tan a
Area of excess metal available for reinforcement A e, sq. in.
Aes = (t s / t) cos (a -~) (ts-t) VR:i: + (te / Ir)
X cos (a-~) (tc-tr)
VRslc / cos a
The distance from the junction within which the centroid of the reinforcement shall
be situated, in.
vR;i;
The distance from the junction within which the centroid of the reinforcement shall
be situated, in.
0.25 x vii;i;
NOTES: When atthe junction compressive loadsj; orji exceed the tensional loads determined by PR/
2 or PR)2 respectively, the design shall be in accordance with U2 (g): ("as safe as those provided by
the rules of the Code, Section VIII, Division 1.")
When the reducers made out of two or more conical sections of different apex angles without knuckle,
and when the half apex angle, a is greater than 30 deg., the design may be based on special analysis.
(Code 1-5 (f) & (g).
161
REINFORCEMENT
AT THE JUNCTION OF CONE TO CYLINDER
EXAMPLE
DESIGN DATA:
a
= 30 deg. half apex angle of cone.
E.EeEr= 30 X 106, modulus of elasticity, psi.
EJEl = 1.0, joint efficiency in shell and cone
EJ
= 0.55, joint efficiency in reinforcing ring
jj
= 800 lb/in, axial load at large end
h
P
RL
R.
S,
Sc
S,
t,
t"
te
tsl
RI .
-:\
~
tS5
trs
"
trL
952 lb/in, axial load at small end
50 psi., internal design pressure
= 100 in., inside radius of large cylinder
= 84 in., inside radius of small cylinder
= 15,700 psi., allowable stress of shell material
= 15,700 psi., allowable stress of cone material
= 17,100 psi., allowable stress of ring material
= 0.429 in., required min. thickness for large cylinder
= 0.360 in., required min. thickness for small cylinder
= 0.500 in. actual thickness of cone.
= 0.4375 in., actual thickness of large cylinder
= 0.375 in., actual thickness of small cylinder
= 0.41 in., required thickness of cone at small cylinder
= 0.49 in., required thickness of cone at large cylinder
=
=
Using the same material for shell and cone.
1. PISsE/ = 15,7t~ x 1 = 0.0032 from table A L1 = 18.6
Since L1 is less than a: reinforcements is required.
2. Using reinforcement ring on the shell
y= SsEs= 15,700 x 30 x 106
3. Factork=yISrEr = 15,700x30x 106 / 17,100x30x 106 =0.92
Use k= 1
4. QL =PRL/2ji , lb/in. = SO x 100 + 800 = 3,300 lb/in.
2
5. The required cross-sectional area of compression ring:
A = kQLRL
~ \tan a-I x 3,300 x 100 11}8.6)tan 300= 4.62 sq in.
rL
a]
15,700 x 1
~ 30
The area of excess in shell available for reinforcement:
AeL =(t,I.-tl.) fRlt'1- + ((-(,/)
vkLtc Icos a
= (0.4375 - 0.429) x ~100 x 0.4375 + (0.5 - 0.49) x ~100 x 0.5/cos 30°
= 0.132 sq. in.
ArL - AeL = 4.62 - 0.132 = 4.49 sq. in. the required cross sectional area of
compression ring
Using 1 in. thick bar, the width of ring: 4.55/1 = 4.55 in.
It _
sp;-. '\
Location of compression ring:
Maximum distance from the junction = vRJ; = ~100 x 0.4375 = 6.60 in.
Maximum distance of centroid from the junction = 0.25 vif;h =
0.25 ~1 00 x 0.4375 = 1.65 in.
162
REINFORCEMENT
AT THE JUNCTION OF CONE TO CYLINDER
EXAMPLE (continued)
JUNCTION AT SMALL CYLINDER
1.
PISs E/ = 0.0032; from table B ..1= 4.8 0
Since .1 is less than a., reinforcement is required.
2.
Factor y = Ss Es = 15,700 x 30 x 106
3.
Factor k = 1
4.
Qs = PR,/2 +1; lb.lin 50 ~ 84 + 952 = 3,052 lb.lin.
5.
The required cross-sectional area of compression ring~
.1) t
1 X 3,052 x 84~J W
300 -792
.
- kQ.Rs
A r'-SsE,
ana.
15,700 x I ~-30Jtan
-.
sq.m.
(1 -u-
The area of excess in shell available for reinforcement:
Aes =(t,/t,) cos (a -.1)(1,.,.-(,)
X
vn;;:+ (lei I,)
cos (a. -.1) (Ie - 1r.1) VR.lelcos
a
(0.375/0.36) x cos(3-4.8) x (0.375 - 0.36) x ~84 x .0375
+ (0.5/0.41) cos (30-4.8)x (0.5-0.41) x ..J84 x 0.5/cos 30°= 0.77 sq. in.
A". - A.s =7.92-0.77 = 7.15 sq. in., the required cross sectional area of com pression ring.
Using 1~ thick bar, the required width of the bar: 7.15/1.5 -= 4.8 in.
Location of the compression ring:
Maximum distance from the junction: vfii:.,= ..J84 x 0.375 = 5.6 in.
Maximum distance of centroid from the junction:
vR;t;,= ..J84 x 0.375 = 1.4 in.
0.25
Insulation ring may be utilized as compression ring provided it is continuous
and the ends of it are joined together.
Since the-moment of in tertia of the ring is not factor, the use of flat bar rolled
easy-way is more economical than the use of structural shapes.
To eliminate the necessity of additional reinforcement by using thicker plate for
the cylinders at the junction in some cases may be more advantageous than the
application of compression rings.
163
REINFORCEMENT
AT THE JUNCTION OF CONE TO CYLINDER
UNDER EXTERNAL PRESSURE
Reinforcement shall be provided at the junction of cone to
cylinder, or at the junction of the large end of conical
section to cylinder when cone, or conical section doesn't
have knuckles and the value of ~, obtained from table E,
is less than a.
TABLE E - VALUES OF A
P/SE
0
0.002 0.005 0.010 0.02
0.04 0.08
7
~, deg
0
15
21
5
10
29
P/SE 0.125 0.15 0.20 0.25 0.30 0.35
~, deg
37
40
47
52
57
60
ex = 60 deg. for greater values of P/SE
Note: Interpolation may be made for intennediate values.
0.10
33
The required moment of intertia and cross-sectional area
of reinforcing (stiffening) ring - when the half apex angle
a is equal to or less than 60 degrees - shall be determined
by the following formulas and procedure.
I. Determine P/Se, and read the value of t1 from table E.
2. Determine the equivalent area of cylinder, cone and stiffening ring, ATL , sq. in. (See page 48 for construction of stiffening ring.)
Make subscripts more visible
- LLts Lctc A
ATL --2-+-2-+
s
3[F~
D )
Calculate factor B. B = -
4
ATL
where
2
2
M = -RL tan a + LL + RL -R,I'
2
2
3RL tana
If FL is a negative number, the design shall be in accordance with U-2 (g).
3. From the applicable chart (pages 43 thru 47) read the value of A entering at the value of B. moving
to the left to the material/temperature line and from the intersecting point moving vertically to the
bottom of the chart.
For values of B falling below the left end of the materialltemperature line for the design temperature, the value of A = 2BI£.
If the value of B is falling above the materialltemperautre line for the design temperature: the cone
or cylinder configuration shall be changed, and/or the stiffening ring relocated, the axial compression stress reduced.
For values of B having multiple values of A, such as when 8 falls on a horizontal portion of the
curve, the smallest value of A shall be used.
4. Compute the value of the required moment of inertia
For the stiffening ring only:
2
I = ADL ATL
s
14.0
For the ring-shelkone section:
2
= ADL Au
Is
10.9
5. Select the type of stiffening ring and determine the available moment of inertia (see page 95) of the
ring only I. or the shell-cone or the ring-shell-cone section 1'.
164
REINFORCEMENT
AT THE JUNCTION OF CONE TO CYLINDER
(continued)
If lor l' is less than Is , or l's respectively, select stiffening ring with larger moment of inertia.
6. Determine the required cross-sectional area of reinforcement, A rL , sq. in.
(when compression governs):
A
= kQLRL tana
SE
rL
[1-
Y4(PR L - QL
QL
Ja~]
Area of excess metal available for reinforcement: AeL sq. in.:
AeL
= O.55~ DLts (ts + tc / cos a)
The distance from the junction within which the additional reinforcement shall be situated, in.
The distance from the junction within which the centroid of the reinforcement shall be situated, in.
-.--;:r-r
O.2SJRL t s
R,
'""-1-
Reinforcing shall be provided at the junction of small
end of conical section without flare to cylinder.
The required moment of inertia and cross-sectional area
of reinforcing (stiffening) ring shall be determined by
the following formulas and procedure.
1. Determine the equivalent area of cylinder, cone and
stiffening ring, A TS sq. in.
Lsts Lctc A
ATS =--+--+
s
2
2
2. Calculate factor B
B
r----
I /
t3J
VESSEL
VESSEL
WITHOUT
WITH
STIFFENING
STIFFENING
RING
RING
FIG. G
=~(FsDsJ
4 A
TS
I
where
F.~ = PN +~tan
N
a.
2
= Rs tana + Ls + LL -Rs
2
2
2
6Rs tan a
If Fs is a negative number, the design shall be in accordance with U-2 (g).
165
REINFORCEMENT
AT THE JUNCTION OF CONE TO CYLINDER
(continued)
3. From the applicable chart (pages 43 thru 47) read the value of A entering at the value of
B, moving to the left to the material/temperature line and from the intersecting point
moving vertically to the bottom of the chart.
For values of B falling below the left end of the material/temperature line for the design
temperature, the value of A = 2BIE.
If the value of B is falling above the material/temperature line for the design temperature: the cone or cylinder configuration shall be changed, and/or the stiffening ring relocated, the axial compression stress reduced.
For values of B having multiple values of A, such as wh n B falls on a horizontal portion of the curve, the smallest value of A shall be used.
4. Compute the value of the required moment of inertia:
For the stiffening ring only:
For the ring-shell-cone section:
2
l'
s
= ADs
= ADs
I
Ars
10.9
s
2
Ars
14.0
5. Select the type of stiffening ring and determine the available moment of inertia (see page
95) of the ring only, I and of the ring-shell-cone section, /'. If lor /' is less than ~\. or ~\.
respectively, select stiffening ring with larger moment of inertia.
6. Determine the required cross-sectional area of reinforcement. Ars ' sq. in:
= kQsRs tan a
A
SE
rs
Area of excess metal available for reinforcement, A e , sq. in.
Aes =
O.55~Dsts ~ts -t)+(tc -tr)/cosa]
The distance from the junction within which the additional reinforcement shall be situated,
in.
~Rsts
The distance from the junction within which the centroid of the reinforcement shall be situated, in.
0.25~Rsts
NOTE: When the reducers made out of two or more conical sections of different apex
angles without knuckle, and when the half apex angle is greater than 60 degrees, the design
may be based on special analysis. (Code 1-8 (d) and (e).)
NOTATION
A = area of excess metal available for
e
reinforcement, sq. in.
ArL = required area of reinforcement
when QL is in compression, sq.
in.
A = required area of reinforcement
TS
when QL is in compression, sq. in.
As = cross-sectional area of the stiffening
ring, sq. in.
AT = equivalent area of cylinder, cone and
stiffening ring, sq. in.
B = factor
D L = outside diameter or cone or large end
of conical section, in.
166
REINFORCEMENT
AT THE JUNCTION OF CONE TO CYLINDER
(continued)
Do
Ds
E
outside diameter ofcylindrical shell,
in.
outside diameter at small end of
conical section, in.
lowest efficiency of the longitudinaljoint in the shell, head or cone; E
= I for butt welds in compression.
E
with subscripts c, r or S modulus of
elasticity of cone, reinforcement or
shell material respectively, psi.
k
S~E./SRER
fi
h
I
I'
I,
I's
L
Le
LL
but not less than 1.0.
axial load at large end due to wind
etc., lb./in. The value offi shal1 be
taken as positive in all calculations.
axial load at small end due to wind,
etc. lb./in. The value ofh shall be
taken as positive in all calculations.
available moment of inertia of the
stiffening ring, in4
available moment ofinertia ofcornbined ring-shell cross-section, in4.
The width ofthe shell which is taken
as contributing to the moment ~f
inertia ofthe combined section:
I.IO--JD"t
required moment of inertia of the
stiffening ring, in4.
required moment of inertia of the
combined ring-shel1-cone crosssection, in4.
axial length of cone, in.
length ofcone along surface ofcone,
or distance between stiffening rings
of cone, in.
design length of a vessel section,
in/or stiffened vessel section: the
distance between the cone-to-Iarge
shell junction and an adjacent stiffening ring on the large shell.
for unstiffened vessel section: the
distance between the cone-to-Iarge-
Ls
P
QL
RL
Rs
S
SR
S,
te
tr
ts
a
~
shelljunction and one-third the depth
ofhead on the other end ofthe large
shell.
design length ofa vessel section, in.
for stiffonedvessel section: distance
between the cone-to-small-shell
junction and an adjacent stiffening
ring on the small shell.
for unstiffoned vessel section: distance between the cone-to-smallshelljunctionandonethirdthedepth
ofhead on the other end ofthe small
shell.
external design pressure, psi.
PRL
PRs
2+fi Q'=-2-+ h
axial compressive force due to pressure and axial load.
outside radius oflarge cylinder, in.
outside radius of small cylinder, in.
allowable working stress, psi. of
cone material.
allowable stress of reinforcing material, psi.
allowable stress of shell material,
psi.
minimum required thickness ofcylinder without allowance for
corosion, in.
actual thickness of cone without
corrosion allowance, in.
minimum required thickness ofcone
without corrosion allowance, in.
actual thickness of shell without
allowance for corrosion., in.
half apex angle, deg.
value to indicate need for reinforcement, from table E, deg.
167
REINFORCEMENT
AT THE JUNCTION OF CONE TO CYLINDER
EXAMPLE
DESIGN DATA
11"
t.
,II .
Design temperature = 500°F
SR
trL
trs
tc
t,
ts
DL = 96 in., outside diameter oflarge cylinder
Ds = 48 in., outside diameter of small cylinder
E = 0.7, efficiency oflongitudal weldedjoints
of shell and cone
Es' Ec' Er=30 X 106 ,modulus ofelasticity of
shell, cone, and ring material, psi.
fi = 100 Ib.in., axial load due to wind
.12 = 30 Ib./in., axial load due to wind
LL = 120 in., design length of large vessel
section
Ls = 244 in., design length of small vessel section
Lc = 48 in.
a = 30 deg., half apex angle of cone
P = 15 psi, external design pressure
RL = 48.00 in. outside radius oflarge cylinder
Rs = 24.00 in. outside radius of small cylinder
Ss = 17,100 psi. maximum allowable working
stress of shell and cone material.
15700 psi. maximum allowable working stress of reinforcement material.
0.25 in. minimum required thicknes of large cylinder.
= 0.1875 in. minimum required thickness of small cylinder.
0.25 in. actual thickness of cone.
= 0.25 in. minimum required thickness of cone.
0.25 in. actual thickness of cylinder.
JUNCTION AT THE LARGE END
1. P/SE = 15/17100 = 0.00088; from table E ~ = 2.2
since ~ is less than a., reinforcement is required.
2. Assuming As= 0, An = LLt/2+L ctcl2+As =
= 120xO.125+48xO.125+0=21 in 2.
48 2- 242
M=
RL tan a +!!:... + RL2 - R/ _
48 x 0.5774+ 120
T+
3
x
48 x 0.5774=66.9
2
2
3RL tan a
2
FL = PM + ji tan a. = 15 x 66.9 + 100 x 0.5774 = 1061
168
REINFORCEMENT
AT THE JUNCTION OF CONE TO CYLINDER
EXAMPLE (continued)
B=
J FD
4(:r)
= 0.75
X
1061 x 96/21 = 3636
TL
3.
A = 0.0003 from chart on page 42.
4.
Required moment of inertia of the combined ring-shell-cone cross section:
ADIAn
0.0003 x 96 2 x 21 _
. 4
I'.~= 10.9 =
10.9
- 5.32 Ifl.
5. Using two 2Y2 x Ih flat bars as shown, and the effective width of the shell:
1.10 x ..JDLI = 1.1 ..J96 x .025 = 5.389 in.,
The available moment of inertia: 5.365 in.4 (see page 95)
It is larger than the required moment of inertia. The stiffening is satisfactory.
6.
The required cross-sectional area of reinforcing:
6
k = S,rEr = 17100 x 30 x 10 = 1 09
S~R
15700 x 30 x 106
.
PR
15 x 48
QL= 2 I +/1
2 + 100=460
ArL
_ kQLRL tan a [,1 II (PRL - QL\ ~]
SE
l.! -/4
Q J 0L
s
= 1.09 x 460 x 48 x 0.5774 r. _ 0 25 (15 x 48 - 460)2.2]=
. 2
17100 x 0.7
l1! .
460
30
1.15 Ifl.
The cross-sectional area of the stiffening -ring is 2.5 in 2. It is larger than the
area required.
The reinforcing shall be situated within a distance from the junction:
..JRLts = ~48 x 0.25 = 3.46 in.
The centroid of the ring shall be within a distance from the junction:
0.25 ..JRLts = 0.25"48 x 0.25 = 0.86 in.
JUNCTION AT THE SMALL END
1.
The conical section having no flare, reinforcement shall be provided.
2.
Asuming A.I
= 0,
Ars = Lstsl2 + Lctcl2 + As =
244 X 0.25/2 + 48 XO.25/2 + 0 = 36.5 inf
N
Rs tan a LJ
RL2 - R.~
2 +2 + 6Rs tan a
24 x 0.5774
2
244
48 2 - 242
+ 2+ 6 x 24 x .5774
= 149.7 in.
169
REINFORCEMENT
AT THE JUNCTION OF CONE TO CYLINDER
EXAMPLE (continued)
F~=PN+ /2
tan a
= 15 x 149.7+30xO.5774=2263
B = 3 FsDs = 3/4(2263 x 48) = 2232
"4 ~
36.5
3. Since value of B falls below the left end of material/temperature line:
A= 2 BIE = 2 x 2232/30 X 106 = 0.00014
Required moment of inertia of the combined ring-shell-cone cross section:
l' = ADi Ars = 0.00014 x 48 2 x 36.5 = 1 08' 4
s
10.9
10.9
. m.
5. Using 2Y2 x Y2 flat bar, and the effective shell width:
4.
1.1 "48 x 0.25 = 3.81 in.
The available moment of inertia 1.67 in.4 (see page 95)
It is larger than the required moment of inertia; the stiffening is satisfactory.
6. The required area of reinforcing:
k
= 1.09
QI'=
A . = kQ,R" tan
S~E
T.I
a
P:~
+/2= 15
~ 24
+ 30 = 210 lb.lin.
= 1.09 x 210 x 24 x 0.5774 = 0.265 in. 2
17100 x 0.7
Area of excess metal available for reinforcement:
Ae
=
=~
R,dc (tc - t r) + "R,d.I· (1.1' - trs )
cos a
~2~~8~~5
(0.25 - 0.25) + "24 x 0.25 (0.25 - 0.1875) = 0.153 in. 2
A T.I· - Ae = 0.265 - 0.153 = 0.112 in. 2
The area of ring used for stiffening 1.25 in. 2 • It is larger than the required
area for reinforcement.
The reinforcing shall be situated within a distance from the junction:
-JR:i\= "24 x 0.25 = 2.44 in.
and the centroid ofthe ring shall be within a distance from the junction:
0.25 "R,II.I = 0.25 "24 x 0.25 = 0.61 in.
170
WELDING
OF PRESSURE VESSELS
There are several methods to make welded joints. In a particular case the choice
of a type from the numerous alternatives depend on:
1. The circumstances of welding
2. The requirements of the Code
3. The aspect of economy
1. THE CIRCUMSTANCES OF WELDING.
In many cases the accessibility of the joint determines the type of welding. In
a small diameter vessel (under 18 - 24 inches) from the inside, no manual
welding can be applied. Using backing strip it must remain in place. In larger
diameter vessels if a man way is not used, the last (closing) joint can be welded
from outside only. The type of welding may be determined also by the
equipment of the manufacturer.
2. CODE REQUIREMENTS.
Regarding the type of joint the Code establishes requirements based on service,
material and location of the welding. The welding processes that may be used
in the construction of vessels are also restricted by the Code as described in
paragraph UW-27.
The Code-regulations are tabulated on the following pages under the titles:
a. Types of Welded Joints
(Joints permitted by the Code, their efficiency and limitations of their
applications.) Table UW-12
b. Design of Welded Joints
(Types of Joints to be used for vessels in various services and under certain design conditions.) UW-2, UW-3
c. Examination of Welded Joints
The efficiency of joints depends only on the type of joint and on the degree of
examination and does not depend on the degree of examination of any other
joint. (Except as required by UW-ll(a)(5)
This rule of the 1989 edition of the Code eliminates the concept of collective
qualification of butt joints, the requirement of stress reduction.
3. THE ECONOMY OF WELDING.
If the two preceding factors allow free choice, then the aspect of economy
must be the deciding factor.
Some considerations concerning the economy of weldings:
V-edge preparation, which can be made by torch cutting, is always more economical than the use of J or U preparation.
171
Double V preparation requires only half the deposited weld metal required for
single V preparation.
Increasing the size of a fillet weld, its strength increases in direct proportion,
while the deposited weld metal increases with the square of its size.
Lower quality welding makes necessary the use of thicker plate for the vessel.
Whether using stronger welding and thinner plate or the opposite is more
economical, depends on the size of vessel, welding equipment, etc. This must
be decided in each particular case.
172
TYPES OF WELDED JOINTS
JOINT EFFICIENCY, E
TYPES
CODE VW-12
1
~
IIZZZI
2
tfI2J
~//~
For circumferential
~
joint only
When the Joint:
a.
Fully
Radiographed
b.
c.
Spot
Not
Examined
Examined
Butt joints as attained by
double-welding or by other
means which will obtain
the same quality of
deposited weld metal on
the inside and outside
weld surface.
Backing strip if used
shall be removed after
completion of weld.
1.00
0.85
0.70
Single-welded butt jomt
with backing stri p
which remains in
place after welding
0.90
0.80
0.65
Single-welded butt joint
without use of backing
strip
-
-
0.60
-
-
0.55
-
-
0.50
-
-
0.45
3
~
4
i\ ,~\\~
?/~
Double-full
fillet lap joint
5
~~!
Single-full fillet
lap joint
with plug welds
tm~
Single full fillet lap joint
without
plug welds
6
173
TYPES OF WELDED JOINTS
LIMITAnONS
IN APPLYING VARIOUS
WELD TYPES
NOTES
FOR TYPE 1: NONE
Joint Category: A, B, C, 0
FOR TYPE 2: NONE
Joint Category: A, B, C, 0
Except butt weld with one plate off-set
- for circumferential joints only.
FOR TYPE 3:
Joint Category: A, B, C
Circumferential joints only, not over 5/8
in. thick and not over 24 in. outside diameter.
FOR TYPE 4:
(a) Longitudinal joints not over 3/8 in.
thick.
Joint Category: A
(b) Circumferential joints not over 5/8 in.
thick.
Joint Category B,C
For C joints these limitations not applicable for bolted flange connections.
FOR TYPE 5:
(a) Circumferential joints for attachment
of heads not over 24 in. outside diameter
to shells not over ~ in. thick. Joints attaching hemispherical heads to shells are
excluded.
Joint Category B:
(b) Circumferential joints for the attachment to shells of jackets not over 5/8 in.
in nominal thickness where the distance
from the center of the plug weld to the
edge of the plate is not less than 1~ times
the diameter of the hole for the plug.
Joint Category: C
FOR TYPE 6:
(a) For the attachment of heads convex
to pressure to shells not over 5/8 in. required thickness, only with use of fillet
weld on inside of shell:
Joint Category: A, B
(b) For attachment of heads having pressure on either side, to shells not over 24
in. inside diameter and not over 'l4 required thickness with fillet weld on outside of flange only.
Joint Category: A, B
1. In this table are shown the types
of welded joints which are permitted by the Code in arc and gas
welding processes.
2. The shape of the edges to be
joined by butt-weld shall be such
as to permit complete fusion and
penetration.
3. Butt joints shall be free from
undercuts, overlaps and abrupt
ridges and valleys. To assure that
the weld-grooves are completely
filled, weld metal may be built up
as reinforcement. The thickness
of the reinforcement shall not
exceed the following thicknesses.
Plate thickness in. Maximum reinf. in.
up to III incl.
3/32
over- Y2 to I incl.
1/8
over 1
3/16
4. Before welding the second side of
a double welded butt joint, the
impurities of the first side welding shall be removed by chipping, grinding or melting out to
secure sound metal for complete
penetration and fusion. For submerged arc welding, chipping out
a groove in the crater is recommended.
5. The maximum allowable joint
efficiencies given in this table
are to be used in formulas, when
the joints made by arc or gas
welding processes.
6. Joint efficiency. E = I for butt joints
in compression.
174
DESIGN OF WELDED JOINTS
formed head
other than
hemispherical
WELDED JOINT LOCATIONS
To the joints under certain condition special requirements apply, which are the
same for joints designated by identical letters.
These special requirements, which are based on service, material, thickness and
other design conditions, are tabulated below.
DESIGN
CONDITION
JOINT TYPE
AND CATEGORY
I. The design is
based on joint
efficiency I. 0
or 0.9
(See design
conditions
listed below
when full
radiography
is
mandatory. )
UW-II
UW-12(d)
All category A and D butt
welds in vessel sections
and heads
All category B or C butt
welds (but not including
those in nozzles or
communicating chambers)
which intersects the
category A welds in vessel
sections or heads or
connect seamless vessel
sections or heads
Category A and B butt
welds in vessel sections
and heads shall be of Type
(I) or Type (2)
2. Full
radiographic
examination
is not
mandatory
UW-Il(b)
Type (I) or Type (2) butt
welded joints
RADIOGRAPHIC
EXAMINATION
JOINT
EFFICIENCY
POST WELD
HEAT
TREATMENT
Full
Spot
Type (I) Type (2)
1.0
0.9
Per Code
UCS·56
None
0.85
Joints Band C bUll welds in
nozzles and communicating
chambers that neither exceed
10 in. nom pipe size nor I 1/8 in
wall thickness do not require
Spot
0.80
any radiographic examination
except as required for ferritic
steel wit h tensile properties
enhanced by heat treatment
UHT-57
Type (I) Type (2)
0.85 0.80
Per Code
UCS-56
175
DESIGN OF WELDED JOINTS (CONT.)
DESIGN
CONDITION
JOINT TYPE
AND CATEGORY
Any type of welded
3. Full
radiographic joints.
examination
is not
manditory.
The vessel is
designed for
external
pressure
only.
UW-II(c)
Joints A shall be
Type No. (I)
UW-2(a)(I)(a)
4. Vessels
containing
lethal
substances.
UW-2(a)
Joints Band C butt
welds in nozzles and
communicating
chambers that neither exceed lain. in
nom. pipe size or 1'1,
in wall thickness do
not require any radiographic examination
except as required
for ferritic steel with
tensile properties enhanced by heat treatment UHT-57.
JOINT
RADIOGRAPHIC
EXAMINATION EFFICIENCY
None
Joints of category C for
the fabricated lap joint
stub ends UW2(a)(I)(c).
5. Vessels
Joints A shall be Type
operated
below -20°F No. (I) (except for
austenitic chromium
or impact
nickel stainless steel).
test is
required for
the material Joints B shall be Type
No. (1) or No. (2).
or weld
metal UW- UW-2(b)(1) and (2).
2(b)
Joints C full penetation
welds extending through
the entire section of the
joint UW-2(b)(3).
(I)
(2)
(3)
(4)
(5)
(6)
Full
Joints Band C shall be
Type No. (I) or
Type No. (2)
UW-2(a)(1)(b)
Joints D shall be full
penetration welds
extending through the
entire thickness of the
vessel or nozzle wall
UW-2(a)(1)(d).
Type
Type
Type
Type
Type
Type
0.70
0.65
0.60
0.55
0.50
0.45
1.0
1.0 Type (I)
0.9 Type (2)
All butt welded
joints in shell
and heads shall
be fully
radiographed
except
exchanger tubes
and exchangers
UW-2(a)(2) and
(3) and per
UW-II (a)(4)
Full
Spot
No
Type (I)
1.0
0.85
0.70
Type (2)
0.90
0.80
0.65
POST WELD
HEAT
TREATMENT
Per Code
USC-56
Vessels
fabricated of
carbon or low
allow steel
shall be post
weld heat
treated
UW-2(a)
Per Code
UCS-56
Joints D full penetration welds extending
through the entire
section at the joint
UW-2(b)(4).
6. Unfired
steam boilers
with design
pressure
exceeding 50
psi
See note above in
this column at
design condition 4:
Joints A shall be Type
No. (I).
Joints B shall be Type
No. (1) or No. (2)
UW-2(c)
All butt welded
joints in shell
heads shall be
fully radiographed except
under the
provisions of
UW-II(a)(4)
TTW_?((")
1.0
1.0 Type (I)
0.9 Type (2)
Vessels fabricated of carbon or low alloy steel shall
be post weld
heat treated
UW-2(c)
176
DESIGN OF WELDED JOINTS (CONT.)
DESIGN
CONDITION
JOINT TYPE
AND CATEGORY
JOINT
EFFICIENCY
POST WELD
HEAT
TREATMENT
Full
Spot
No
Type (I) Type (2)
1.0
0.90
0.85
0.80
0.70
0.65
When the thickness at welded
joints of carbon
steels (P-No. 1)
exceeds 5/8 in.
and all thicknesses for low
alloy steels
(other than PNo. I) post weld
heat treatment is
mandatory
Full
1.0 Type (I)
0.9 Type (2)
Per Code
UCS-56
1.0 Type (I)
0.9 Type (2)
Per Code
UCS-56
RADIOGRAPHIC
EXAMINATION
Joints A shall be type No.
(I)
7. Pressure vessels subject to
direct firing
Joints B shall be type No.
(I) or No. (2) when the
thickness exceeds 5/8 in.
No welded joints of type
(3) are permitted for either
A or B joints in any
thickness
UW-2(d)
All but welds UW-II(a)
(6)
8. Electroslag
welding
Full
9. Final closure
of vessels
10. Seamless
vessel
sections or
heads
UW-II(a)
(5) (b)
UW-12(d)
II.
Joints
completed
by pressure
UW-12(f)
Ultrasonic examination when the
construction
does not permit
radiographs
Any welds
UW-Il(a) (7)
Joints connecting vessel
sections and heads
Spot
1.0*
None
or when A or B
welds are type 3,
4, 5, 6
0.85*
Per Code
UCS-56
Not greater than
.80
Any Welds
EFFICIENCY (E) TO BE USED IN CALCULATIONS
OF SEAMLESS HEAD THICKNESS ASME Code UW-l2(d)
TYPE OF
HEAD
TYPE OF
JOINT
DEGREE OF EXAMINATION
OF HEAD TO SHELL JOINT
FULL
SPOT
NO
Hemi
spherical
NOl
1.00
0.85
0.70
N02
0.90
0.80
0.65
Others
ANY
*For calculation involving
circumferential stress or for
thickness of seamless head
1.00
0.85
177
EXAMINATION OF WELDED JOINTS
RADIOGRAPHIC EXAMINATION
Full radiography is mandatory of joints: (Code UW-11)
1. All butt welds in shells, heads, nozzles, communicating chambers of unfired
steam boilers having design pressures exceeding 50 psi and vessels containing
lethal substances.
2. All butt welds in vessels in which the least nominal thickness at the welded
joint exceeds:
1 1/4 in. of carbon steel and 1 1/2 in. of SA-240 stainless steel
Exemption: Categories Band C butt welds in nozzles and communicating
chambers that neither exceed 10 in pipe size nor 1 1/8 in. wall thickness do not
require radiographic examination in any of the above cases.
3. All category A and D butt welds in vessel sections and heads where the design
of the joint or part is based on joint efficiency: 1.0, or 0.9. (see preceding
pages: Design of Welding Joints).
4. All butt welds joined by electroslag welding and all electrogas welding with any
single pass greater than 1 1/2 in.
Spot radiography, as a minimum, is mandatory of
1. Category B or C welds which intersect the Category A butt welds in vessel
sections (including nozzles and communicating chambers above 10 in. pipe
size and 1 in. wall thickness) or connect seamless vessel sections or heads when
the design of Category A and D butt welds in vessel sections and heads based on
a joint efficiency of 1.0 or 0.9.
2. Spot radiography is optional of butt welded joints (Type 1 or 2) which are not
required to be fully radiographed. If spot radiography specified for the entire
vessel, radiographic examination is not required of Category B and C butt
welds in nozzles and communicating chambers.
No Radiography. No radiographic examination of welded jOints is required when
the vessel or vessel part is designed for external pressure only, or when the
design of joints based on no radiographic examination.
ULTRASONIC EXAMINATION
1. In ferritic materials electroslag welds and electrogas welds with any single
pass greater than 1 1/2 in. shall be ultrasonically examined throughout their
entire length.
2. In addition to the requirements of radiographic examination, all welds made by the
electron beam process or by the inertia and continuous drive friction
welding process shall be ultrasonically examined for their entire length.
3. Ultrasonic examination may be substituted for radiography for the final closure
seam if the construction of the vessel does not permit interpretable radiograph.
178
BUTT WELDED JOINTS
OF PLATES OF UNEQ UAL THICKNESSES
JOINING PLATES OF UNEQUAL THICKNESSES WITH BUTT WELD, THE THICKER
PLATE SHALL BE TAPERED IF THE DIFFERENCE IN THICKNESS IS MORE THAN 1/8
IN. OR ONE-FOURTH OF THE THINNER PLATE. CODE UW-9(c), UW-13.
THE LENGTH OF THE TAPERED TRANSITION SHALL BE MINIMUM 3 TIMES THE
OFFSET BETWEEN THE ADJACENT SURFACES. THE WELD MAY BE PARTLY OR
ENTIRELY IN THE TAPERED SECTION OR ADJACENT TO IT.
r~
l
+-: 7----+
y
I
I
t ~ 3y
Taper either inside or outside
of vessel
t -, 1. -I
Tangent Line Y
t.f]f'£~
Tangent Line
~
HEADS TO SHELLS
ATTACHMENT
,l ~ 3y Z z 1/2(ts-tW
The shell plate centerline may
be on either side of the head
plate centerline.
HEADS TO SHELLS
ATTACHMENT
J,
il:
3y
Z=..I/2 (th-ts)
When th exceeds ts" the minimum length of straight
flange is 3th. but need not exceed 1-112 in. except
when necessary to provide required length of taper.
When th is equal to or less than 1.25Is• the length of
straight flange shall be sufficient for any required
taper. The shell plate centerline may be on either side
of the head plate centerline.
179
APPLICATION OF WELDING SYMBOLS
WELD
MEANING OF SYMBO L
SYMBOL
/Y
dO
f I !
60°
~
l I J
'C7
i ~ ~
60°
t 2 t
r±!
f ¥ } t~
r:±;
D
60°
cff
&
rrJ
, ,
OJ]
~
~
"g"
a
.....
Yl"
I
~
'\"
j
>
1
I
S
~Yl
~
v( ,Y.
SYMBOL INDICATES SQUARE
GROOYE WELD ON ARROW
SIDE. ROOT GAP 1/8 IN.
SYMBOL INDICATES y.
GROOYE WELD WITH AN
ANGLE OF 60 DEGREES
ON ARROW SIDE
SYMBOL INDICATES Y·GROOYE
WELD WITH AN ANGLE OF 60
DEGREES ON ARROW SIDE AND
BEAD·TYPE BACK WELD ON
THE OTHER SIDE
SYMBOL INDICATES 1/2 IN.
Y·GROOYE WELD
SYMBOL INDICATES y.
GROOYE WELD ON ARROW
SIDE AND ON OTHER SIDE
WITH AN ANGLE OF 60 DEGREES
SYMBOL INDICATES y.
GROOYE WELD ON ARROW
SIDE AND ON OTHER SIDE
WITH A ROOT OPENING
OF 1/8 IN.
SYMBOL INDICATES PLUG
WELD OF 1/21N. DIAMETER
AND WITH AN ANGLE OF
60 DEGREES
SYMBOL INDICATES 1/4 IN.
FILLET WELD
180
APPLICATION OF WELDING SYMBOLS
WELD
MEANING OF SYMBOL
SYMBOL
~
b
~
[b
SYMBOL INDICATES 3/8 IN.
FILLET WELD ON ARROW SIDE
AND 1/4 IN. FILLET WELD ON
THE OTHER SIDE
SYMBOL INDICATES BEVEL
GROOVE WITH AN ANGLE OF
45 DEGREES, 3/8 FILLET WELD
ON ARROW SIDE AND BEAD
TYPE BACK WELD ON
OTHER SIDE
G
~
[b
Y4~
[b
J1
D=f~
~
~22r
~
f,
-
/7
~v.
-1
~Y:~
I W
'7"
I
La---1
t
~
I11III
~
t
~t>
I
1/ S
SYMBOL INDICATES 1/4 IN.
FILLET WELD ON ARROW
SIDE AND BEVEL GROOVE
WELD ON OTHER SIDE
GRIND FLUSH ON OTHER SIDE
SYMBOL INDICATES BEVEL
GROOVE WELD AND 3/8 FILLET
WELD ON ARROW SIDE, BEVEL
GROOVE AND 1/4 FILLET WELD
ON OTHER SIDE
SYMBOL INDICATES WELD
ALL AROUND 1/4 IN.
FILLET WELD
SYMBOL INDICATES 1/4 IN.
INTERMITTENT FILLET
WELDS EACH 31N. LONG
AND SPACED ON 6 IN.
CENTERS. FIELD
WELDED
SYMBOL INDICATES 1/4 IN.
INTERMITTENT FILLET WELD.
EACH 2 IN. LONG AND SPACED
ON '8 IN. CENTERS. THE
WELDS ARE STAGGERED.
SYMBOL INDICATES 1/4 IN.
FILLET WELD ON ARRDW
SIDE AND 3/8 FILLET WELD
ON OTHER SIDE
181
CODE RULES RELATED TO VARIOUS SERVICES
Service
Air
Brief extracts of Code requirements
Code
Paragraph
All pressure vessels for use with compressed air, except
as permitted otherwise in this paragraph shall be provided with suitable inspection opening.
UG-46(a)
Min. thickness
UG-16(b)(4)
3/32
in.
Flammable
and or
noxIOUS
gases and
liquids
Expanded connections shall not be used.
UG-43 (b)(f)
Lethal
substances
Butt welded joints in vessels to contain lethal substances shall be fully radiographed.
UW-2(a)
When fabricated of carbon or low allow steel shall
be post weld heat treated.
UW-2(a)
The joints of various categories shall conform to
paragraph UW-2.
Steel plates conforming to sppecifications SA-36,
SA-283 shall not be used.
USC-6(b)( 1)
Steam
Min. thickness
UG-16(b)(4)
Unfired
steam
boilers (1)
With design pressures exceeding 50 psi., the joints
of various categories shall conform to paragraph
UW-2.
Water (2)
3/32
in. shells and heads
Steel plates conforming to specifications SA-36, and
SA-283 shall not be used.
USC-6(b)(2)
Min. thickness 1f4 in. shells and heads.
UG-16(b)(3)
Minimum thickness
3/32
in. shells and heads.
UG-16(b)(4)
NOTES:
I
1.
Unfired steam boilers may also be constructed in accordance with the rules
of Code Section I. (Code V-leg)
2.
Vessels in water service excluded from the jurisdiction of the Code are listed
in U-l(c)(6) and (7).
182
CODE RULES RELATED TO
VARIOUS WALL THICKNESSES OF VESSEL
Wall Thickness, in.
~
2,4, IS
~
~6
2,4,5,6,
8,9, II,
12, 14
4,6,8,9
11,12,14
15
~
1;{6
7, 10, 13,
16,20
7, 10, 13,
16,20
7, 10, 13,
16,20
1 ;{6
l~
7, 13, 16,
17,20
7, 13, 16,
17, 20, 19,
22
%'2
;{6
2,4,15
2,3,4,5,
5,6,8,9, 6,8,9, II
II, 12, 14 12, 14, 15
Applicable
Notes
5,6,8,9,
11,12,14
Wall thickness, in.
Us
Applicable
Notes
7, 10, II,
12, 14, IS
7, 10, II,
12,14, IS
Wall Thickness, in.
1 !{6
lYs
Applicable
Notes
7, 13, 16,
17,20
7, 13, 16,
17,20
%
l~
~6
%
Y2
4,6,8,9 ,
7,8,9, II, 7,8,9, II,
11,12, .14
12, 14, IS 12, 14, IS
15
1~6
I
7, 10, 13,
16,20
7, 10, 13,
16,20
7, 10, 13,
16,20
1 ~6
1%
I%;
1~
& over
7, 13, 16,
17, 18,21
19, 20, 22
7, 13, 16,
17, 18,21
19,20,22
7, 13, 16,
17, 18,21
19,20,22
7, 13, 16,
17, 18, 19,
20,21
Ys
.
_.
Notes
(Brief Extracts of Code Requirements)
1. The minimum thickness of plate for welded construction shall be not UG-16 (b)
less than 1116.
The minimum thickness of shells and heads used in compressed air
UG-16 (b) (4)
service, steam service and water service shall be 3/32 in.
2. Manufacturers' marking shall be other than deep die stamping.
UG-77 (b)
3. In compressed air, steam and water service corrosion allowance not
less than 116 of the calculated plat-e thickness shall be provided.
UCS-2S
4. Single, welded openings up to 3 in. pipe size do not require
reinforcement.
UG-36 (c) (3)
S. The minimum thickness of shells and heads of unfired steam boilers
UG-16 (b) (S)
shall not be less than Y<I in.
6. Double full fillet lap joint for longitudinal welded joints is acceptable.
Table UW-12
7. Single, welded openings up to 2 in. pipe size do not require reinforceforcement.
UG-36 (c) (3)
8. Single full fillet lap joint with plug weld for attachment of heads not
over 24 in. outside diameter to shells, acceptable.
Table UW-12
9. Maximum thickness of reinforcement for butt weld 3/32 in.
UW-3S (a)
10. Maximum thickness of reinforcement for butt weld 118 in.
11. Single full fillet lap joint with plug welds for circumferential joint
acceptable.
UW-3S (a)
Table UW-12
183
CODE RULES RELATED TO VARIOUS WALL THICKNESSES OF VESSEL
(Continued)
Notes
(Brief Extracts of Code Requirements)
12. Single full fillet lap joints without plug welds acceptable for attachment of heads convex to pressure to shells.
Table UW-12
13. Welded joints of pres sure vessels subject to direct firing in category
B shall be type (1) or (2). Post weld heat treatment required.
UW-2 (d)
(I) (2)
14. Single welded butt joint without use of backing strip acceptable for
circumferential joints not over 24 in. outside diameter.
Table UW-12
15. Double full fillet lap joints for circumferential joint acceptable.
Table UW-12
16. Steel plates conforming to SA-36 and SA-283 shall not be used.
ueS-6 (b)(4)
17. The maximum thickness of reinforcement for but weld 31J 6 in.
UW-35 (a)
18. Butt welded joints in materials classified P-I shall be fully radiographed.
ueS-57
19. Post weld heat treatment ofP-1 materials is mandatory for all welded
connections and attachments.
Table ueS-56
20. Double welded butt joint or single welded butt joint with backing
strip shall be used for circumferential or longitudinal joints.
Table UW-12
21. Full radiographic examination of butt welded joints ofP-1 Grade 1,2,
and 3 materials is mandatory.
UW-II(a)(2)
22. Post weld heat treatment ofP-1 materials is not mandatory provided
that the material is pre-heated.
Table ueS-56
Note (2)(a)(b)
The governing thickness of pressure vessels and parts joined by
welding shall be determined by:
UW-JJ, UCS-57 for radiographing,
UCS-66 for impact testing
UW-lO, UW40(f), UCS-56,
UHA-32 for post weld heat treatment.
See page 185 for low temperature operation.
184
TANKS AND VESSELS
CONT AINING FLAMMABLE AND COMBUSTIBLE LIQUIDS
Excerpt from the Department of Labor Occupational Safety and Health
Standards (OSHA), Chapter XVII, Part 1910.106,
(Federal Register, July 1, 1985)
REGULATION
CLASSIFICATION
ATMOSPHERIC TANKS
Storage tank which has been
designed to operate at
pressures from atmospheric
through 0.5 psig.
Atmospheric tanks shall be built in accordance with acceptable good standards of
design.
Atmospheric tanks may be built in accordance with:
1. Underwriters' Laboratories, Inc. Standards
2. American Petroleum Institute Standards
No. 12A, No. 650, No. 12B, No. 120,
& No. 12F.
LOW PRESSURE TANKS
Low-Pressure tanks shall be built in accordance with acceptable standards of design.
Storage tank which has
been designed to operate
Low-Pressure tanks may be built in accordance with
at pressures above 0.5 psig.
1. American Petroleum Institute Standard
No. 620.
but not more than 15 psig.
2. ASME Code for Pressure Vessels, Section
VIII.
(These tanks are not within the jurisdiction
of the ASME Code Section VIII (U-ld) but
may be stamped with the Code U Symbol
U-lg)
PRESSURE VESSEL
Storage tank or vessel
which nas been designed
to operate at pressures
above 15 psig.
Pressure Vessels shall be built in accordance
with the ASME Code for Pressure Vessels,
Section VIII.
In addition to the regulations of the above mentioned standards and code, the
occupational safety and health standards contain rules concerning tanks and vessels
as follows:
1.
2.
3.
4.
5.
6.
7.
Definition of combustible and flammable liquids
Material of storage tanks
Location of tanks
Venting for tanks
Emergency relief venting
Drainage
Installation of tanks
185
LOW TEMPERATURE OPERATION
If a minimum design metal temperatureand thickness-combination of carbon and
low alloy steels is below the curves in
FIG UCS-66, impact testing is required.
~
140
120
0..
100
80
~
If the thickness at any welded joint exceeds 4
in. and the minimum design metal temperature is colder than 120°F. impact tested material shall be used.UCS-66(b).
I
g..
~
J
.VL-nr-
II
E-'
I, I
:
~ :~
Cl
§
:E
~
~
/
='
AH carbon and aHoy steels listed in the following pages and not shown below.
&
&
~~
/t"
1/~
-20
-40
-55_°60
f-~t\~COde.
_r-r-r-I\
\SA-5I5 Gr 60, SA-285 Gr A B
_ f-i\.\SA-516 Gr 65 70 if not normalized
VI""'"'
2~ JlL
1 _ _
c-
..L
b---"III /V
C
~
NOTE: In the Handbook the most commonly
used materials are listed. For others see ASME
A
:E
~
For stationary vessels, when the coincident
ratio in Fig. UCS-66.1 is less than one, this
Figure provides basis to use material without impact testing. UG-66(b)
SA-516 Gr 55 & 60 ifnot normalized.
V
L
SA-516 all grades if normalized.
-
-I- -t- -j- t::'t=-If--+i+-Im"'
l
""-pa""tc_t
....,~r-es_ti1""n....
g ..,.R_~-tu_i..,rer-d-t-......,
-80
I
0.394
:E
I
2
I
4
Nominal Thickness, in.
NO IMPACT TEST IS
REQUIRED:
For bolts:
FIG. UCS-66 IMPACT TEST CURVES
For nuts:
~
r----
~
\
----
-_.
l"-t
~
I
~
r-- - -
REDUCTION OF MINIMUM METAL
TEMPERATURE .
I
r---- r--
-~
--
---
SA-193 B7 to -55°F
SA-307 B to -20°F
SA-194 2H to -55°F
For I Y2 thick, SA-515 Gr 60 plate the minimum design temperature is from Fig. USC66 - 50°F.
1"-- ,.....
Rll":;~" ";lnOI "q~i;'~i; ~
/: ~ -50 to-ISO· F, at ratio
// ~:>V~~;f;~f;;i-~ /-~/)-//10:::/t;~d/'~~
EXAMPLE:
r~
1;;-
If the actual stress in tension from internal
pressure and other loads is 12,000 PSI, and
the maximum allowable stress of the material is 17,100 psi, the ratio:
12,000/17,100=0.7
Temperature, FO
and from FIG. USC 66.1 the reduction is
30°F. The minimum design temperature is:
50-30 = 200F.
FIG. UCS-66.1 REDUCTION OF
MINIMlJM MET AL TEMPERATURE
(Applicable joint efficiencies shall be included
in the calculation of stresses.)
Impact test is not mandatory for materials which satisfy all of the following:
I. the thickness of material listed in curve
A does not exceed Y2 in.
2. the thickness of material listed in curves
B. C and D does not exceed I in.
3. The vessel is hydrostatically tested.
4. the design temperature is not lower than
-20°F and not higher than 650°F.
5. thermal, mechanical shock loading or
cylindrical loading is not controlling design requirement.
20
40
60
80100120140
186
PROPERTIES OF MATERIALS
CARBON & ALLOW STEEL *
Form
Specifications
Nominal
Number
Number
Composition
SA-283
C
C
APPLICATION
Structural quality. For pressure vessel
may be used with limitations see note: 1
C
SA-285
C
Boilers for stationary service and other
pressure vessels.
C-Si
SA-515
(j)
For intermediate and higher temperature
C-Si
SA-515
65
For intermediate and higher temperature
C-Si
SA-515
70
For intermediate and higher temperature
C-Si
SA-516
55
For moderatee and lower temperature
service
C-Si
SA-516
(j)
For moderate and lower temperature
service
C-Mn-Si
SA-516
65
For moderate and lower temperature
service
C-Mn-Si
SA-516
70
For ~oderate and lower temperature
serVIce
C-Si
SA-234
WPB
'€
C-Mn-Si
SA-105
-
For ambient and higher temperature
ad
C-Si
SA-I8I
-
For general service
C-Mn-Si
SA-350
LFI
For low temperature service
C-Mn
SA-350
LF2
For low temperature service
C-Mn
SA-53
B
For general service
C-Mn
SA-106
B
For high temperature service
ICr-1I5 Mo SA-I93
B7
For high temperature service
Bolt 21;2 in. diam or less
C
SA-194
2H
For high temperature service nut
C
SA-307
B
C
SA-36
-
For general structural purposes
C
SA-36
-
For general structural pU!]Joses
II)
~
0::
OJ)
c:
w:
For moderate and elevated temperature
II)
OJ)
c:
ro
't:i:
II)
0..
0:
OJ)
..§
'0
co
....
ro
co
Machine bolt for general use
*Data of the most frequently used materials from ASME Code Section II and VIII.
187
PROPERTIES OF MATERIALS
CARBON & ALLOW STEEL *
(continued)
Form
Specification
Tensile
Strength
1,000 psi
Grade
p
Number
SA-283
C
1
55.0
30.0
2
SA-285
C
1
55.0
30.0
1,4
SA-515
(j)
1
60.0
32.0
1,4
SA-515
65
1
65.0
35.0
1,4
SA-515
70
1
70.0
38.0
1,4
SA-516
55
1
55.0
30.0
1,4
SA-516
(j)
1
60.0
32.0
1,4
SA-516
65
1
65.0
35.0
1,4
SA-516
70
1
70.0
38.0
1,4
SA-234
WPB
1
60.0
35.0
1,3
1
70.0
36.0
1,4
Number
Yield Point
1,000 psi
See
Notes
<lJ
~
0::
O/J
c::
'13
SA-105
~
SA-I8I
I
1
60.0
30.0
1,4
SA-350
LFI
1
60.0
30.0
1,4
SA-350
LF2
1
70.0
36.0
1,3
SA-53
B
1
60.0
35.0
1,3
SA-106
B
1
60.0
35.0
1,3
SA-193
B7
-
125.0_
105.0
SA-194
2H
-
SA-307
B
-
~
<lJ
O/J
c::
G:'"
Seamless
Pipe
O/J
.§
"0
co
.....
co'"
Diam.':;::2Yz in.
5
55.0
-
-
60.0
-
-
SA-36
1
58.0
1
SA-36
1
36.0
1,3
188
PROPERTIES OF MATERIALS
CARBON & LOW ALLOY STEEL
(continued)
NOTES
1.
Upon prolonged exposure to temperatures above 800 0 F, the carbide phase of
carbon steel may be converted to graphite.
2.
SA-36 and SA-283 ABeD plate may be used for pressure parts in pressure
vessels provided all of the following requirements are met: UCS-6 (b)
(l) The vessels are not used to contain lethal substances, either liquid or
gaseous;
(2) The material is not used in the construction of unfired steam boilers (sec
Code U-l (g);
(3) With the exception of flanges, flat bolted covers, and stiffening rings the
thicckness of plates on which strength welding is applies does not exceed
5/8 in.
3.
Allowable stresses for temperatures of 700 0 F and above are values obtained
from time-dependent properties.
4.
Allowable stresses for temperatures of 750 0 F and above are values obtained
from time-dependent properties.
5.
Stress values in bearing shall be 1.60 times the values in tables.
MODULI OF ELASTICITY FOR FERROUS MATERIALS
Materials
-100
Carbon steels with
C < 0.30%
Carbon steels with
C> 0.30%
70
29.5
200
28.8
30.2
29.3
30.0
28.6
Million psi, for Temperature of. of:
400
500
600
700
800
27.3
25.5
27.7
24.2
26.7
28.1
27.1
25.3
27.5
26.5
24.0
300
28.3
900
22.4
1000
20.4
22.3
20.2
The values in the External Pressure Charts are intended for external pressure calculations only.
189
PROPERTIES OF lVIATERIALS
CARBON & LOW ALLOY STEEL
Maximum Allowable Stress Values in Tension 1000 psi."
Specitication
Numbcr Grade
-20
400
500
For l'.letal Temperature Not Exceedin~ De~. F.
650
750
850
600
700
800
950
900
SA-283
C
15.7
15.7
15.3
14.8
-
-
-
-
-
SA-285
C
15.7
15.7
15.3
14.8
14.3
13.0
10.8
8.7
5.9
SA-SIS
60
17.1
17.1
16.4
15.8
15.3
13.0
10.8
8.7
SA-SIS
65
18.6
18.6
17.9
17.3
16.7
13.9
11.4
SA-SIS
70
20.0
20.0
19.4
18.8
18.1
14.8
SA-516
55
15.7
15.7
15.3
14.8
14.3
SA-516
60
17.1
17.1
16.4
15.8
SA-516
65
18.6
IR.6
17.9
5A-516
70
20.0
20.0
SA-234
WPB
17.1
SA-lOS
-
SA-181
I
SA-350
1000
-
-
5.9
4.0
2.S
8.7
5.9
4.0
2.5
12.0
9.3
6.7
4.0
2.5
13.0
10.8
8.7
5.9
4.0
2.5
15.3
13.0
10.8
8.7
5.9
4.0
2.5
17.3
16.7
13.9
11.4
8.7
5.9
4.0
2.5
19.4
18.8
18.1
14.8
12.0
9.3
6.7
4.0
2.5
17.1
. 17.1
17.1
15.6
13.0
10.8
8.7
5.9
4.0. 2.5
20.0
19.6
18.4
17.8
17.2
14.8
12.0
9.3
6.7
4.0
2.5
17.1
16.3
15.3
14.8
14.3
13.0
10.8
8.7
5.9
4.0
2.5
LFI
17.1 .
16.3
15.3
14.8
14.3
13.0
10.8
8.7
5.9
4.0
2.5
SA-350
LF2
20.0
19.6
18.4
17.8
17.2
14.8
12.0
9.3
6.7
4.0
2.5
SA-53
B
17.1
17.1
17.1
17.1
15.6
13.0
10.8
8.7
5.9
-
-
SA-lOG
B
17.1
17.1
17.1
17.1
15.6
13.0
10.8
8.7
5.9
4.0
2.5
SA-193
B7:S;2W'
25.0
25.0
25.0
25.0 -
25.0
23.6
21.0
17.0 12.5
8.5
4.5
SA-194
2H
SA-307
B
SA-36
-
15.2
15.2
15.2
15.2
-
-
-
-
-
-
-
SI\-36
-
16.6
16.6
16.6
16.6
15.6
130
10.8
8.7
5.9
-
-
I
---.--+--~-1·-·---- -_._- ..
1"--
--. ----.--- f-.--_.........--....·.-...·· ..
r- '" The
Stre~s
.!
: - - - - f-.
-_.
Values in this table may be intcrpolated to detennin'e values for intennediate temperatures._
The value~ shown in bold obtained from time-dependentpl'Ope/'/ies.
J
!
l
L_~..J..-· _L~..,.. r
L ..__+-...-.J.~,,,~
The stress values shown in this table are used throughout tIllS book.
Pressure Vessel Handbook - 12th Edition
190
PROPERTIES OF MATERIALS
STAINLESS STEEL
P-No. 8 Group No. 1
TABLE 1
Product
o~
~~
Z
00
r;)
0
~
til
Smls. Pp.
SA·312
TP304H
-
;:....~
Smls. Pp.
SA·376
TP304
2
U
TP304H
F304
-
Forg.
SA·376
SA·182
'D
Forg.
Bar
SA·182
SA-479
F304H
-
304
23
~
SA·240
SA·213
316
TP316
23
2
Smls. Th.
SA·213
TP316H
-
SA·312
SA·312
TP316
2
til
Smls. Pp.
Smls. Pp.
TP316H
-
;:....~
Smls. Pp.
SA·376
TP316
2
Smls. Pp.
Forg.
SA·376
SA·182
TP316H
-
~
I
-Z
2
F316
2
Forg.
SA·182
SA-479
F316H
316
-
23
Spec. No.
Grade
Notes
SA·240
SA-213
316L
TP316L
TP316L
-
o~
]~
2
0...
Notes
Z
-
Smls. Pp.
Grade
~~
TP304
1=1
Spec. No.
I
N
TP304H
d
~~
E=
Product
0
SA·213
.5
0
23
2
SA·312
.2:!
Z
Notes
304
TP304
Smls. Pp.
.
U "oc;::
-
Grade
SA·240
SA·213
Smls. Th.
til
~..I<i
00
Spec. No.
Plate
Smls. Th.
~
.-
I
TABLE 3
.
"oc;::
~
-
.2:!
1=1
.5
d
~~
0
E=
r;)
0
0
Plate
Smls. Th.
Bar
0...
U
~
TABLE 2
.....:I
<t:
Z
Product
~
Spec. No.
Grade
Notes
""'0
Nt-"0 til
Z
"01=1
">=~
SA·240
SA-213
Smls. Pp.
SA·312
304L
TP304H
TP304L
Bar
SA·479
304L
Plate
Smls. Th.
25
-
-
~
0
Z
-
Product
.....:I
<t:
00
0
TABLE 4
0
u
00
""'0
Nt-"0 til
"01=1
">=~
Plate
Smls. Th.
Smls. Pp.
Bar
SA·312
SA-479
-
316L
-
MAXIMUM ALLOWABLE STRESS VALUES, 1,000 psi.
FOR METAL TEMPERATURES NOT EXCEEDING DEG. OF.
MATERIALS
IN TABLE
1
2
3
4
-20-100 200
20.0
20.0
20.0
16.7
16.7
16.7
16.7
14.3
20.0
20.0
20.0
17.3
16.7
16.7
16.7
14.2
MATERIALS
IN TABLE
I
3
950
1000
14.3
10.6
15.4
11.4
14.0
lOA
15.3
11.3
300
18.9
IS.0
16.7
12.8
20.0
15.6
16.7
12.7
400
800
18.3
15.2
11.2
500
600
650
700
750
IS.8
15.5
17.5
16.6
16.2
11.7
12.9
12.3
12.0
11.5
13.8
14.7
14.0
13.7
13.5
13.3
15.8
10.2
10.9
10.4
10.0
9.8
11.7
17.0
16.3
18.0
16.6
16.1
19.3
12.6
12.1
11.9
14.3
13.3
12.3
14.8
14.0
13.5
13.2
15.1
13.7
10.9
10.2
10.0
9.8
11.7
10.4
FOR METAL TEMPERATURES NOT EXCEEDING
1300 1350
1050 1100
11 SO
1200
12S0
12.4
10.1
15.1
11.2
9.8
9.8
12.4
11.1
7.7
7.7
9.8
9.8
6.1
6.1
7.4
7.4
4.7
4.7
5.5
5.5
3.7
3.7
4.1
4.1
2.9
2.9
3.1
3.1
850
14.9
900
14.6
11.0
10.8
13.0
-
-
9.7
15.9
11.8
-
-
12.9
9.6
Note!
I
I
15.7
11.6
IS.6
11.5
I
12.7
-
1
9.4
DEG. OF.
1400
14S0
1500
2.3
2.3
2.3
2.3
1.8
1.8
1.7
1.7
1.4
1.4
1.3
1.3
I
I
NOTES:
1. These higher stress values exceed 2/3 but do not exceed 90% of the yield strength at temperature. Use 0
these stress values may result in dimensional changes due to permanent strain. These stress values are
not recommended for flanges or gasketed joints or other applications where slight amounts of distortion
can cause leakage or malfunction.
2. At temperatures above 1,000° F, these stress values apply only when the carbon is 0.04% or higher.
3. For temperatures above 1,000° F, these stress values may be used only if the material is heat treated by
heating it to a minimum temperature of 1,900° F and quenching in water or rapidly cooling by other
means.
191
THERMAL EXPANSION
Linear Thermal Expansion between 70F and Im:licated Temperature, Inches/IOO Feet
THE DATA OF THIS TABLE ARE TAKEN FROM THE AMERICAN STANDARD CODE
FOR PRESSURE PIPING. IT IS NOT TO BE IMPLIED THAT MATERIALS ARE SUITABLE
FOR ALL THE TEMPERATURES SHOWN IN THE TABLE.
MATERIAL
Carbon Steel
Austenitic
remp. Carbon·Moly 5CrMo Stainl_
thru
IegF Low·Chrome
St..ls
Ithru 3 Cr Mol 9 CrMo 18 Cr 8 Ni
-325
-2.37
-2.22
-3.85
-300
-2.24
-2.10
-3.63
-275
-2.11
-1.98
-3.41
-250
-1.98
-1.86
-3.19
-225
-1:85
-1.74
-2.96
-200
-1.71
-1.62
-2.73
-175
-1.58
-1.50
-2.50
-150
-1.45
-1.37
-2.27
-125
-1.30
-1.23
-2.01
-LIS
-100
-1.08
-1.75
-t.OO
-0.94
-1.50
- 75
-0.84
-0.79
-1.24
- 50
-0.98
-0.68
-0.63
- 25
-0.49
-0.46
-0.72
0
-0.32
-0.46
25
-0.30
-0.14
-0.13
50
-0.21
70
0
0
0
0.22
100
0.23
0.34
125
0.42
0.40
0.62
0.61
0.58
150
0.90
175
1.18
0.76
0.80
1.46
0.99
0.94
200
1.75
1.21
1.13
225
1.40
250
1.33
2.03
275
1.61
2.32
1.52
2.61
300
1.82
1.71
325
2.04
2.90
1.90
350
2.26
2.10
3.20
375
2.48
2.30
3.50
400
2.70
2.50
3.80
4.10
425
2.93
2.72
2.93
4.41
450
3.16
4.71
3.14
475
3.39
3.62
3.35
5.01
500
3.86
3.58
5.31
525
550
4.11
3.80
5.62
4.35
4.02
5.93
575
4.60
4.24
6.24
600
4.86
4.47
6.55
625
4.69
6.87
5.11
650
4.92
7.18
675
5.37
7.50
5.63
S.14
700
5.38
7.82
725
5.90
8.15
750
6.16
5.62
775
6.43
5.86
8.47
8.80
6.70
6.10
800
9.13
6.34
6.97
825
6.59
9.46
7.25
850
6.83
875
9.79
7.53
7.07
10.n
900
7.81
7.31
10.46
925
8.08
7.56
10.80
8.35
950
7.81
11.14
975
8.62
8.06
11.48
1000
8.89
11.82
9.17
8.30
1025
n.16
1050
9.46
8.55
12.50
9.75
8.80
1075
12.84
10.04
9.05
1100
13.18
9.28
10.31
1125
13.52
9.52
10.57
I ISO
9.76
13.86
10.83
1175
14.20
11.10
10.00
1200
14.54
10.26
1225
11.38
10.53
14.88
11.66
1250
15.22
11.94
10.79
1275
11.06
15.56
17.22
1300
15.90
12.50
11.30
1325
16.24
n.78
11.55
1350
11.80
16.58
13.06
1375
n.05
16.92
13.34
1400
17.30
1425
17.69
1450
18.08
1475
18.47
1500
12Cr
nCr
27Cr
-2.04
-1.92
-1.80
-1.68
-1.57
-1.46
-1.35
-1.24
-1.11
-0.98
-0.85
-0.72
-0.57
-0.42
-0.27
-0.12
0
0.20
0.36
0.53
0.69
0.86
1.03
1.21
1.38
1.56
1.74
1.93
2.11
2.30
2.50
2.69
2.89
3.08
3.28
3.49
3.69
3.90
4.10
4.31
4.52
4.73
4.94
5.16
5.38
5.60
5.82
6.05
6.27
6.49
6.71
6.94
7.17
7.40
7.62
7.95
8.18
8.31
8.53
8.76
8.98
9.20
9.42
9.65
9.88.
10.11
10.33
10.56
10.78
11.01
25 Cr
20Ni
0
0.32
0.58
0.84
1.10
1.37
1.64
1.91
2.18
2.45
2.72
2.99
3.26
3.53
3.80
4.07
4.34
4.61
4.88
5.15
5.42
5.69
5.96
6.23
6.50
6.77
7.04
7.31
7.58
7.85
8.15
8.45
8.75
9.05
9.35
9.65
9.95
10.25
10.55
10.85
11.15
11.45
11.78
n.ll
12.44
12.77
13 ..10
13.43
13.76
14.09
14.39
14.69
14.99
15.29
Monel
67 Ni 30Cu
-2.62
-2.50
-2.38
-2.26
-2.14
2.02
-1.90
-1.79
-1.59
-1.38
-1.18
-0.98
-0.77
-0.57
-0.37
-0.20
0
0.28
0.52
0.75
0.99
1.22
1.46
1.71
1.96
2.21
2.44
2.68
2.91
3.25
3.52
3.79
4.06
4.33
4.61
4.90
5.18
5.46
5.75
6.05
6.34
6.64
6.94
7.25
7.55
7.85
8.16
8.48
8.80
9.n
9.44
9.77
10.09
10.42
10.75
11.09
11.43
11.77
12.11
n.47
12.81
13.15
13.50
13.86
14.22
14.58
14.94
15.30
15.66
16.02
3~
Nickel Aluminum
-2.25
-2.17
-2.07
-1.96
-1.86
-1.76
-1.62
-1.48
-1.33
-1.17
-1.01
-0.84
-0.67
-0.50
-0.32
-0.15
0
0.23
0.42
0.61
0.81
1.01
1.21
1.42
1.63
1.84
2.05
2.26
2.47
2.69
2.91
3.13
3.35
3.58
3.81
4.04
4.27
4.50
4.74
4.98
5.22
5.46
5.70
5.94
6.18
6.43
6.68
6.93
7.18
7.43
7.68
7.93
8.17
8.41
-4.68
-4.46
-4.21
-3.97
-3.71
-3.44
-3.16
-2.88
-2.57
-2.27
-1.97
-1.67
-1.32
-0.97
-0.63
-0.28
0
0.46
0.85
1.23
1.62
2.00
2.41
2.83
3.24
3.67
4.09
4.52
4.95
5.39
5.83
6.28
6.72
7.17
7.63
8.10
8.56
9.03
Gray
Bronze
ClISt Iron
0
0.21
0.38
0.5~
0.73
6.90
1.08
1.27
1.45
1.64
1.83
2.01
2.2
2.4
2.62
2.83
3.03
3.24
3.46
3.67
3.89
4.11
4.34
4.57
4.80
5.03
5.26
5.50
5.74
5.98
6.22
6.47
6.72
6.97
7.23
7.50
7.76
8.02
-3.98
-3.74
-3.50
-3.26
-3.02
-2.78
-2.54
-2.31
-2.06
-1.81
-1.56
-1.32
-1.25
-0.77
-0.49
-0.22
0
0.36
0.66
0.96
1.26
1.56
1.86
2.17
2.48
2.79
3.11
3.42
3.74
4.05
4.37
4.69
5.01
5.33
5.65
5.98
6.31
6.64
6.96
7.29
7.62
7.95
8.28
8.62
8.96
9.30
9.64
9.99
10.33
10.68
11.02
11.37
11.71
12.05
12.40
12.76
13.11
13.47
192
DESCRIPTION OF MATERIALS
When describing various vessel components and parts on drawings and in bill of
materials, it is advisable that a standard method be followed. For this purpose
it is recommended the use of the widely accepted abbreviations in the sequences
exemplified below. For ordering material the requirements of manufacturers
should be observed.
PART
DESCRIPTION
MATERIAL
SPECIFICATION
~
BAR
Bar 2 x 1/4 x 3' - 6
Bar 3/4 ¢ x 2 '- 0
Bar 1 cp x 3'- 0
[J::a
BOLT
3/4 ¢ x 2-1/2 H. Hd. M. B. w/ (1) sq. nut SA-193 B7 bolt
1 f/J x 5-1/2 stud w/ (2) h. nuts
SA-194 2H nut
0
CAP
8" Std. Cap
ICJ
Screwed
COUPLING
I" - 6000 #
2" - 3000 #
1" - 6000 #
1" - 6000 #
~
Welding
ELBOW
6" - Std. 90 0 L. R. Ell.
4" - X Stg. 45 0 S. R. Ell.
6" x 4" Std. L. R. Red. Eli
SA-234 WPB
FLANGE
4" - 300# RF. So. Fig.
6" - 150# RF. Wn. Fig. Std. Bore
6" - 600# RTJ. Wn. FIg. X Stg. Bore
3" - 150# FF. So. FIg.
8" - 150# R.F. Bid. FIg.
SA-181 1
Screwed
Socket
Welding
FORGED
FITTING
1" - 6000 # 90 0 Scr'd. Ell.
1" - 3000 # 90 0 Scr'd. Street Ell.
2" - 3000 # S.W. Cplg.
1" - 3000# Sq. Hd. Plug
2" - 6000 # Scr'd. Tee
2" - 3000 # 45 0 S. W. Ell.
SA-lOS
GASKET
18 - 150 # 1/16" Servo Sht. Gasket
18 - 300 # Spiral Wound ASB. Filled
ASB.
HEAD
48" ID x 0.375 min. 2: 1 eHip. head
2" S.F.
48" OD x 0.500" min. ASME F & D
Head 2 S.F. L =48" r = 3"
54" ID x 0.375" min. Hemis. Head
@
• •
~
(JJ
~
©
8
Cplg.
Cplg.
Half Cplg.
4-1/2 Lg. Cplg.
SA-7
SA-lOS
SA-285 C
SA-515-70
SA-516-70
193
DESCRIPTION OF MATERIALS (cont.)
Long
[p Welding
Neck
18" - 300
RF. LWN
SA-181 1
PIPE
6" - Std. Pipe x 2'-1
8" -X Stg. Pipe x l' - 6-1/2
4" - S. 160 Pipe x 2'-4
24" - 0.438" Wall Pipe xl' - 0
SA-53 B
cJ
PLATE
It 96" x 3/8 x 12' - 6
It24"ODx 1/2x 18"ID
1l18" OD x 1-1/2
SA-285 C
[::J
Welding
REDUCER
6" x 4" Std. Conc. Reducer
8" x 6" X Stg. Ecc. Reducer
SA-234 WPB
~
Welding
RETURN
6" - Std. 1800 L. R. Return
4" - X Stg. 1800 S. R. Return
SA-234 WPB
0
Welding
TEE
4" - Std. Tee
6" x 6" x 4" X Stg. Red. Tee
SA-234 WPB
~
\0
+;:..
EQUIVALENT & COMPARABLE MATERIALS OF FOREIGN COUNTRIES
European Standard
U.S.A.
Germany
United Kingdom
Japan
SA285 Gr. B
P235 GH
HI
161 Gr400
SB410
SA 515 Gr60
SA 515 Gr70
SA 299
SA204Gr A
SA 387 Gr 12 Class 2
SA 387 Gr 22 Class 2
SA 516 Gr60
SA516Gr70
SA 572 Gr65
P265 GH
P295 GH
P355 GH
16 Mo3
13 CrMo4-5
10 Cr Mo 9-10
P275NH
P355NH
P460NH
HII
17 Mn4
161 Gr430
224 Gr340
225 Gr490
SB480
SPY 315
SPV356
SB480M
SCMV2Div.2
SCMV4Div.4
SA 240 - 410 S
X6Cr 13
X6 Cr Al13
X5 CrNi 18-10
X2 Cr N i 19-11
X5CrNiMo 17-12-2
X2CrNiMo 17-12-2
X2 CrNi Mo 18-15-4
SA 240 - 405
SA 240 - 304
SA240- 304 L
SA 240 - 316
SA 240 - 316 L
SA 240 - 317 L
19Mn6
15 Mo3
13 CrMo 44
10 CrMo 910
WStE285
,WStE 355
WStE460
-
630 Gr27
620 Gr 31
164 Gr 400, Lt 20
225 Gr 490, Lt. 20
SGV450
-
-
-
1.4000
1.4002
1.4301
1.4306
1.4401
403 S 17
405 S 17
304 S 31
304 S 11
316S31
410 S
405
304
304L
316
1.4404
1.4438
316S11
316L
317 L
-
CODES, STANDARDS, SPECIFICATIONS
EN 10028-2,
AS ME Code II.
-_.
_ _ .-
_1 0028=-~,1 0088
DIN 17 102,
17155,17440
BS 1501,4360,
970, 1442
JIS G 3103,3115,4109,
3118,4304 sus
I
195
SPECIFICATION
FOR THE DESIGN AND FABRICATION OF PRESSURE VESSELS
NOTES:
Pressure vessel users and manufacturers have developed certain standard practices
which have proven advantageous in the design and construction of pressure vessels. This
specification includes those practices which have become the most widely accepted and
followed.
These standards are partly references to the selected alternatives permitted by the
ASME Code, and partly described design and construction methods not covered by the
Code. The regulations of the Code are not quoted in this Specification.
AGENERAL
1. This Specification, together with the purchase order and drawings, covers the requirements for the design and fabrication of pressure vessels.
2. In case of conflicts, the purchase order and drawings take precedence over this
Specification.
3. Pressure vessels shall be designed, fabricated, inspected and stamped in accordance with the latest edition ofthe ASME Boiler and Pressure Vessel Code, Section
VIII, Division 1, and its subsequent addenda.
4. Vessels and vessel appurtenances shall comply with the regulations of the Occupational Safety and Health Act (OSHA).
5. Vessel Manufacturers are invited to quote prices on alternate materials and construction methods if economics or other aspects make it reasonable to do so.
6. All deviations from this Specification, the purchase order, or the drawings shall have
the written approval of the purchaser.
7. Vessel fabricator, after receipt of purchase order, shall furnish to purchaser checked
shop drawings for approval.
B. DESIGN
1. Pressure Vessels shall be designed to withstand the loadings exerted by internal or
external pressure, weight of the vessel, wind, earthquake, reaction of supports, impact, and temperature.
2. The maximum allowable working pressure shall be limited by the shell or head, not
by minor parts.
3. Wind load and earthquake. All vessels shall be designed to be free-standing. To
determine the magnitude of wind pressure, the probability of earthquakes and seismic coefficients in various areas of the United States, Standard ANSIIASCE 7-95
(Minimum Design Loads in Buildings and Other Structures) shall be applied.
It is assumed that wind and earthquake loads do not occur simultaneously, thus the
vessel should be designed for either wind or earthquake loading, whichever is greater.
4. Horizontal vessels supported by saddles shall be designed according to the method
of L. P. Zick (Stresses in Large Horizontal Pressure Vessels on Two Saddle Supports).
5. The deflection of vertical vessels under normal operating conditions shall not exceed 6 inches per 100 feet oflength.
196
Specification for the Design and Fabrication of Pressure Vessels (continued)
6. Stresses in skirts, saddles, or other supports and their attachment welds may exceed
the maximum allowable stress values of materials given in Part UCS of the ASME
Code by 33-1/3 percent.
7. Vessel manufacturers shall submit designs for approval when purchaser does not
furnish a design or does not specify the required plate thickness.
c. FABRICATIUN
1. Materials shall be specified by purchaser and their designation indicated on the
shop drawings. Materials shall not be substituted for those specified without prior
written approval of purchaser.
2. The thickness of plate used for shell and heads shall be 1/4-inch minimum.
3. Manufacturer's welding procedure and qualification records shall be submitted for
approval upon receipt of purchase order. Welding shall not be performed prior
to purchaser's approval of welding procedure and qualification.
All welding shall be done by the metallic shielded arc or the submerged arc
welding process.
Permanently installed backing strips shall not be used without written approval of
purchaser. When used, backing strips shall be the same composition steel as that
which they are attached to.
4. Longitudinal seams in cylindrical or conical shells, all seams in spherical shells and
built-up heads shall be located to clear openings, their reinforcing pads, and saddlewear plates. Circumferential seams of shell shall be located to clear openings,
their reinforcing pads, tray and insulation support rings, and saddle wear plates.
When the covering of circumferential seam by reinforcing pad is unavoidable, the
seam shall be ground flush and examined prior to welding the reinforcing pad
in place.
No longitudinal joints shall be allowed within the downcomer area or at any other
place where proper visual inspection of the weld is impossible.
The minimum size of fillet weld serving as strength weld for internals shall be
1/4 inch.
5. Skirt. Vertical vessels shall be provided with a skirt which shall have an outside
diameter equal to the outside diameter of the supported vessel .. The minimum
thickness for a skirt shall be 1/4 inch.
Skirts shall be provided with a minimum of two 2-inch vent holes located as high
as possible 180 degrees apart.
Skirts 4 feet in diameter and less shall have one access opening; larger than 4-foot
diameter skirts shall have two I8-inch 0.0. access openings reinforced with sleeves.
6. Base rings shall be designed for an allowable bearing pressure on concrete of 625 psi.
7. Anchor bolt chairs or lug rings shall be used where required and in all cases where
vessel height exceeds 60 feet. The number of anchor bolts shall be in multiples
of 4; a minimum of 8 is preferred.
8. Saddle. Horizontal vessels shall be supported by saddles, preferably by only two
whenever possible.
Saddles shall be welded to the vessel, except when specifically ordered to be
shipped loose. Saddles to be shipped loose shall be fitted to the vessel and matchmarked for field installation. The shop drawing shall bear detailed instruction
concerning this.
197
Specification for the Design and Fabrication of Pressure Vessels (continued)
When temperature expansion will cause more thao 3/8 inch change in the distance
between the saddles, a slide bearing plate shall be used. Where the vessel is
supported by concrete saddles 1/4 inch thick, corrosion plate 2 inches wider than
the concrete saddle shall be welded to the shell with a continuous weld. The
corrosion plate shall be provided with a 1/4 inch vent hole plugged with plastic
sealant after the vessel has been pressure tested.
9. Openings of 2 inches and smaller shall be 6000 lb forged steel full or half
coupling.
Openings 2-1/2 inches and larger shall be flanged.
Flanges shall conform to Standard ANSI BI6.5-1973.
Flange faces shall be as follows:
Raised face.
below rating 600 lb ANSI
Raised face.
rating 600 lb ANSI, pipe size 3 inches and smaller
Ring type joint.
rating 600 lb ANSI, pipe size 4 inches and larger
Ring type joint.
above rating 600 lb ANSI.
Flange-bolt-holes shall straddle the principal centerlines of the vessel. Openings
shall be flush with inside of vessel when used as drains or when located so that
there would be interference with vessel internals. Internal edges of openings shall
be rounded to a minimum radius of 1/8 inch or to a radius equal to one-half of the
pipe wall thickness when it is less than 1/4 inch.
When the inside diameter of the nozzle neck and the welding neck flange or
welding fitting differ by 1/16 inch or more, the part of smaller diameter shall be
tapered at a ratio 1:4.
Openings shall be reinforced for new and cold, as well as for corroded condition.
The plate used for reinforcing pad shall be the same composition steel as that used
for the shell or head to which it is connected.
Reinforcing pads shall be provided with a" 1/4 inch tapped tell-tale hole located at
90° off the longitudinal axis of vessel.
The minimum outside diameter of the reinforcing pad shall be 4 inches plus the
outside diameter of the opening's neck.
When covers are to be provided for openings according to the purchaser's requisition, manufacturer shall furnish the required gaskets and studs; these shall not be
used for testing the vessel.
Manway covers shall be provided with davits.
Coupling threads must be clean and free from defects after installation.
10. Internals. Trays shall be furnished by tray fabricator and installed by vessel
manufacturer. Tray support rings and downcomer bolting bars shall be furnished
and installed by vessel manufacturer. The tray fabricator shall submit complete
shop details, including installation instructions and packing list, to purchaser for
approval and transmittal to vessel fabricator.
Trays shall be designed for a uniform live load ·of 10 psf or the weight of water
setting, whibhever is greater, and for a concentrated live load of 250 lb.
At the design loading the maximum deflection of trays shall not exceed
up to 10-foot diameter - 1/8 inch
larger than 10-foot diameter - 3/16 inch
198
Specification for the Design and Fabrication of Pressure Vessels (continued)
The minimum thickness of internal plateworks and support rings shall not be less
than 1/4 inch.
Internal carbon steel piping shall be standard weight.
Internal flanges shall be ANSI 150-lb slip-on type or fabricated from plate.
Carbon steel internal flanges shall be fastened with carbon steel square-head
machine bolts and square nuts tack-welded to the flanges to avoid loosening.
Removable internals shall be made in sections which can be removed through
the manways.
Removable internals shall not be provided with corrosion allowance. For openings
connected to pump suction, a vortex breaker shall be provided.
11. Appurtenances. Vessels provided with manways, liquid level controls or relief
valves 12 feet above grade, shall be equipped with caged ladders and platforms.
Ladder and platform lugs shall be shop-welded to the vessel. Where vertical vessels
require insulation, fabricator shall furnish and install support rings. Reinforcing
rings may also be utilized in supporting insulation.
Insulation support rings shall be 1/2 inch less in width than the thickness of
insulation and spaced 12 foot-I/2 inch clear starting at the top tangent line. The
top ring shall be continuously welded to the head; all other rings may be attached
by a I-inch long fillet weld on 12-inch centers. The bottom head of insulated
vertical vessel shall be equipped with I/2-inch square nuts welded with their edges
to the outside of the head on approximately 12-inch square centers.
12. Fabrication tolerances shall not exceed the limits indicated in the table beginning on
page 200.
D. INSPECTION
1. Purchaser reserves the right to inspect the vessel at any time during fabrication to
assure that the vessel materials and the workmanship are in accordance with this
specification.
.
2. The approval of any work by the purchaser's representative and his release of a
vessel shall not relieve the manufacturer of any responsibility for carrying out the
provisions of this specification.
E. MISCELLANEOUS
1. Radiographic examination shall be performed when required by the ASME Code
or when determined by the economics of design.
2. The completed vessel shall be provided with a name plate securely attached to the
vessel by welding.
3. If the vessel is post-weld heat-treated, no welding is permitted after stress relieving.
4. Removable internals shall be installed after stress relieving.
5. The location of all vessel components openings, seams, internals, etc., of the vessel
shall be indicated on the shop drawings by the distance to a common reference
line. The reference line shall be permanently marked on the shell.
6. The hydrostatic test pressure shall be maintained for an adequate time to permit
a thorough inspection, in any case not less than 30 minutes.
7. Vessels shall not be painted unless specifically stated on order.
199
Specification for the Design and Fabrication of Pressure Vessels (continued)
F. PREPARATION FOR SHIPMENT
1. After final hydrostatic test, vessel shall be dried and cleaned thoroughly inside and
outside to remove grease, loose scale, rust and dirt.
2. All finished surfaces which are not protected by blind flanges shall be coated with
rust preventative.
3. All flanged openings which are not provided with covers shall be protected by
suitable steel plates.
4. Threaded openings shall be plugged.
5. For internal parts, suitable supports shall be provided to avoid damage during
shipment.
6. Bolts and nuts shall be coated with waterproof lubricant.
7. Vessels shall be clearly identified by painting the order and item n urn ber in a
conspicuous location on the vessel.
8. Small parts which are to be shipped loose shall be bagged or boxed and marked
with the order and item number of the vessel.
9. Vessel fabricator shall take all necessary precautions in loading by blocking and
bracing the vessel and furnishing all necessary material to prevent damages.
G. FINAL REPORTS
1. Before the vessel is ready for shipment the manufacturer shall furnish purchaser
copies or reproducible transparency each of the following reports:
a. Manufacturer's data report.
b. Shop dra wings showing the vessel and dimensions "as built".
c. Photostatic copies of recording charts showing pressure during hydrostatic test.
d. Photostatic copies of recording charts showing temperature during post-weld
heat treatment.
e. Rubbing of name plate.
H. GUARANTEE
Manufacturer guarantees that the vessel fulfills all conditions as stated in this
Specification and that it is free from fault in design, workmanship and materiaL
Should any defect develop during the first year of operation, the manufacturer agrees
to make all necessary alterations, repairs and replacements free of charge.
200
VESSEL FABRICATION TOLERANCES
The dimensional tolerances in this table - unless otherwise noted - are based on
practice widely followed by users and manufacturers of pressure vessels.
All tolerances are inches, unless otherwise indicated.
Tolerances not listed in this table shall be held within a practical limit.
Base Ring
a. Flatness
b. Out of level
+ 1/16
+ 1/8
Clips, Brackets
c. Distance to the reference line
+
1/4
d. Deviation circumferentially measured
+ 1/4
at the joint of structure
+
Distance between two adjacent clips.
1/16
Manway
e. Distance from the face of flange or
centerline of man way to reference line,
vessel support lug, bottom of saddle,
centerline of vessel, whichever is
+ 1/2
applicable
f. Deviation circumferentially measured
+ 1/2
on the outer surface of vessel
g. Projection; shortest distance from
outside surface of vessel to the face
of manway
+ 1/2
h. Deviation from horizontal, vertical
or the intended position in any
direction.
+ 10
i. Deviation of bolt holes in any
direction.
Nozzle, Coupling which are not to be
connected to piping.
....
_...'
+ 1/4
The tolerances for manways shall be
applied.
Nozzle, Coupling which are to be
connected to piping.
Distance from the face of flange or
centerline of opening to reference line,
vessel support lug, bottom of saddle,
centerline of vessel, whichever is
+ 1/4
applicable.
f. Deviation circumferentially measured
+ 1/4
on the outer surface of vessel
g. Projection; shortest distance from
outside surface of vessel to the face
of opening.
+ 1/4
201
VESSEL FABRICATION TOLERANCES
(continued)
Nozzles, (continued)
~
ill:=:::l
~11Fl
h
h. Deviation from horizontal, vertical or
the intended position in any
direction. . . . . . . . . . . .
+ 1/2 0
i. Deviation of bolt holes in any
direction. . . . . . . . . . . .
+ 1/8
Nozzles, Couplings used for level gage,
level control, etc.
Distance between centerline of
openings . . . . . . . . . . . .
+ 1/16
Saddle
k. Distance centerline of boltholes to
reference line . . .'. . . . . . . .
k. Distance centerline of boltholes to
centerline of shell . . . . . . . . .
+ 1/8
::t 1/8
l. Distance between bolt holes in base
plate or between boltholes or slots of
::t 1/8
two saddles. . . . . . . . .
m. Transverse tilt of base plate . .
::t 1/32
n. Longitudinal tilt of base plate.
::t 1/8
per Ft.
Shell
O.
Deviation from verticallity for vessels
of up to 30 ft overaU length . . . . . ::t 1/2
for vessels of over 30 ft overall length
±
1/8
per 10ft.
max. 1-1/2
p. Vessels for internal pressure. The difference
between the maximum and minimum inside
diameters at any cross section shall not exceed
one percent of the nominal diameter at the
cross section. . . . . . . . . . . . . ± 1%
Omax -
0min = p
Deviation from nominal inside diameter
as determined by strapping . .
::t 1/32
per Ft.
Out of roundness Code UG-80
External pressure. See Code UG-80
Formed Heads, Code UG-81
Tray Installation
r. Out of level in any direction.
::t 1/32
per Ft.
Tray Support
r. Out of level in any direction.
::t 1/32
per Ft.
202
VESSEL FABRICATION TOLERANCES
( continued)
Tray Support (continued)
'L~
wH
x
1F4
-+4-
s. Distance between adjacent tray
supports . . . . . . . . .
v. Distance to downcomer support.
+
+
+
+
w. Tilt for any width of support ring.
+ 1/16
t. Distance to reference line . . .
s. Distance to seal pan . . . . . .
1/8
1/4
1/8
1/8
Weir Plate
y. Height . . .
+ 1/16
+ 1/8
z. Distance to inside of vessel wall
:t 1/4
x. Out of level
203
API Specification for
SHOP WELDED TANKS
Summary of Major Requirements of API. Standard 12F, Eleventh Edition 1994
SCOPE - This Specification covers material, design, fabrication and testing requirements for vertical, cylindrical, above-ground, shop fabricated, welded, steel
storage tanks for oilfield service in standard sizes as tabulated below.
A
MATERIAL
Plates shall conform to the following ASTM Standards:
A26, A283, C or D, and A285 C.
MINIMUM PLATE TIllCKNESS
Shell and deck: 3/16 in., Bottom: l;4 in., Sump:
15-6 diam Deck: l;4 in.
n
B
c
3fs in.
CONSTRUCTION
The bottom of the tank shall be flat or conical; the latter
may be skirted or unskirted. Fig. A, B, C. The deck shall be
conical. The slope of the bottom and deck cone = 1: 12.
WELDING
Bottom shell and deck plate joints shall be double-welded
butt joints with complete penetration. Fig. D. The bottom
and the deck shall be attached to the shell by doublewelded butt joint or 3/16 in filet welds, both inside and outside. Fig. E through K.
OPENINGS
Tanks shall be furnished with 24 in. x 36 in. extended neck
cleanout. API Std. 12F Fig. 4.
D
TESTING
The tank will be tested with air 1Yz times the maximum design pressure.
PAINTING
One coat Primer.
TANK DIMENSIONS
Nominal
Capacity
bbl.
90
100
IS 0
200
210
250
300
400
500
500
750
Tolerance
Working
Capacity
bbl.
72
79
129
166
200
224
266
366
466
479
746
-
Outside
Diameter
ft. in.
Height
ft.
7-11
9- 6
9- 6
12- 0
10- 0
11- 0
12- 0
12- 0
12- 0
15- 6
15- 6
10
12
10
15
15
15
20
25
16
24
±l/g in.
±3/8 in.
8
204
WELDED STEEL TANKS FOR OIL STORAGE
API. Standard 650, Ninth Edition, 1993
APPENDIX A - OPTIONAL DESIGN BASIS FOR SMALL TANKS
(Summary of major requirements)
SCOPE
This appendix provides rules for relatively small capacity, field-erected tanks in
which the stressed components are limited to a maximum of~ inch nominal thickness, including any corrosion allowance specified by the purchaser.
MATERIALS
The most commonly used plate materials of those permitted by this standard:
A 283 C, A 285 C, A 36, A 516-55, A 516-60
The plate materials shall be limited to
~
thickness.
WELDED JOINTS
The type of joints at various locations shall be:
Vertical Joints in Shell
Butt joints with complete penetration and complete fusion as attained by double
welding or by other means, which will obtain the same quality of joint.
Horizontal Joints in Shell
Complete penetration and complete fusion butt weld.
Bottom Plates
Single-welded, full-fillet lap joint, or single-welded butt joint with backing strip.
Roof Plates
Single-welded, full-fillet lap joint. Roofplates shall be welded to the top angle of
the tank with continuous fillet weld on the top side only.
Shell to Bottom Plate Joint
Continuous fillet weld laid on each side of the shell plate. The size of each weld
shall be the thickness of the thinner plate.
The bottom plates shall project at least 1 inch width beyond the outside edge of
the weld attaching the bottom to shell plate.
INSPECTION
Butt Welds
Inspection for quality of welds shall be made by the radiographic method. By
agreement between purchaser and manufacturer, the spot radiography may be
deleted.
Fillet Welds
Inspection of fillet welds shall be made by visual inspection.
205
WELDED STEEL TANKS FOR OIL STORAGE
API. Standard 650, Ninth Edition, 1993
TESTING
Bottom Welds
1.
Air pressure or vacuum shall be applied using soapsuds, linseed oil, or other
suitable material for detection of leaks, or
2.
After attachment of at least the lowest shell course, water shall be pumped
underneath the bottom and a head of 6 inches shall be maintained inside a
temporary dam.
Tank Shell
1.
The tank shall be filled with water, or
2.
Painting all joints on the inside with highly penetrating oil, and examining
outside for leakage.
3.
Applying vacuum.
Appendix A -
Optional Design Basis for Small Tanks
Appendix B -
Recommendations for Design and Construction of Foundations
for Above Ground Oil Storage Tanks
Appendix C -
External Floating Roofs
Appendix D -
Technical Inquiries
Appendix E -
Seismic Design of Storage Tanks
Appendix F -
Design of Tanks for Small Internal Pressures
Appendix G -
Structurally Supported Aluminum Dome Roofs
Appendix H -
Internal Floating Roofs
Appendix I -
Undertank Leak Detection and Subgrade Protection
Appendix J -
Shop-Assembled Storage Tanks
Appendix K -
Sample Application of the Variable-Design-Point Method
to Determine Shell-Plate Thickness
Appendix L -
API Standard 650 Storage Tank Data Sheets
Apprndix M -
Requirements for Tanks Operating at Elevated Temperatures
Appendix N -
Use of New Materials That Are Not Identified
Appendix 0 -
Recommendations for Under-Bottom Connections
Appendix P -
Allowable External Loads on Tank Shell Openings
Appendix S -
Austenitic Stainless Steel Storage Tanks
206
WELDED STEEL TANKS API. Standard 650-APPENDIX A
FORMULAS
NOTATION
CA. = corrosion allowance, in.
D = nominal diameter of tank, ft.
E = joint efficiency, 0.85 when
spot radiographed 0.70
when not radiographed
0 = specific gravity of liquid to
be stored, but in no case
less than 1.0
H = design liquid level, ft.
t = minimum required plate
thickness, in.
R = radius of curvature of roof, ft.
= angle of cone elements with
horizontal, deg.
e
(2.6) (D) (H-O (0) + C.A.
(E) (21,000)
but in no case less than the following:
t
D
...
SHELL
Plate
Mean diameter
of tank
thickness
feet
inches
Smaller than 50 ......................................... ..... 3h 6
50 to 120, excl. ................................................ 14
120 to 200, incl. .............................................. 5/16
Over 200 ......................................................... 3/g
t=
SELF-SUPPORTING
CONE ROOF
=
400
SIll
e
but not less than 3/16 in.
Maximum t = Yz in.
9: 12 slope
Maximum e = 37 deg.
Minimum e = 9 deg. 28 min. 2: 12 slope
t = RI
SELF-SUPPORTING
DOME AND
UMBRELLA ROOF
n.
200 but not less than 3/16 in.
Maximum t = Yz in.
R = radius of curvature of roof, in feet
Maximum R = 0.8 D (unless otherwise specified
by the purchaser.
Maximum R = l.2D
The cross-sectional area of the top angle plus the participating area ofthe shell and roof plate shall be equal
or exceed the following:
For Self-Supporting
Cone Roofs:
For Self-Supporting
Dome and Umbrella Roofs:
D2
DR
3,000 sin e
1,500
The participating area shall be determined using Figure
F -1 of this Standard.
BOTTOM
All bottom plates shall have a minimum nominal thickness of 14 in.
207
WELDED STEEL TANKS FOR OIL STORAGE
API. Standard 650, Ninth Edition 1993
APPENDIX J - SHOP-ASSEMBLED STORAGE TANKS
(Summary of major requirements)
SCOPE
This appendix provides design and fabrication requirements for vertical storage
tanks in sizes that permit complete shop assembly and delivery to the installation
site in one piece. Storage tanks designed on this basis are not to exceed 20 feet in
diameter.
MATERIALS
The most commonly used plate materials of those permitted by this standard:
A 36, A 283 C, A 285 C, A 516-55, A 516-60
WELDED JOINTS
As described in Appendix A (see preceeding page) with the following modifications:
Lap-welded joints in bottoms are not permissible.
All shell joints shall be full penetration, butt-welded without the use of backup
bars.
Top angles shall not be required for flanged roof tanks.
Joints in bottom plates shall be full penetrations butt-welded.
Flat bottoms shall be attached to the shell by continuous fillet weld laid on each
side of the shell plate.
BOTTOM DESIGN
All bottom plate shall have a minimum thickness of '14 inch.
Bottoms may be flat or flat-flanged.
Flat bottoms shall project at least 1 inch beyond the outside diameter of weld
attaching the bottom shell.
SHELL DESIGN
Shell plate thickness shall be designed with the formula:
(for notations see Appendix A on the preceeding page.)
t
= (2.6) (D) (H-l) (G) + C A
(E) (21,000)
. .
but in no case shall the nominal thickness be less than:
Nominal Tank
Nominal Plate
Diameter (feet)
Thickness (inches)
Up to 10.5, incl ....................................
3~6
Over 10.5..............................................
'14
ROOF DESIGN
Roofs shall be self supporting cone or dome and umbrella roofs. See Appendix A
for design formulas.
TESTING
Apply 2 to 3 pounds per square inch internal pressure. For tanks with a diameter
of 12 feet or less, a maximum pressure of 5 psig shall be used.
208
Summary of Major Requirements of
PIPING CODES
PIPE WALL THICKNESS AND ALLOWABLE PRESSURE
CODE & SCOPE
FORMULAS
Straight Pipe Under Internal Pressure
ANSI B31.1 -1998
POWER PIPING
This Code describes minimum requirements
for the design. materials, fabrication, erection,
test. and inspection of power and auxiliary service piping systems for electric generation
atations, industrial and institutional plants. central and district heating systems. except as limited by Para. 100.1.3. These systems are not
limited by plant or other property lines unless
they are specifically limited in Para. 100.1.
t
=
t
=
P =
PD()
2(SE + Py)
+A
Pd + 2SEA + 2J:!.PA
2(SE + Py P)
2SE(tm -A)
D() - 2y(tm - A)
2SE(tm -A)
P = d - 2y(t - A) + 2tl/1
m
V ALUES OF S, 1000 psi.
For materials ASTM A53B and AI06B
For metal temperatures not exceeding Deg. F.
-20 to 650
700
750
800
15.0
14.4
13.0
10.8
External Pressure
For determining wall thickness and stiffening
requirements, the procedures outlined in Paras.
UG-28, 29 and 30, Section VIII, Division 2 of
the ASME Boiler and Pressure Vessel Code
shall be followed.
USAS B31.2-1968
FUEL GAS PIPING
This Code covers the design, fabrication,
installation and testing of piping systems for
fuel gases such as natural gas, manufactured
gas, liquefied petroleum gas (LPG) - air mixtures above the upper combustible limit, liquetied petroleum gas (LPG) in the gaseous phase,
or mixtures of these gases.
ANSI B31.3-1999
CHENnCALPLANTAND
PETROLEUM REFINERY PIPING
(a) This Code prescribes requirements for
the materials, design. fabrication. assembly, erection, examination. inspection, and testing of
piping systems subject to pressure or vacuum.
(b) This Code applies to piping systems
handling all tluids, including fluidized solids,
and to all types of service . including raw, intermediate and finished chemicals, oil and other
petroleum products, gas, steam, air. water, and
refrigerants. except as provided in 300.1.2 or
300.1.3. Only Category D and M fluid services
as defined in 300.2 are segregated for special
consideration.
Internal Pressure
tl/1
=t+A
P = 2SEt
D
t =
PD
2SE
(see notes 1, 3, 4, 5, 6 & 8)
VALVES OF S, 1000 psi.
For materials ASTM A53B and AI06B
For metal temperatures not exceeding Deg. F.
-20 to 100 200
300
400
450
20.00
19.10
18.15
17.25 16.80
Internal Pressure
1m
=t+c
t
= 2[SE
Pd
P (I
Y) J
PD
t = 2(SE + PY)
(see notes 1, 7 & 8)
V ALVES OF S, 1000 psi.
For materials ASTM A53B and AI06B
For metal temperatures not exceeding Deg. F.
-20 to 100
200
300
400
500
1.gtg 20.00 20.0 20.0 20.0 18.9
External Pressure
For determining wall thickness and stiffening
requirements the procedures outlined in Paras.
UG-28, 29 and 30, Section VIII, Div. I of the
ASME Boiler and Pressure Vessel Code shall
be followed.
209
Summary of Major Requirements of
PIPING CODES
(Continued from facing page)
NOTATION
NOTES
A = an additional thickness in inches to
compensate for material removed in
threading, grooving, etc., and to provide for mechanical strength, corrosion and erosion.
Centrifugally cast 0.14 in.
Statically cast
0.18 in.
the sum in inches of the mechanical
allowances (thread or groove depth)
plus corrosion and erosion allowance.
c
=
d
= inside diameter of the pipe in corroded conditions, inches.
D& Do= outside diameter of the pipe, inches
E
=
efficiency factor of welded joint in
pipe (see applicable code) For seamless pipe E = 2.0.
F = for cast iron pipe casting quality factor F shall be used in place of E.
P = internal design pressure, or maximum
1. The minimum thickness for the pipe selected, considering manufacturer's minus
tolerance, shall not be less than tm . The minus tolerance for seamless steel pipe is
12.5% of the nominal pipe wall thickness.
2. Where steel pipe is threaded and used for
steam service at pressure above 250 psi, or
for water service above 100 psi with water
temperature above 200 oF, the pipe shall be
seamless, having the minimum ultimate tensile strength of 48,000 psi and weight at
least equal to sch. 80 of ANSI B36.20. (Code
ANSI B31.1, Para. 104.1.2C.l)
3. Piping systems installed in open easements
which are accessible to the general public or
to individuals other than the owner of the
piping system or his employee or agent,
shall be designed in accordance with ANSI
B31.8. (Code ANSI B31.02, Para. 201.1)
allowable working pressure, psig.
S
=
maximum allowable stress in material due to internal pressure and the
design temperature, psig.
t
=
thickness of pipe required for pressure, inches
tm
=
minimum thickness of pipe in inches
required for pressure and to compensate for material removed for threading, grooving, etc., and to provide for
mechanical strength, corrosion and
erosion.
y&Y
=
coefficients as tabulated below
VALUES OF y & y
900 1
Temperature
and
F
below 950 1000 1050
FerriticSteels
0.40.50.7 0.7
Austenitic Steels 0.4 0.4 0.4 0.4
1250
and
llOO above
0.7 0.7
0.5 0.7
Note:For intermediate temperatures the values
may be interpolated. For nonferrous materials
and cast iron, y equals 0.4.
IFor pipe with a D,/tm ratio less than 6, the value
of y for ferritic and austenitic steels designed for
temperatures of 900 0 F and below shall be taken
as:
y= _d_
d + Do
4. When not specifically required by a gas using process or equipment, the maximum
working pressure for piping systems installed in buildings intended for human use
and occupancy shall not exceed 20 psig.
{Code ANSI B31.2, Para. 201.2.1)
5. Every piping system, regardless of anticipated service conditions, shall have a design
pressure of at least 10 psig between the temperatures of minus 20 0 F and 250 oF. (Code
ANSI B31.2, Para. 201.2.2,b)
6. Where the minimum wall thickness is in excess of 0.10 of the nominal diameter, the
piping system shall meet the requirements
of ANSI B31.3. (Code ANSI B31.2, Para.
203)
7. Pipe with t equal to or greater than D/6, or
P/SE greater than 0.385, requires special
consideration, taking into account design and
material factors such as theory of failure,
fatigue and thermal stresses.
8. Pipe bends shall meet the flattening limitations of the applicable Code.
210
Summary of Major Requirements of
PIPING CODES
PIPE WALL THICKNESS AND ALLOW ABLE PRESSURE
CODE & SCOPE
FORMULAS
Straight Pipe Under Internal Pressure
ANSI B3I.4-1998
LIQUID TRANSPORTATION SYSTEMS
=t+A
PiD
t = 2S ' where
til
This Code prescribes requirements for the
design, materials, construction, assembly, inspection. and testing of piping transporting
liquids such as crude oil. condensate, natural S = allowable stress value, psi. For pipe
gasoline, natural gas liquids, liquidied petromaterials ASTM A 53 B and A 106
leum gas, liquid alcohol, liquid anhydrous
B, S = 25,200 psi. at -20 o F to 250°F.
ammonia, and liquid petroleum products between producers' lease facilities, tank farms, t = pressure design wall thickness inches
(See notes 1, 2).
naatural gas processing plants, refineries, stations, terminals, and other delivery and receiving points.
ANSI B31.5-2000
REFRIGERATION PIPING
Internal Pressure
t/ll
This Code provides minimum requirements for the materials, design, fabrication,
assembly, erection, test, and inspection of
refrigerant and secondary coolant piping for
temperatures as low as 320°F (whether erected
on the premises or factory assembled) except
as specifically excluded in the following paragraphs.
Users are advised that other piping Code
Sections may provide requirements for refrigeration piping in their respectivejurisdictions.
This Code shall not apply to:
1
(b) water pi ping;
S
=
2St
Do - 2yt
or
1
=
Pd
2 (S + Py - P)
-=-:-:--..::.......:,~-,...,
, where
maximum allowable stress, psi. For pipe
materials ASTM A 53 B and A 106 B,
S = 15,000 psi, at 1OOoF to 400 oF.
t = pressure design wall thickness, inches.
(See notes 1, 2).
External Pressure
The pressure design thickness, t, shall be determined in accordance with Code, Para.
504.1.3.
ANSI B3I.8-1999
GAS TRANSMISSION AND
DISTRIBUTING PIPING SYSTEMS
This Code covers the design, fabrication,
installation, inspection, testing, and the safety
aspects of operation and maintenance of gas
transmission and distribution systems, including gas pipelines, gas compressor stations, gas
metering and regulating stations, gas mains, and
service lines up to the outlet of customer's meter
set assembly. Included within the scope of this
Code are gas storage equipment of the closed
type, fabricated or forged from pipe or fabricated from pipe and fittings and gas storage
lines.
PD,)
= 2 (S + Py)
P =
(a) any self-contained or unit systems subject to the requirements of Underwriters' Laboratories or other nationally recognized testing laboratory;
(c) piping designed for external or internal
gage pressure not exceeding 15 psi (103 kPa)
regardless of size.
=t+c
Steel Pipe Design Formula
Internal Pressure
P =2S1 x Fx Ex T where
D
'
S = specified minimum yield strength, psi.
For pipe materials ASTM A 53 Band
A 106 B, S - 35,000 psi.
t
= nominal wall thickness, inches (See
notes 1,2,3,4 & 5).
211
Summary of Major Requirements of
PIPING CODES
(Continued from facing page)
NOTATION:
A = Sum of allowance, inches for threading and grooving as required under
Code, Para. 402.4.2, corrosion as required under Code, Para 402.4.2, and
increase in wall thickness if used as
protective measure under Code Para.
402.1.
c
For internal pressure, the sum of allowances in inches thread and groove
depth, manufacturers' minus tolerance,
plus corrosion and erosion allowance.
For external pressure, the sum in
inches of corrosion and erosion allowances, plus manufacturers' minus tolerance.
T = Temperature Derating Factor for Steel
Pipe.
Temperature
Degrees Fahrenheit
250 F or less
300 F
350 F
400 F
450 F
Factor T
1.000
0.967
0.933
0.900
0.867
Note: Interpolate for intermediate values.
y = Coefficient for materials indicated:
For nonferrous materials, ferritic
steels and austenitic steels y = 0.4.
Dr in range of 4-6, use
If
_
d
d = Inside diameter of pipe, inches.
y - d+ Do
D&
for ductile materials.
Do = Outside diameter of pipe, inches.
For brittle materials use y = 0.0.
E = Longitudinal joint factor obtained from
Code, table 841.12. For seamless pipe,
E= 1.0.
F = Values of Design Factor F
Construction Type Design Factor F
(See Code 841.114A)
Type
Type
Type
Type
-
A
B
C
D
0.72
0.60
0.50
0.40
P&
Pi = Internal design pressure, psig.
S
As described at the formulas, and in
applicable Code, psi.
tt
As described at the formulas, inches.
tn
Nominal wall thickness of straight part
of steel pipe satisfying requirements
for pressure and allowances.
tmj=
Minimum required thickness, inches,
satisfying requirements for design
pressure and mechanical, corrosion and
erosion allowances.
NOTES:
1. In selection of pipe the manufacturers' minus tolerance shall be taken into consideration. The minus tolerance for seamless steel
pipes is 12.5% of the nominal wall thickness. This tolerance may be used also when
specification is not available.
2. Pipe bends shall meet the flattening limitations of the applicable Code.
3. Classification of Locations. In Code B31.8,
Para. 840.2, four classes are described as a
basis for prescribing the types of construction.
4. Limitation by Pipe Design Factors, Code
B3 1. 8, Para. 841. 111-114.
5. Least Nominal Wall Thickness, Code B31.8,
Table 841.141.
The formulas and regulations are extracted from
the American National Standard Code for Pressure Piping with the permission of the publisher, The American Society of Mechanical
Engineers.
212
NOTES
213
RECTANGULAR
TANKS
UNDER HYDROSTATIC PRESSURE
:;'lat-walled tanks due to their mechanically disadvantageous shape are used for low
lydrostatic pressure only. The quantity of material required for rectangular tanks is
righer than for cylindrical vessels of the same capacity. However, sometimes the applicaion of rectangular tanks is preferable because of their easy fabrication and the good
ltilization of space.
MAXIMUM SIZE
Unstiffened tanks may be not larger than 30 cu. ft. and tanks with stiffenings, 140 cubic
feet capacity.
::;or larger tanks, the use of stay rods is advisable for economic reasons.
~ATIO OF SIDES
[f all sides are equal, the length of one side: B =
where V
Preferable ratio: Longer side: 1.5 B; Shorter side: 0.667 B
W;
= volume
cu. ft.
DESIGN
rhe formulas on the following pages are based on maximum allowable deflection:
.1, = ti2, where ta denotes the thickness of side-plate.
Values of a and {J
R aho,"[
. H ofl
H
0.25
Constant, {J 0.024
Constant, a 0.00027
0.286
0.031
0.00046
R allo,"[
. H of7
H
Constant, {J
Constant, a
1.5
0.26
0.043
H
=
1.0
0.16
0.022
height of tank
L
=
0.333
0.041
0.00083
2.0
0.34
0.060
length of tank
0.4
0.056
0.0016
2.5
0.38
0.070
3.0
0.43
0.078
0.5
0.080
0.0035
3.5
0.47
0.086
0.667
0.116
0.0083
4.0
0.49
0.091
maximum distance between supports
WELDING OF PLATE EDGES
Some preferable welded joints of plate edges:
LL~
[he stiffenings may be attached to the tank wall either by intermittent or continuous
welding and may be placed inside or outside.
~IBLIOGRAPHY
)ther design methods are offered in the following papers:
lojtaszak, I. A.: Stress and Deflection of Rectangular Plates, ASME Paper A-71, Journal Appl.
lIecl•. , Vol. 3 No.2, 1936.
rimoshenko, S. and S. Woinowsky-Krieger:
{ill Book Company, 1959.
"Theory of Plates and Shells", 2nd edition, McGraw-
:anti K. Mahajan: "Design of Procas Equipment.", Pressure Vessel Handbook Publishing. Inc. 1990.
214
RECTANGULAR TANKS
UNDER HYDROSTATIC PRESSURE
WITH TOP-EDGE STIFFENING
NOTATION
a
E
G
= factor depending on ratio of length and height of tank, H/L (See Table)
= modulus of elasticity, psi.; 30,000,000 for carbon steel
= specific gravity of liquid
H = height of tank, in
I = moment of inertia, in.4
I = maximum distance between supports, inches
L = length of tank, nches
R = reaction with subscripts indicating the location, lb./in.
S = stress value of plate, psi. as tabulated in Code, Tables ues - 23
t = required plate thickness, inches
ta = actual plate thickness, inches
tb = required plate thickness for bottom, inches
t8 = actual thickness of bottom, inches
w = load perunit of length lb./in.
y = deflection of plate, inches
REQUIRED PLATE THICKNESS
L
t =
B
'\ IPHO.036G
V
S
Thickness, t may be used also for the
bottom plate if its entire surface is
supported.
Thickness, t shall be increased in
corrosive service.
Maximum deflection of plate:
_ aO.036GHL4
L
Ed
max -
I - - - - . -..----~-~-----------
STIFFENING FRAME
w=
R1 = O.3w
0.036 GH2
R2
O.7w
Minimum required moment of inertia
for top-edge stiffening:
2
=
lmin=
BOTTOM PLATE
WHEN SUPPORTED BY BEAMS
t b
w
1:
:r
18
!. S
1.254 yO.036 G H
..
Maximum spacing of supports for a
given thickness of bottom:
215
RECTANGULAR TANKS
EXAMPL.ES
DESIGN DATA
Capacity of the tank: 600 gallon = 80
Content: water; G = 1
The side of a cube-shaped tank for the
Preferred proportion of sides:
L = 4.31 x 1.5 = 6.47 ft. =
H = 4.31 x .667 = 2.87 ft. =
Width of the tank 4.31 ft. =
S = 15,700, using SA 285 C material
Corrosion allowance: 1/16 in.
H/L = 34178 = 0.43; fJ = 0.063
cu. ft. approximately
3
designed capacity:
V80 = 4.31 ft.
78 inches
34 inches
52 inches
REQUIRED PLATE THICKNESS
'\ / 0.063
t = 78
V
X
·34 '>( 10.036
15,700
+ 0.0625
X
1 = 0 1729 .
.
m.
corr. allow = 1/4 in.
STIFFENING FRAME
0.036
1
X
X
342 =
20.808 lbiin
W
2
I
_ =
mm
R 1 - = 0.3
R2 = 0.6
X
X
20.808 = 6.24 lb/in
20.808 = 14.57 lh/in
6.24 X 784
= 0.214 in4
192 x 30.000,000 x 0.1875
1-3/4 x 1-3/4 x 3/16 (.18 in4) satisfactory for stiffening at the top of the tank
BOTTOM PLATE WHEN SUPPORTED BY BEAMS
if number of beams = 3; 1 = 39 inches
Ib
39
= ----"-~~~=
= 0.275
/15,700
1.254
in.,
0.036x 1x34
Or using the plate thicknessO.1875 as calculated above, the maximum
spacing for supports:
I = 1.254
Using 4 beams, .1
x
0.1875
-= 26 in.
Jo0.036
15,700
x 1 x 34
= 26.63 in.
216
RECTANGULAR TANKS
WITH VERTICAL STIFFENINGS
NOTATION
p =
E
]{
I
G
I
L
S
w
Z
=
=
=
=
=
=
=
=
=
=
Factor depending on ratio of length and height, 1111
(See Table on page 213)
modulus of elasticity, ~i.
height of tank inches
moment ofinenia, in4
specific gravity of liquid
the maximum distance between stiffenings
on the longer or shorter side of the tank, inches.
length of tank, inches
stress value of plate, psi.
required plate thickness, inches I(J = actual plate thickness, inches
10ad,lbs.
section modulus, in 3
I---L-J
I.
L
REQUIRED PLATE THICKNESS
t = I
V
PH 0.036 G
S
LOADS, lb/in
- O.036GH2
W2
STIFFENING FRAME
Required section modulus of vertical stiffening
3
0.0642. 0.036 GH 1
z=------S
Minimum required moment of inertia for top-edge stiffening:
RJ L"
I min = 192
E I(J
217
RECTANGULAR TANKS
WITH VERTICAL STIFFENINGS
EXAMPLES
DESIGN DATA
E = 30,000,00 psi
L
=
H=
B=
S =
I =
78 in.
34 in.
52 in.
J 5,700 psi
26 in.
Content: Water
G= 1
34
HII= 26= 1.31:jJ=0.22
REQUIRED PLATE THICKNESS
t
=26 X /.22 X34 XO.036 XI =01077'
15700
.
tn.
,
+ corr. allow
0.0625 in.
0.1702 in.
+ use 3116 in. plate
STIFFENING FRAME
X 1 X 34 3 X 26 = 0 1504' 3
Zmm. = 0.0642 X 0.036
15700
.
m.
,
2 X 2 X 31J 6 (.19 in. 3) satisfactory for vertical stiffening
w=
0.036 X 1 X 342
2
'min
_
6.24 X 78 in.4
_ 0 "'2' 4
-192 X 30,000,000 X 0.125 - .J m.
20.81b.lin.
Rl = 0.3 X 20.8 - 6.24Ib.lin.
218
RECfANGULAR TANKS
Under Hydrostatic Pressure
WITH HORIZONTAL STIFFENINGS
NOTATION
E
G
H
I
L
p
R
S
t
ta
w
= modulus of elasticity, psi.; 30,000,000 for carbon steel
= specific gravity of liquid
= height of tank, in
= moment of inertia, in.4
= length of tank,inches
= pressure of liquid, psi.
= reaction with subscripts indicating the location, lb./in.
= stress value of plate, psi.
= required plate thickness, inches
= actual plate thickness, inches
= load per unit of length lb./in.
H
I.
SPACING OF
STIFFENINGS
L
.1
HI = 0.6H
REQUIRED PLATE
THICKNESS
n
H2 = O.4H
..
0.036 GH
S
/
= 0. 311 V
t
w = 0.036 GH 2
LOAD Ib./in.
2
RJ
= 0.06
W
R2
= 0.3 w
R2
= 0.64 w
Minimum required moment of inertia
for top-edge stiffening
MINIMUM MOMENT
OF INERTIA FOR
STIFFENING
I I
-
RI L
4
192 E ta
Minimum required moment of inertia
for intermediate stiffening
=
I
2
R2
L4
192 E ta
I
219
RECTANGULAR TANKS
WITH INTERMEDIATE HORIZONTAL STIFFENINGS
EXAMPLES
DESIGN DATA:
Designed capacity = 1,000 gallon = 134 cu. ft. (approx.)
Content: water
s= 15,700 psi, using SA 285 Cmaterial
Corrosion allowance = lit 6 in.
The side of a cube-shaped tank for the designed capacity:
Preferred proportion of sides:
width = 0.667 X 5.12 = 3.41 ft; approx. 42 inches
length = 1.500 X 5.12 = 7.68 ft; approx. 92 inches
height =
5.12 ft; approx. 60 inches
3
134 = 5.12 ft.
For height 60 inches, intermediate stiffening is required.
SPACING OF STIFFENINGS:
HI = 0.6
H= 36 in.
H2 = O.4H= 24 in.
REQUIRED PLATE TIDCKNESS:
=01X60jO.036XI560 =02111'
15,700
.
m.
t.J
+ corr. allow 0.0625 in.
0.2736 in.
LOADS:
2
/.
w = 0.036 X 21 X 60 = 64 .81b .m.
R2 =0.3w= 19.441b'/in.
RI =0.06w=3.891b'/in.
MINIMUM MOMENT OF INERTIA FORSTIFFENINGS:
4
3.89 X 92
-04690' 4
II - 192 X 30,000,000 X 0.25 - .
m.
_
19.44 X 92 4
_
12 - 192 X 30,000,000 X 0.25 - 0.
96 . 4
7 m.
220
TIE
ROD
S U p.p 0 R T
FOR RECTANGULAR TANKS
Under Hydrostatic Pressure
To avoid the use of heavy stiffenings, the sides of large tanks may be supported
most economically by tie rods.
NOTATIONS
A
Req uired cross sectional area of
a
~
tie rod, sq. in.
a
horizontal pitch, in.
b
vertical pitch, in.
'hI 2
~
G = specific gravity of liquid
f
P
pressure of liquid, lb.
Ib
~
S = stress value of rod material, psi.
t = required plate thickness, in.
Sp = stress value of plate material, psi
..
-+
+-
REQUIRED
PLATE
THICKNESS
when a:!!b
LOAD ON
TIE ROD
EXAMPLE
DESIGN DATA
Length=30 ft., width=12 ft., height=15 ft.
a
hJ = 60 in
G = I
S = 20,000 psi.
S = 20,000 psi.
Sp = 20,000 psi
h2 = 120 in
= 0.7
t
x 60
V
0.036 x 1 x 120
20,000
A = 15,552 = 0.778 sq. in.
2
20,000
PI
1
= It/> rods
=abO.036Gh l =6Ox60x0.036x60 = 7,776 lb.
A =
7,776 - 0.389 sq. in. = 3/4 ¢> rods
20,000
V
P=ab 0.036 Gh
REQUIRED CROSS
SECTIONAL AREA
OF TIE ROD
= 60 in.
b = 60 in.
t = 0.7b
• ...
0.036 G h
Sp
221
CORROSION
Vessels or parts of vessels subject to thinning by corrosion, erosion or mechanical
abrasion shall have provision made for the desired life of the vessel by suitable
increase in the thickness of the material over that determined by the design
formulas, or by using some other suitable method for protection (Code UG-25b).
The Code does not prescribe the magnitude of corrosion allowance except for vessels
with a required minimum thickness of less than 0.25 in. that are to be used in steam,
water or compressed air service, shall be provided with corrosion allowance of not less
than one-sixth of the required minimum thickness. The sum of the required minimum
thickness and corrosion allowance need not exceed 1/4 in. This requirement does not
apply to vessel parts designed with no x-ray examination or seamless vessel parts
designed with 0.85 joint efficiency. (Code UCS-25).
For other vessels when the rate of corrosion is predictable, the desired life of the vessel
will determine the corrosion allowance and if the effect of the corrosion is indeterminated, the judgment of the designer. A corrosion rate of 5 mils per year (lI16 in. = 12
years) is usually satisfactory for vessels and piping.
The desired life time of a vessel is an economical question. Major vessels are
usually designed for longer (15-20 years) operating life time, while minor vesse1s
for shorter time (8-10 years).
The corrosion allowance need not be the same thickness for all parts of the vessel if
different rates of attack are expected for the various parts (Code UG-25 c).
There are several different methods for measuring corrosion. The simplest way is the
use ofteltale holes (Code UG-25 e) or corrosion gauges.
Vessels subject to corrosion shall be supplied with drain-opening (Code UG-25 0.
All pressure vessels subject to iinternal corrosion, erosion, or mechanical abrasion
shall be provided with inspection opening (Code UG-46).
To eliminate corrosion, corrosion resistant materials are used as lining only, or for the
entire thickness of the vessel wall.
The rules of lining are outlined in the Code in Part UCL, Apendix F and Par. UG-26.
The vessel can be protected against mechanical abrasion by plate pads which are
welded or fastened by other means to the exposed area of the vessel.
In vessels where corrosion occurs, all gaps and narrow pockets shall be avoided by
joining parts to the vessel wall with continuous weld.
Internal heads may be subject to corrosion, erosion or abrasion on both sides.
222
SELECTION OF CORROSION RESISTANT MATERIALS
The tabular information on the following pages is an attempt to present a summarized
analysis of existing test data. It is necessarily brief and, while the utmost precautions
have been taken in its preparation, it should not be considered as infallible or applicable
under all conditions. Rather, it should be looked upon as a convenient tool for use in
determining the degree of safety which various materials are capable of providing and
in narrowing down the field of investigation required for final selection. This particularly applies where failure due to corrosion may produce a hazardous situation or result
in expensive down-time.
Footnotes have been generously used to explain and further clarify information contained in this table. It is most important that these notes be carefully read when using
the table.
In rating materials, the letter "A" has been used to indicate materials which are
generally recognized as satisfactory for use under the conditions given. The letter "F"
signifies materials which are somewhat less desirable but which may be used where a low
rate of corrosion is permiSSible or where cost considerations justify the use of a less
resistant material. Materials rated under the letter "c" may be satisfactory under certain
conditions. Caution should be exercised in the use of materials in this classification
unless specific information is available on the corroding medium and previous experience
justifies their use for the service intended. The letter "X" has been used to indicate
materials generally recognized as not acceptable for the service.
Information on metals has been obtained from the International Nickel Company,
the Dow Chemical Company, the Crane Company, the Haynes-Stellite Company,
"Corrosion Resistance of Metals and Alloys" by McKay & Worthington, "Metals and
Alloys Data Book" by Samuel L. White, "Chemical and Metallurgical Engineering" and
"The Chemical Engineers' Handbook," Third Edition by McGraw-Hill.
NOTES - GASKET MATERIALS
I.
The generally accepted temperature limit for a good grade compressed asbestos sheet, also called
asbestos composition sheet, is 7500F. However, some grades are successfully used at considerable higher temperatures. This type of sheet is used for smooth flanges. For rough flanges,
gaskets cut from asbestos-metallic sheet or formed by folding asbestos-metallic cloth are preferred. The latter ,and gaskets cut from felted asbestos sheet, are indicated for flanges when
bolt pressures are necessarily limited because of the type of flange meterial.
II. Data from the Pfaulder Company are given from the special point of view of the suitability of the
gasket material for use with glass-lined steel equipment.
III. Data in this column apply specifically to Silastic 181, a special silicone rubber for use in gasketing
produced by Dow-Corning Corporation.
IV. Fiberglas fabric filled with Silastic silicone rubber (polysiloxane elastomer) has a usable compressibility of about 20 per cent and shows the chemical resistance cited here over the temperature
range from -85 to 3920F. For Fiberglas fabric filled with chemically resistant synthetic rubber,
the temperature range is approximately -40 to 2570F. Both the silicone rubber and the ordinary
synthetic rubber are available as gasket materials in which the reinforcing fabric is a metal cloth
(brass, aluminum, iron, stainless steel). The chemical properties of these constructions are the
same as those given here for the Fiberglas-reinforced material, with the properties of the metal in
the cloth imposed upon them. The metal-cloth construction for increased mechanical strength
and electrical conductivity.
223
V. Teflon is the DuPont trade-name for polymerized tetrafluorethylene. It is completely inert in the
presence of all known chemicals. It is not affected by any known solvent or combination of
solvents. It is chemically stable up to 6170F but, being a plastic, it is not recommended for
gasket applications above 3920F or for high pressures unless confined in a tongue-and-groove or
similar joint.
Sources of Data: A - Armstrong Cork Co.; C - Connecticut Hard Rubber Co.; D - Dow-Corning
Corp.; E - E. I. DuPont de Nemours & Co.; J - Johns-Manville Corp.; P - The Pfaudler Co.;
S - Stanco Distributors, Inc.; U - United States Rubber Co.
Information on gasket materials compiled by McGraw-Hili, "Chemical Engineers Handbook,"
Third Edition.
224
CHEMICAL RESISTANCE OF METALS
Resistance Ratings: A = Good; F = Fair;
C = Caution- depends on conditions;
X = Not recommended.
Caution: Do not use table
without reading footnotes and text.
u
rJ:i
rJ:i
N
.
-;
'" 'u..
'".."
e
c:
0
Ch~mical
U
rii"
~
c:
"c:0
~
.. ·s
Q,o
~
~
Q,o
e0
"
u
;: Z ..5
0
F
F
F
F
A
A
C
....J
acid. crude................................. C
Pure ...................................................... X
Vapors................................................. X
150 Ib/sq.in. @ 4(X)·F..........._.......... X
Acetic anhydride.................................. C
Acetone....................... _.......................... A
Acetylene ................................................ A
Aluminum chloride .............................. X
Aluminum sulfate....................... _....... X
Alun1s ....................................................... X
Ammonia gas. dry ............................... F
~Ioist .................................................... F
Ammonium chloride............................ F
Ammonium hydroxide ................ _...... A
Ammonium nitrate .............................. F
Ammonium phosphate ....................... C
Ammonium sulfate.............................. F
Aniline. aniline oiL ............................. A
Aniline dyes........................................... Barium chloride .................................... Barium hydroxide....................... _....... Hariul11 sulfide ...................................... Beer .......................................................... C
Beet sugar liquors ................................ C
Benzene. benzoL ................................. A
Benzine. petroleum ether. naphtha A
Black sulfate liquor............................. A
Boric acid ............................................... X
Bromine .................................................. X
C
C
C
F
F
F
C
C
C
F
A
C
X
AI F
A A
Xe A Xs
C X C
F A C
F A F
A A A
X A X
X A X
X A X
X X X
C A C
C A C
X
X -
-
-
X
C
F
F
A
X
X
X
X
C
-
A
A
-
A
C
F
A
-
A
-
A
A
F
A
C
Notes continued on opposite page
1. In absence of oxygen.
0
2. 125 maximum.
3. All percents; 70°.
4. To boiling.
5. 5% room temperature.
6. To 122°.
7. Iron and steel may rust considerably
U
X
In
presence of water and air.
8. HifLh copper al/oys prohibited by Codes;
ye low brass acceptable.
9. Haslel/oy "c" recommended to 105°.
-
-
-
-
X
X
A
X
-
A
A
A
A
X
C
C
-
A
A
F
C
-
"ij
"ii
:...>
X
"ij
c:
Q,
:I::
-
c:
Q,o
~
0
Q,o
Q,
~
..=
Ac~tic
'3
e::l
::l
C
A
A
A
C
C
F
A
C
C
A
A
C
As
X
-
X
-
A
C
A
A
-
A
X
..lII
U
C
F
C
-A
A
A
C
C
C
8
C
A
C
C
A
A
C
C
c:
~
C
A
C
C
A
A
A
C
F
C
rJ:i
rJ:i
rJ:i
rJ:i
rJ:i
rJ:i
~..
P..
0
~
~
~ ;;; ~ c:" ]
">. ">. " . II'"
f-o E-o ?: U" :=
IC)
Q,o
Q,
Q,
Q,
C
F
C
C C A
Ao C A
X C A
A C A
A A A
A A A
A A A
C X A2
A A A
A C A
A A A
A A A
C C A
A A A
A - A
A A A
C A A
A A A
A A A
C - F
A - A
A A
A A A A A
A A A
A A A
A
A A A A
X X C
-
F
A
A
X
A
A
- A3 - A
C A C A
A C A C
C A C A
- - C A
A4 ~ ~ A
F A A C
- - A A
- - A A
- C
A A - A
- - A A
A A A A
A A A A
A A A A
A A A A
A A A A
- - C A
C C C X
Q,
A
A
A
A
A
A
A
A2
A
-
A
-
Ao
A
A
As
A
A
A
Ao
-
- AA
A
A
-
A
A
10. Where color is not important. Do not use
with c.p. acid.
11. Room temperature to 212°. Moisture In·
hibits attack.
12. Gas; 70°.
13. To 500°.
14. Hastel/oy ItC" at room temperature.
15- Room temperature to 158°.
16. At room temperature.
17. Where discoloration is nol objectionable.
18. 5% maximum; 150° maximum.
19. Satisfactory vapors to 212°.
225
CHEMICAL RESISTANCE OF GASKETS
(SEE CHEMICALS ON OPPOSITE PAGE)
Resistance Ratings: Same as facing page
... ...
C ,-.
">0 c">
~
...0
c:i.
e
0
~
~
:c
~
0
~
...0
A
A
A
A
A
A
A
C
A
0
~
u
:J
as
A
A
A
A
A
-
A
A
C
C
C
A
A
A
A
-
C
A
A
A
A
A
A
A
A
X
t:u
.c
."
c:i. "C
...u
e ...
.] ]
C
C
C
C
C
Asbestos
(omp.,
Rubber
Bonded
-
...uae
0
u
U
- -"...
... ..........
......
til
~
C
:J
e
~
:c
cu
a-
.~
.c
C
C
C
A
A
A
A
A
A
A
-
-
A
X
A
X
A
A
A
A
A
A
A
A
F
A
A
-
A
A
A
A
A
-
A
A
A
A
A
-
-
A
A
F
A
A
-
-
...... ......
.-..
c"
u
............ ...c a-...u
-
-
U
-u
:J
~
u
:J
as as
P
A
A
A
-
A
X
-
A
A
A
A
-
A
A
A
A
F
A
A
A
A
-
-
-
Miscellaneous
::... >...
u
,-.
...
,-.
F
-
P
A
A
A
-
A
X
-
A
A
..
:.a -u
u
:J
~
as
P
P
A
A
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20. Highly corroJive to nickel al/oYJ at elevated temperatureJ. Recommendation applieJ to "dry" gaJ at ordinary temperatureJ.
21. 4S% - boil at 330°.
22. Room temperature - over SO%.
23· Not for temperatureJ over 390°F.
24. Up to 140°F.
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26. Up to 176°F.
27. 10% maximum; boiling.
2S. ~O%; 320°.
29. Do not UJe if iron contamination is not
permiIJible.
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Hot.
Unsatisfactory for hot gases.
Hastelloy "C" to 15So,
Room temperature to 15So. Corrosion increases with increaJe in concentration aJ
well as temperature.
3~. Dilute at room temperature.
36. AI/ack increaseJ when only partially Jubmerged; fume! very corrosive.
37. HaJtelloy "C" to 212°.
30.
31.
32.
33.
34.
226
CHEMICAL RESISTANCE OF METALS
=
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1. In absenre 0/ oxygen.
2. 12J· maximllm.
3. AlJ c.er(enlS " 70·.
4. To oiling.
5. J% room lemperatllre.
6. To 122·.
7. Iron and steel may rllst ronsiderably in
presenre 0/ water and air.
S. HiBh (opper alloys prohibited by Codes;
ye ow brass aueplable.
9. Haslelloy "C" recommended 10 10J·.
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10. Where rolor is not important. Do not lise
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11. Room temperatllre to 212·. Moistllre in.
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12. Gas; 70·.
13. To JOO·.
14. Hastel/oy "C" at room temperatllre.
IJ· Room temperatllre to US·.
16. At room tem£eratllre.
17. Where disco oration is nOI objetlionable.
IS. .5% maximllm; IJO· maximllm.
19. Satis/arlory vapors 10 212·.
227
CHEMICAL RESISTANCE OF GASKETS
(SEE CHEMICALS ON OPPOSITE PAGE)
Resistance Ratings: Same as facing page
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20. Highly (orrosille 10 ni(ltel alloys al eleIIalea lemperatures. Re(ommenaalion applies 10 "ary" gas al orainary lemperalures.
21. 4S% - boil at 330-.
22. Room lemperature - oller SO%.
23· NOllor lemperatures oller 390-F.
24. Up to 140-F.
2'. Up 10 200-F.
26. Up 10 176-F.
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29. Do "01 use il iro" (o"lami"atio" is "01
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HOI.
Unsalisla(lory lor hOI gases.
Haslelloy "c" 10 USe.
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30.
31.
32.
33.
34.
228
CHEMICAL RESISTANCE OF METALS
Resistance Ratings: A = Good; F = Fair;
C = Caution - depends on conditions;
X = Not recommended.
Caution: Do not use table
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Concentrated............................. X
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Palmitic acid .................................. C
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Notes continued on opposite page
1. In absence of oxygen.
2. 125° maximum.
3. All cercenJs j 70·.
4. To oiling.
5. 5% room temperature.
6. To 122°.
7. Iron and steel may rust considerably in
presence of waleI' tlnd air,
S. Hifl copper alloys prohibited by Codes j
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10. Where color is not important. Do not use
with c.p. add.
11. Room temperature to 212·. Moisture in·
hibits attack.
12. Gas; 70·.
13. To 500·.
14. Hastel/oy "C" at room temperature.
15· Room temperature to 15S·.
16. AI room lemperature.
17. Where discoloration is not ob;ectionable.
IS. .5% maximum; 150° maximum.
19. Salis/aclory vapors 10 212°.
229
CHEMICAL RESISTANCE OF GASKETS
(SEE CHEMICALS ON OPPOSITE PAGE)
Resistance Ratings: Same as facing page
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20. HIghly corroslfle to nickel alloys at elevated temperatures. Recommendation applies to "dry" gas at ordinary temperatures.
21. 48% - boil at 330°.
22. Room temperature - over 80%.
23· Not for temperatures over 390°F.
24. Up to 140°F.
25. Up to 200°F.
26. Up to 176°F.
27. 10% maximum; boiling.
28. 50%; 320°.
29. Do not use if iron contamination is not
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permissible.
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HOI.
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Hastelloy "c" to 158°·
Room temperature to 158°. Corrosion increases with increase in concentration as
well as temperature.
35. Dilute at room temperature.
36. Attack increases when only partially submerged; fumes very rorrosive.
37. Hastelloy "C" to 212°.
30.
31.
32.
33.
34.
230
CHEMICAL RESISTANCE OF METALS
=
=
Resistance Ratings: A
Good; F
Fair;
Caution - depends on conditions;
X
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(=
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Caution: Do not use table
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S teari c aci d................................ F
SuI fur .......................................... A
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Fuming.................................... A
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Tartaric acid .............................. X
Tol ue n e............................. ·········· A
Trichloroethylene, dry ........... A
vVet .......................................... X
Turpen tine ................................. (
Water, fresh (tap, boiler
feed, etc.) ................................ A
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Notes continued on opposite page
1- In absence of oxygen.
125° maximum.
All percents .. 70°.
To boiling.
5% room temperature.
To 122°.
Iron and steel may rust considerably In
presence of water and air.
8. Hi"h copper alloys prohibited by Codes ..
ye low brass acceptable.
9. Hastelloy "c" recommended to 105°.
2.
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Where color is not important. Do not use
with c.p. acid.
Room temperature to 212°. Moisture In·
hibits attack.
Gas .. 70°.
To 500°.
Hastelloy "c" at room temperature.
Room temperature to 158°.
At room temperature.
W here discoloration is not objectionable.
5% maximum; 150° maximum.
Satisfactory vapors to 212°.
-
231
CHEMICAL RESISTANCE OF GASKETS
(SEE CHEMICALS ON OPPOSITE PAGE)
Resistance Ratings: Same as facing page
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20. Highly corrosive to nickel alloys at elevated temperatures. Recommendation applies to "dry" gas at ordinary temperatures.
21. 48% - boil at 330°.
22. Room temperature - over 80%.
23· Not for temperatures over 390°F.
24. Up to 140°F.
25. Up to 200°F.
26. Up to 176°F.
27. 10% maximum; boiling.
28. 50%; 320°.
29. Do not use if iron contamination is not
30.
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permissible.
10% - room temperature.
Hot.
U1zsatisfactory for hot gases.
Hastelloy "c" to 158°·
Room temperature to 158°. Corrosion increases with increase in concentration as
well as temperature.
Dilute at room temperature.
Attack increases when only partially sub·
merged; fumes very corrosive.
Hastelloy "c" to 212°.
232
FABRICATING CAPACITIES
THE TABLES BELOW ARE FOR DATA OF FABRICATING CAPACITIES OF THE SHOP
WHICH HAVE TO BE KNOWN BY THE VESSEL DESIGNER. THE COLUMNS HAVE BEEN
LEFT OPEN AND ARE TO BE FILLED IN BY THE USER OF THIS HANDBOOK
ACCORDING TO THE FACILITIES OF THE SHOP CONSIDERED.
MAXIMUM
WIDTH in.
MAXIMUM
THICKNESS in.
MINIMUM
DIAMETER in.
MAXIMUM
SIZE
MINIMUM
DIAMETER in.
MINIMUM
SIZE
MINIMUM
DIAMETER in.
MAXIMUM
SIZE
MINIMUM
DIAMETER in.
MAXIMUM
SIZE
MINIMUM
DIAMETER in.
MAXIMUM
SIZE
MINIMUM
DIAMETER in.
ROLLING PLATES
TENSILE STRENGTH
OF PLATE
psi.
NOTE:
FOR MATERIAL OF HIGHER
STRENGTH THE THICKNESS
OR WIDTH OF THE PLATE
MUST BE REDUCED IN
DIRECT PROPORTION TO
THE HIGHER STRENGTH
~
ROLLING ANGLES
~
~
~
ROLLING BEAMS
ROLLING CHANNELS
LEG
IN
LEG
OUT
LEG
IN
LEG
OUT
~ FLANGES
ON
~FLANGES
IN
e:::tFLANGES
OUT
ROLLING FLAT BAR
~ ON
EDGE
I
233
FABRICATING CAPACITIES
NOMINAL
PIPE SIZE
MINIMUM
RADIUS in.
SCHEDULE
BENDING PIPES
PLATE
THICKNESS in.
MINIMUM
INSIDE
RADIUS in.
PLATE
THICKNESS in.
MINIMUM
INSIDE
RADIUS in.
PLATE
THICKNESS in.
MAXIMUM
DIAMETER
OF HOLE in.
PLATE
THICKNESS in.
MAXIMUM
DIAMETER
OF HOLE in.
BENDING PLATES
WITH PRESS BRAKE
PUNCHING HOLES
MINIMUM INSIDE DIAMETER
OF VESSEL ACCESSIBLE FOR
INSIDE WELDING
inches
TYPES OF WELDINGS
AVAILABLE
FURNACES FOR STRESS
RELIEVING
HEIGHT
WIDTH
ft.
MAX. TEMPERA TU RE
ft.
f.
LENGTH
ft.
234
PIPE AND TUBE BENDING *
In bending a pipe or tube, the outer part of the bend is stretched and the inner
section compressed, and as the result of opposite and unequal stresses, the pipe
or tube tends to flatten or collapse. To prevent such distortion, the common
practice is to support the wall of the pipe or tube in some manner during the
bending operation.
This support may be in the form of a filling material, or,
when a bending machine or fixture is used, an internal mandrel or ball-shaped
member may support the inner wall when required.
MINIMUM RADIUS:
The safe minimum radius for a given diameter, material,
and method of bending depends upon the thickness of the pipe waU, it being
possible, for example, to bend extra heavy pipe to a smaller radius than pipe of
standard weight. As a general rule, wrought iron or steel pipe of standard weight
may readily be bent to a radius equal to five or six times the nominal pipe diameter. The minimum radius for standard weight pipe should, as a rule, be three
and one-half to four times the diameter. It will be understood, however, that
the minimum radius may vary considerably, depending upon the method of bending. Extra heavy pipe may be bent to radii varying from two and one-half times
the diameter for smaller sizes to three and one-half to four times the diameter for
larger sizes.
R
R
(3 Y2 to 4d)
(2Y2 to 4d)
Standard Pipe
Extra Heavy Pipe
MINIMUN( RADIUS
*From Machinery's Handbook, 1969 Industrial Press, Inc. - New York
235
PIPE ENGAGEMENT
LENGTH OF THREAD ON PIPE TO MAKE A TIGHT JOINT
t/1~~~
l
C
-i--(
t--
TIl'.
~ .r...
Nominal
Pipe
Size
Dimension
A
inches
Nominal
Pipe
Size
Dimension
A
inches
1/8
1/4
3-1/2
1-1/16
1/4
3/8
4
1-1/8
3/8
3/8
5
1-1/4
1/2
1/2
6
1-5/16
3/4
9/16
8
1-7/16
11/16
10
1-5/8
1-1/4
11/16
12
1-3/4
1-1/2
11/16
2
3/4
2-1/2
15/16
3
1
~J
~~~
DIMENSIONS DO NOT ALLOW FOR VARIATION
IN TAPPING OR THREADING
DRILL SIZES FOR PIPE TAPS
Nominal
Pipe
Size
Tap
Drill
Size in.
Nominal
Pipe
Size
Size in.
1/8
11/32
2
2-3/16
1/4
7/16
2-1/2
2-9/16
3/8
19/32
3
3-3/16
1/2
23/32
3-1/2
3-11/16
3/4
15/16
4
4-3/16
1
1-5/32
5
5-5/16
1-1/4
1-1/2
6
6-5/16
1-1/2
1-23/32
Tap
Drill
236
BEND ALLOWANCES
For 90 0 Bends in Low-Carbon Steel
Metal
Thickness
(t) in.
1/32
1/16
3/32
1/8
1/4
1/2
0.032
0.050
0.062
0.078
0.090
0.125
0.188
0.250
0.313
0.375
0.437
0.500
0.059
0.087
0.105
0.128
0.146
0.198
0.289
0.382
0.474
0.566
0.658
0.750
0.066
0.101
0.118
0.142
0.160
0.211
0.302
0.395
0.488
0.580
0.672
0.764
0.079
0.114
0.132
0.155
0.173
0.224
0.316
0.409
0.501
0.593
0.685
0.777
0.093
0.129
0.145
0.169
0.187
0.243
0.329
0.424
0.515
0.607
0.699
0.791
0.146
0.168
0.183
0.202
0.217
0.260
0.383
0.476
0.569
0.661
0.752
0.845
0.254
0.276
0.290
0.310
0.324
0.367
0.443
0.519
0.676
0.768
0.860
0.952
Bend Allowance Inches With Inside Radius (r) in.
w=a+b-
bend allowance
w=a+b+c-
w=a+b+c+d-
w=a+b+c+d+e-
(2 x bend allowance) (3 x bend allowance) (4 x bend allowance)
Note: w = developed width (length) of blank, t
r = inside radius of bend.
= metal thickness,
EXAMPLE: Carbon steel bar bent at two places.
The required length of a 1/4 in. thick bar bent to 90 degrees with 1/4 in inside
radius as shown above when the sum of dimensions a, band c equals 12 inches, is
12 - (2 x 0.476) = 11.048 inches
MINIMUM RADIUS FOR COLD BENDING:
The minimum permissible inside radius of cold bending of metals when bend lines
are transverse to the direction of the final rolling, varies in terms of the thickness,
t from 1-1/2 t up to 6 t depending on thickness and ductility of material.
When bend lines are parallel to the direction of the final rolling the above values
may have to be approximately doubled.
237
LENGTH OF STUD BOLTS
FOR FLANGES *
.-_______~~==~~--------------------------1-.--------_4~--,_
Height of Heavy Nut
(Equals nominal stud diam.)
Min. Thickness of Flange
A
/ 2 . Plus tolerance for
flange thickness
'Raised Face or Depth of Groove
L
L
1/16" See Note 5.
L = 2A + t + r
---L3.
"t" Minus Tolerance for Stud Length
L---~~~!!Sr.===]fC=::rr:::=-- 4.
"r" Rounding-off
1. Length of the stud bolts do not include the heights of the point.
(1.5 times thread pitch)
2. Plus tolerance of fig. thk's.
Sizes 18 in. & smaller 0.12 in.
Sizes 20 in. and larger 0.19 in.
3. Minus tolera'nce of stud length
For lengths up to 12" incl. 0.06 in.
For lengths over 12" to 18" incl. 0.12 in.
For lengths over 18" 0.25 in.
4. Rounding-off to the next larger 0.25 in. increment.
5. Gasket thickness for raised face, M & F and T & G flanges 0.12 in. For ring type
j oint see table on page 356 and take half of the dimensions shown, since in dimension "A" only half of the gasket thickness is included.
*Extracted from American National Standard:
ANSI B 16.5 - 1973 Steel Pipe Flanges and Flanged Fittings.
238
PRESSURE VESSEL DETAILING
IN THE PRACTICE THERE ARE SEVERAL DIFFERENT WAYS OF DETAILING
PRESSURE VESSELS. BY MAKING THE DRAWINGS ALWAYS WITH THE SAME
METHOD, CONSIDERABLE TIME CAN BE SAVED AND ALSO THE POSSIBILITIES OF
ERRORS ARE LESS. THE RECOMMENDED METHOD IN THE FOLLOWING PROVED
PRACTICAL AND GENERALLY ACCEPTED.
HORIZONTAL VESSELS
,-
,
$-C~-·-·~
End View
Ref. line
&
ELEVATION
Saddle
MISCELLANEOUS
DETAILS
1
GENERAL
SPECIFICATIONS
TITLE BLOCK
A. Select the scale so that all
openings, seams, etc., can
be shown without making
the picture overcrowded
or confusing.
B. Show right-end view if
necessary only for clarity
because of numerous connections, etc., on heads.
In this case it is not necessary to show on both
views the connections etc.,
in shell.
C. Show the saddles separately, if showing them on the
end view would overcrowd
the picture. On elevation
show only a simple picture of saddle and 1he
centerlines.
D. Locate davit.
E. Locate name plate.
F. Locate seams, after everything is in place on elevation. The seams have to
clear nozzles, lugs and
saddles.
G. Show on the elevation and
end view a simple picture
of openings, internaIs, etc.,
if a separate detail has to
be made for these.
H. Dimensioning on the elevation drawmg. All locations shall be shown with
tailed dimensions measured from the reference line.
The distance from ref. line
to be shown for one saddle
only. The other saddle
shall be located showing
the dimension between the
anchor bolt holes of the
saddles.
END VIEW
I. Two symbolic bolt holes
shown in flanges make
clear that the noles are
straddling the parallel lines
with the principal centerlines of vessel.
239
PRESSURE VESSEL DETAILING (cont.)
VERTICAL VESSELS
I-
I I
~ IJE--------E
Elevation
Orien tation
Base
MISCELLANEOUS DETAILS
I
rr.
General
SpecifiCations
Tille Block
A. Select the scale so that all
openings, trays, seams,
etc., can be shown without making the picture
overcrowded or confusing.
B. If the vessel diameter is
unproportionally small to
the length, draw the width
of the vessel in a larger
scale to have space enough
for all details.
C. The orientation is not a
top view, but a schematic
information about the location of nozzles, etc.
D. Show the orientation so
rotated that the downcomers on the elevation
can be shown in their true
position.
<i. Name
t
00
- :t.a-Seam Shell No_ 1,3
B.-_l. .....~_
ORIENTATION PLAN
E. Dimensioning.
All locations on the elevation
drawing shall be shown
with tailed dimensions
measured from the reference line.
F. Locate long seams, after
everything is in place on
elevation.
G. Mark vessel centerlines vi!
degrees: 0 0 , 90 0 , 180 0 ,
270 0 and use it in the
same position on all other
orientations.
240
PRESSURE VESSEL DETAILING (cont.)
00
Nozzle on
Top or Bottom
\
H. It is not necessary to show
internals on vessel orientation if their position is
clear from detail drawings
or otherwise.
N
®
J. Draw separate orientations
for showing different internals, lugs, etc. if there
is not space enough to
show everything on one.
K. For vessels with
sections, show 2
tions if necessary,
the upper section,
the lower section.
Seal Pan
Baffle
-->---~ Partition t
00
L. Two, symbolic bolt holes
shown in flanges make
clear that the holes are
straddling the lines parallel
with the principal centerlines of vessel.
270 0
90 0
Ladder Lugs
--I
...
conical
orientaone for
one for
L
'1
M. If there is a sloping tray,
partition plate, coil, etc.,
in the vessel, show in the
orientation the direction
of slope.
180 0
00
270 0
Lowest
Point of
Plate "D"
180 0
ORIENTATIONS
241
PREFERRED LOCATIONS
Of Vessel Components and Appurtenances
L
A. Anchor bolts straddle principal centerlines of
vessel.
B. Skirt access openings above base minimum to
clear anchor lugs, maximum 3'-0".
c.
E
I
Skirt vent holes as high as possible.
D. Name plate above manway or liquid level control, or level gauge. If there is no man way ,
5'-0" above base.
E. Lifting lugs - if the weight of the vessel is uniform, "E" dimension is equal .207 times the
overall length of vessel.
I
H
~J
F. Manway 3'-0" above top of platform - floor
plate.
G. Insulation ring must clear girth seam and shall
be cut out to clear nozzles, etc.
H. Insulation ring spacing 8 - 12 feet (approx.
length of _metal jacket sheet).
J. Girth seams shall clear trays, nozzles, lugs.
K. Long seams to clear nozzles, lugs, tray downcomers. Do not locate long seams behind downcomers. Seams shall be located so that visual
inspection can be made with all internals in
place.
Longitudinal seams to be staggered
1800 if possible.
o
L. Ladder and platform relation.
M. Davit and hinge to be located as the manway
is most accessible, or right hand side.
N. Ladder rung level with top of platform floor
plate. The height of first rung above base varies,
minimum 6", maximum 1'-6".
242
COMMON ERRORS
in detailing pressure vessels
A.
Interferences
Openings, seams, lugs, etc. interfere with each other. This can occur:
1. When the location on the elevation and orientation is not checked. The
practice of not showing openings etc. on the elevation in their true position,
may increase the probability of this mistake.
2. The tail dimensions or the distances between openings on the orientation
do not show interference, but it is disregarded, that the nozzles, lugs etc.,
have certain extension. Thus it can take place that:
a.
b.
c.
d.
e.
Skirt access opening does not clear the anchor lugs.
Ladder lug interferes with nozzles.
The reinforcing pads of two nozzles overlap each other.
Reinforcing pad covers seam.
Vessel-davit interferes with nozzles. This can be overlooked especially if
the manufacturer does not furnish the vessel-davit itself, but the lugs only.
f. Lugs, open~lgs, etc. are on the vessel seam.
g. There is no room on perimeter of the skirt for the required number of
anchor lugs.
Particular care should be taken when ladder, platform, vessel-davit etc., are
shown on separate drawings, or more than one orientations are used.
B.
Changes.
Certain changes are necessary on the drawing which are carried out on the elevation, but not shown 011 the orientation or reversed. Making changes, it is
advisable to ask the question: "What does it affect?"
For example:
The change of material affects:
Bill of material
Schedule of openings
General specification
Legend
The change of location affects:
Orientation
Elevation
Location of internals
Location of other components.
C.
Showing O.D. (outside diameter) instead of LD. (inside diameter) or reversed.
D.
Dimensions shown erroneously:
I'-O·instead of 102!.O'instead of 20·etc.
E.
Overlooking the requirement of special material
243
PRESSURE VESSEL DETAILING (cont.)
GENERAL SPECIFICATIONS
VESSEL TO BE CONSTRUCTED IN STRICT ACCORDANCE WITH THE LATEST
EDITION OF THE ASME CODE SECTION VIII. DIV. I. FOR PRESSURE VESSELS
AND IS TO BE SO STAMPED. INSPECTION BY COMMERCIAL UNION INSURANCE
CO. OF AMERICA.
DESIGN
MAX. A.
WORKING.
MAX. A.
N. &C.
HYDRO.
TEST
PRESSURE PSIG. @
TEMPERATURE of.
~~L-I-M-I-T-E-D-B-y------------~--------+---------4----------4--------~
a~------------------~--------~--------~---------+--------~
WIND PRESS. LBS/SQ. FT.
CORROSION ALLOW. IN.
z
ffi~~------------------~--------~-------------------+--------~
SEISMIC COEFFICIENT
~~2~~~:~r~~c
Q~E~R~E~C=T~IO~N~(-S-H-IP~P-I-N-G~)--~---------+~L~O~N~G~I=T~U~D~I~N~A~L-J~O~I~N~T~~------~
WEIGHT LBS.
EFFICIENCY
WEIGHT FULL
W/WATER LBS.
POST WELD HEAT
TREATMENT@1100oF
OPERATING WEIGHT LBS.
DATA NOT SHOWN ARE NOT FACTOR OF DESIGN
SA.
SA.
SHELL
HEAD
THK.
...
FLANGE
TYPE
THK
-SKIRT
~
a::
w
NOZZLE NECK
BASE
BOLTING
ANCH. BOLT
:IE
COUPLING
SADDLES
~
WELDED
FITTING
GASKET
PAINT
VESSELS
REQUIRED:
APPROX.
SHIPPING
WEIGHT LBS.
N
~
~
CHIP I.S. TO SOUND
CH. 1.1. TO SOUNO
METAL. WELD 'b'
METAL. WELD
'"0
:;0
tTl
CHIP I.S. TO SOUND
en
en
METAL. WELD 'b'
VIII
C
IX
:;0
tTl
Go·
a
f
,
iii
o
c3
f
"!
-
I CHIP 1.5. TO SOUND
METAL. WELD 'b'
GoO
~
i-~~~::::
CHIP 1.5. TO SOUND
0
IoC
~
<
tTl
en
en
tTl
Z r
Z 0tTl
C1 -i
rJJ
METAL. WELD
~
r
(;0·
\7
Z
SHOP NOTES
0
,-..
(')
0
1. Drill and Tap %" 0 Telltale hole in reinforcing
~
pacts.
2. Flange bolt holes to straddle principal centerlines
CHIP TO SOUNDJ
of vessel.
METAL. WELD
LONG & GIRTH SEAM
WELD DETAIL
•
HEAD TO SHELL
WELD DETAIL
3. Inside edges of Nozzle Necks shall be rounded.
The radius of roundness 1/8" min. or one-half the
wall thickness if the pipe wall is less than %".
~
-:......
Detailing openings as shown on the opposite page with data exemplified in the schedule of
openings below, eliminates the necessity of detailing every single opening on the shop
drawing.
'"t:I
~
tTl
til
til
c::
~
o""'C
~
<:
tTl
til
til
Z
tTl
Z
otTl
~
rJJ
t"'"
~
~
C
z
o
'6
o
::s
.....
~
c-/
DRAIN
N-I
11-/
INLET
MAR"
MAtVWAY
I
SERVICE
2" 6000~ CPLG.
n
W,N.
3 300*
18" 300"
ISIZEI RATING I
W.N.
IXH·lxH
lXH !XH.
TYPE
: 15CH.
IBORE,
• .3(}()
5Ye
.5"00 6~" ~A53-8
WALL
LG.
cff.... 1MIN.I v 1 - 1%"1"'11\1.
8" IMW.I /I 1/1/ I%"1 ""IN.
SA 5".JB
MAT"L.
NECK
24"xf2" ISA6"ls"70 110"
O.D .• THK.
RE'AD
MAT'L.
I g" I VI IIY 1%·jNll\I·I%"
0.5. I
1.5.
PROJ.
WELD
DETAIL
DWG.
• I b I C
WELD SIZE
N
SCHEDULE
OF
OPENINGS
~
Vl
246
TRANSPORTATION OF VESSELS
Shipping capabilities and limitations.
1.
TRANSPORTATION BY TRUCK.
The maximum size of loads which may be carried without special permits
a. weight approximately 40.000 lbs.
b. width of load 8 ft., 0 in.
c. height above road 13 ft., 6 in. (height of truck 4 ft., 6 in. to 5 ft., 0 in.)
d. length of load 40 ft., 0 in.
Truck shipments over 12 ft., 0 in. width require escort. It increases considerably the costs of transportation.
2.
TRANSPORTATION BY RAILROAD.
Maximum dimensions of load which may be carried without special routing.
a. width of load 10ft., 0 in.
b. height above bed of car 10 ft.-, 0 in.
With special routing, loads up to 14 ft., 0 in. width and 14 ft., 0 in. height
may be handled.
247
PAINTING
OF STEEL SURF ACES
PURPOSE
The main purpose of painting is the preservation of a steel surface. The paint retards
the corrosion 1., by preventing the contact of corrosive agents from the vessel surface and
2., by rust inhibitive, electro-chemical properties of the paint material.
The paints must be suitable to resist the effects of the environment, heat, impact,
abrasion and action of chemicals.
SURFACE PREPARATION
The primary requisite for a successful paint job is the removal of mill scale, rust, dirt,
grease, oil and foreign matter. Mill scale is the bluish-gray, thick layer of iron oxides
which forms on structural steel subsequent to the hot rolling operation. If the mill
scale is intact and adheres tightly to the metal, it provides protection to the steel, however, due to the rolling and dishing of plates, completely intact mill scale is seldom
encountered in practice.
If mill scale is not badly cracked, a shop primer will give long life in mild environments,
provided that the loose mill scale, rust, oil, grease, etc. are removed.
ECONOMIC CONSIDERATIONS
The selection of paint and surface preparation beyond the technical aspects is naturally
a problem of economics.
The cost of paint is normally 25-30% or less of the cost of painting a structure, thus the
advantage of using high quality paint is apparent. Sixty percent or more of the total
expense of a paint job lies in the surface preparation and the cost of preparation to
different degrees is varying in a proportion of 1 to 10-12. For example, the cost of
sandblasting is .about 10-12 times higher than that of the hand wire brushing. The cost
of surface preparation should be balanced against the increased life of the vessel.
SELECTION OF PAINT SYSTEMS
The tables on the following pages serve as guides to select the proper painting system
and estimate the required quantity of paint for various service conditions. The data
tabulated there have been taken from the Steel Structures Painting Council's specifications and recommendations.
Considering the several variables of painting problems, it is advisable to request the
assistance of paint manufacturers.
SPECIAL CONDITIONS
ABRASION
When the painting must resist abrasion, the good adhesion of the coating is particularly
important. For maximum adhesion, blast cleaning is the best and also pickling is satisfactory. Pretreatments such as hot phosphate or wash primer are excellent for etching
and roughening the surface.
Urethane coatings, epoxies and vinyl paints have very good abrasion resistance. Zincrich coating, and phenolic paints are also good. Oleoresinous paints may develop much
greater resistance by incorporation of sand reinforcement.
248
HIGH TEMPERATURE
Below temperatures of 500-600 0 F to obtain a good surface for coating, hot phosphate
treatment is satisfactory. Above 500-600 0 F a blast cleaned surface is desirable.
Recommended Paints:
Up to
200 200 300 300 700 -
250 F
300 F
400 F
550 F
800 F
Oil base paints limited period
An alkyd or phenolic vehicle
Specially modified alkyds
Colored silicones
Inorganic zinc coatings above 550 F
Black or Aluminum silicones
800 - 1200 F Aluminum silicones up to 1600-1800 F
Silicone ceramic coatings
CORROSIVE CHEMICALS
See tables I and V for the selection of paint systems.
THE REQUIRED QUANTITY OF PAINT
Theoretically, one gallon of paint covers 1600 square feet surface with 1 mil (0.001 inch)
thick coat when it is wet.
The dry thickness is determined by the solid (non volatile) content of the paint, which
can be found in the specification on the label, or in the supplier's literature.
If the content of solids by volume is, for example, 60%, then the maximum dry coverage
(spreading rate) theoretically will be 1600 x .60 = 960 square feet.
THE CONTENT OF SOLIDS OF PAINTS BY VOLUME %
Spec.
No.
1
2
3
4
5
6
a
9
11
Paint
Red Lead and Raw linseed Oil
Primer
Red Lead, Iron Oxide, Raw Linseed Oil and Alkyd Primer
Red Lead, Iron Oxide, and Fractionated Linseed Oil Primer
Extended Red Lead, Raw and
Bodied Linseed Oil Primer
Zinc Dust, Zinc Oxide, and Phenolic
Varnish Paint
Red Lead, Iron Oxide, and Phenolic
Varnish Paint
Aluminum Vinyl Paint
White (or Colored) Vinyl Paint
Red Iron Oxide, Zinc Chromate,
Raw Linseed Oil and Alkyd
Primer
%
Spec.
No.
96
12
~2
13
96
14
70
15
16
60
47
14
17
70
101
102
103
104
106
107
Paint
%
Cold Applied Asphalt Mastic
50
(Extra Thick Film)
Red or Brown One-Coat Shop
60
Paint
Red Lead, Iron Oxide & Linseed
96
Oil Primer
Steel Joist Steel Shop Paint
70
Coal Tar Epoxy-Polyamide Black
75
(or Dark Red) Paint
40
Aluminum Alkyd Paint
37
Black Alkyd Paint
57
Black Phenolic Paint
White or Tinted Alkyd Paint,
47 - 50
Types I, II, III, IV
13
Black Vinyl Paint
Red Lead, Iron Oxide and
60
Alkyd Intermediate Paint
In practice, especially with spray application, the paint never can be utilized at 100
percent. Losses due to overspray, complexity of surface (piping, etc.) may decrease the
actual coverage to 40-60%, or even more.
249
PAINTING
TABLE I, PAINT SYSTEMS
System
Number
SSPCPS
Paint and Dry Thickness, mils
See Table IV
CONDITION
1.01
Not
1.02
1.03
Condensation, chemical fumes, brine drippings and other extremely corrosive conditions are not present
Req'd
or
2.01
Steel surfaces exposed to the weather,
high humidity, infrequent immersion in
fresh or salt water or to mild chemical
atmospheres
6
Not
or
Req'd
Total
4th 5th ThickCoat Coat ness
14
(1.7)
14
(1.7)
I
(1.7)
104
(1.3)
14
104
(1.0)
104
104
104
(1.3)
104
104
(1.0)
104
104
104
C
104
A
(1.7)
C
(1.5)
D
(1.5)
B
(l.5)
E
8
2.04
4.0
5.0
4.0
4.0
4.0
(1.5)
104
( 1.5)
104
( 1.5)
104
104
5.0
104
( 1.0)
104
(1.0)
104
4.0
4.0
3.5
(1.5)
Steel surfaces exposed to alternate immersion, high humidity and condensation
3.00 or to the weather or moderately severe
chemical atmospheres or immersed in
fresh water
Immersion in salt water or in many chemical solutions, condensation, very severe
4.01
weather exposure or chemical atmospheres
4.02
Fresh water immersion, condensation,
very severe weather or chemical atmospheres
4.03
Complete or alternate immersion in salt
water, high humidity, condensation, and
exposure to the weather
4.04
3rd
Coat
(1.7)
1.06
2.03
2nd
Coat
2
1.05
2.02
1st
Coat
Condensation, or very severe weather exposure, or chemical atmospheres
4.05 Condensation, severe weather, mild chemical atmospheres
5,6,
8, or
10
1,2,
3, or
4
10
( 1.5)
5, or 6
( 1.5)
103
( 1.0)
5,6
or 103
G
G
9
9
5, or 6
5.5
( 1.5)
10
6
Not
Req'd
..
..
-3
or
8
6
or 8
6
or 8
Not
Req'd
3
H
(1.5)
H
G
9
H
H
fl.O
8
(1.5 )
4.0
9
(1.2)
9
9
G
(1.5)
F
F
9
4.0
0.02
6.03
7.01
8.01
9.01
10.01
10.02
8
6 or
8
3
( 1.5)
Not
Req'd
13
(1.0)
1.0
Not
Req'd
M
31
(wet)
31
(wet)
Not
Req'd
12
63
6
Not
Req'd
N
6
Not
Req'd
6 or
Dry, non corrosive environment, inside nomina
of buildings or temporary weather pro- cleantection
ing
I and
Longti me protection in sheltered or in2 or
accessible places, short term or temporary
3
protection in corrosive environments
Corrosive or chemical atmospheres, but
should not be used in contact with oils,
solvents, or other agents
Underground and underwater steel structures
Underground. underwater or for damp,
corrosive environments. Not recommended for potable water or for high temperature
• Four coats are recommended in severe exposures
7.0
0.5)
G
0.5)
10
Steel vessels and noating structures exposed to fresh or salt water, fouling water
and weather
4.5
1
G
0.01
4.0
or
5.0
6
G
(2.0)
G
J
J
7.0
G
L
K
6.25
G
G
G
G
G
63
N
(.5-2)
N
(31 )
(31 )
0
(15-18)
0
(25)
(8-15)
63100
P
35
"The dry film thickness of the wash coat 0,3-0,5 mils.
250
TABLE I, PAINT SYSTEMS (continued)
Paint and Dry Thickness, mils
See Table IV
System
Number
SSPCPS
1st
Coat
CONDITION
2nd
Coat
3rd
Coat
Total
4th 5th ThickCoat Coat ness
11.01
Fresh or sea water immersion, tidal and
splash zone exposure, condensation, burial in soil and exposure of brine, crude oil,
sewage and alkalies, chemical fumes, mists
12.00
High humidity or marine atmospheric exposures, fresh water immersion. With
proper topcoating in brackish and seawater immersion and exposure to chemical acid and alkali fumes
Zinc-rich coatings comprise a number of
different commercial types such as;
chlorinated rubber, styrene, epoxies,
polyesters, vinyls, urethanes, silicones,
silicate esters, silicates, phosphates.
13.00
Industrial exposure, marine environment
fresh and salt water immersion, and areas
subject to chemical exposure such as acid
and alkali.
Epoxy Paint System
6
or
10
Not
Req'd
16
16
(16)
(16)
32
T ABLE III, PRETREATMENT SPECIFICATIONS
Reference
to
Table I
Title and Purpose
WETTING OIL TREATMENT
Specification
Number
SSPC ..PT 1-64
Saturation of the surface layer of rusty and
scaled steel with wetting oil that is compatible
with the priming paint, thus improving the adhesion and performance oT the paint system to be
applied.
2
COLD PHOSPHATE SURFACE TREATMENT
SSPC-PT 2-64
Converting the surface of steel to insoluble salts
of phosphoric acid for the purpose of inhibiting
corrosion and improving the adhesion and performance of paints to be applied.
3
BASIC ZINC CHROMATE-VINYL BUTYRAL
WASHCOAT (Wash Primer)
SSPC-PT 3-64
Pretreatment which reacts with the metal and at
the same time forms a protective vinyl film which
contains an inhibitive pigment to help prevent
rusting.
4
HOT PHOSPHATE SURFACE TREATMENT
Converting the surface of steel to a heavy crystaline layer of insoluble salts of phosporic acid for
the purpose of inhibiting corrosion and improving
the adhesion and performance of paints to be
applied.
SSPC-PT 4-64
251
PAINTING
TABLE Il,SURFACE PREPARATION SPECIFICATIONS
Reference
to
Table I
Title and Purpose
SOLVENT CLEANING
Specification
Number
SSPC-SP 1-63
Removal of oil, grease, dirt, soil, saits, and contaminants with solvents, emulsions, cleaning compounds, or steam.
2
HAND TOOL CLEANING
SSPC-SP 2-63
Removal of loose mill scale, loose rust, and loose
paint by hand brushing, hand sanding, hand scraping, hand chipping or other hand impact tools, or
by combination of these methods.
3
POWER TOOL CLEANING
SSPC-SP 3-63
Removal of loose mill scale, loose rust, and loose
paint with power wire brushes, power impact
tools, power grinders, power sanders, or by combination of these methods.
4
FLAME CLEANING OF NEW STEEL
SSPC-SP 4-63
Removal of scale, rust and other detrimental
foreign matter by high-velocity oxyacetylene
flames, followed by wire brushing.
5
WHITE METAL BLAST CLEANING
SSPC-SP 5-63
Removal of all mill scale, rust, rust-scale, paint or
foreign matter by the use of sand, grit or shot to
obtain a gray-white, uniform metallic color surface.
6
7
COMMERCIAL BLAST CLEANING
SSPC-SP 6-63
Removal of mill scale, rust, rust-scale, paint or
foreign matter completely except for slight shadows, streaks, or discolorations caused by rust,
stain, mill scale oxides or slight, tight residues of
paint or coating that may remain.
BRUSH-OFF BLAST CLEANING
SSPC-SP 7-63
Removal of all except tightly adhering residues
of mill scale, rust and paint by the impact of
abrasives. (Sand, grit or shot)
8
PICKLING
SSPC-SP 8-63
Complete removal of all mill scale, rust, and rustscale by chemical reaction, or by electrolysis, or
by both. The surface shall be free of unreacted
or harmful acid, alkali, or smut.
10
NEAR-WHITE BLAST CLEANING
Removal of nearly all mill scale, rust, rust-scale,
paint, or foreign matter by the use of abrasives
(sand, grit, shot). Very light shadows, very slight
streaks, or slight discolorations caused by rust
stain, mill scale OXides, or slight, tight residues of
paint or coating may remain.
SSPC-SP 10-63T
252
PAINTING
T ABLE IV. P AIN:rS
Reference
to
Table I
1
2
3
4
5
6
8
9
11
12
13
14
15
16
102
103
104
106
107
Material
Red Lead and Raw Linseed Oil Primer
Red Lead, Iron Oxide, Raw Linseed Oil and
Alkyd Primer
Red Lead, Iron Oxide, and Fractionated Linseed
Oil Primer
Extended Red Lead, Raw and Bodied Linseed Oil
Primer
Zinc Dust, Zink Oxide, and Phenolic Varnish Paint
Red Lead, Iron Oxide, and Phenolic Varnish Paint
Aluminum Vinyl Paint
White (or Colored) Vinyl Paint
Red Iron Oxide, Zinc Chromate, Raw Linseed Oil
and Alkyd Primer
Cold Applied Asphalt Mastic (Extra Thick Film)
Red or Brown One-Coat Shop Paint
Red Lead, Iron Oxide & Linseed Oil Primer
Steel Joist Shop Paint
Coal Tar Epoxy-Polyamide Black (or Dark Red) Paint
Black Alkyd Paint
Black Phenolic Paint
White or Tinted Alkyd Paint, Types I, II, III, IV
Black Vinyl Paint
Red Lead, Iron Oxide and Alkyd Intermediate Paint
Number
1-64TNo.
1
2-64 No.
2
3-64T No.
3
tfl
4-64TNo.
5-64TNo.
6-64TNo.
8-64 No.
9-64 No.
4
Z
0
--
5
E-o
6 -<
8 u
9 ~
u
11-64T No. 11 ~
12-6.J No. 12 Q.,
13-64 No. 13 tfl
14-64T No. 14 u
15-68T No. 15 Q.,
16-68T No. 16 ~
102-64 No.1 02
103-64T No.1 03
104-64 No.1 04
106-64 No. 106
107-64T No.1 07
-.------r-----~------------~~--------------~~~~~~~--~
A
B
C
D
E
F
G
H
I
J
K
L
M
N
o
P
Paint; Red-Lead Base, Ready-Mixed
Type I red lead-raw and bodied linseed oil
Type II red lead, iron oxide, mixed pigmentalkyd-linseed oil
Type III red lead alkyd
Primer; Paint; Zinc Chromate, alkyd Type
Paint; Zinc Yellow-Iron Oxide Base, Ready
Mixed, Type II-yellow, alkyd
Paint; Outside, White, Vinyl, Alkyd Type
Primer; Vinyl-Red Lead Type
Vinyl Resin Paint
Paint; Antifouling, Vinyl Type
Paints; Boottopping, Vinyl-Alkyd, Bright Red
Undercoat and Indian Red Finish Coat
Enamel, Outside, Gray No. 11 (Vinyl-Alkyd)
Enamel, Outside, Gray No. 27 (Vinyl-Alkyd)
Compounds; Rust Preventive
Coal Tar Enamel and Primers
Coal Tar Base Coating
Coating, Bituminous Emulsion
TT-P-86c
TT-P-86c
TT-P-86c
TT-P-645
II
•
::s-< .~....=
1-0
C':I
o S
C':I
<'U
::s~
~
g~'-0
MIL-P-15929B CI')
o...::s
C':I
MIL-P-16738B "; ~
1-0 ::s
MIL-P-15929B Q)~
~
II
VR-3
~~
MIL-P-15931A II >
~
~
~ d
MAP-44
>:
MIL-E-15935B ;"1:1
.~ -<
MIL-E-15936B :-= Q)
52-MA-602a
::s\I .S+=l
MIL-P-15147C
MIL-C-18480A i ~
MIL-C-15203c
·s
...J·c
253
PAINTING
TABLE V, CHEMICAL RESISTANCE OF COATING MATERIAL
'"
;::I
~
o
t::
or;;
>. <I)
>< ..
0
c.~
o
~o
Acetaldehyde . . . . . . . .
Acetic acid, 10% ......
Acetic acid, glacial . . . . .
Acetone . . . . . . . . . . . .
Alcohol, amyl . . . . . . . .
Alcohol butyl, normal ...
Alcohol, ethyl . . . . . . . .
Alcohol, isopropyl . . . . .
Alcohol, methyl . . . . . . .
Aluminum chloride . . . . .
Aluminum sulphate. . . . .
Ammonia, liquid . . . . . .
Ammonium chloride ....
Ammonium hydroxide ..
Ammonium nitrate . . . . .
Ammonium sulphate ....
Aniline . . . . . . . . . . . . .
Benzene . . . . . . . . . . . .
Boric acid. . . . . . . . . . .
Butyl acetate. . . . . . . . .
Calcium chloride. . . . . . .
Calcium hydroxide . . . . .
Calcium hypochlorite ...
Carbon disulphide . . . . .
Carbon tetrachloride ....
Chlorine gas . . . . . . . . .
Chlorobenzene . . . . . . . .
Chloroform . . . . . . . . . .
Chromic acid, 10% .....
Chromic acid, 60% .....
Citric acid. . . . . . . . . . .
Copper sulphate . . . . . . .
Diethyl ether. . . . . . . . .
Ethylene glycol . . . . . . .
Ferric chloride. . . . . . . .
Ferric sulphate . . . . . . . .
Formaldehyde, 40% ....
Formic acid, 20%. . . . . .
Formic acid, conc . . . . . .
Gasoline . . . . . . . . . . . .
Glycerine . . . . . . . . . . .
Hydrochloric acid, 10%. .
Hydrochloric acid, 30% ..
Hydrochloric 4cid, conc ..
Hydrofluoric acid, 10%. .
Hydrofluoric acid, 40% . .
1 2 1 1 1 1 3 223 323
1 211 1 143 344 3 4
1 2 1 1 1 143 344 3 4
3 331 1 1 4 4 4 4 4 3 4
1 1 1 1 1 143 333 2 3
1 111 1 1 3 2 2 2 2 1 3
1 111112111112
1 I I I 1 121 1 1 1 1 2
1 111112111112
1 112224113313
1 111114112212
1 11322313313
1 111113113312
1 11322313313
1 1 1 1 1 131 133 1 2
1 1 1 1 1 131 133 1 2
4 4 2 4
2 3 2 244
4 441 1 133 344 3 4
1 111111111111
1 I I I 1 1 344 3 3 1 3
1 111112112212
1 1 121 121 122 1 2
1 2 2 3 224 1 } 221 3
4 441 1 144 444 3 4
4 441114444444
1 224 444 2 1 443 4
4 441114444444
4 441 1 144 444 4 4
2 224 3 342 244 2 4
2 224 3 3 4 2 244 2 4
1 111112112212
1 111111111111
4 441 1 144 4 4 444
1 1 1 1 1 121 1 1 1 1 2
1 111 1 131 133 1 3
1 1 1 1 1 121 122 1 2
1 111113112213
1 1 1 1 1 131 122 1 3
1 111113112213
4 4 1 1 1 121 1 4 4 2 4
1 1 1 1 1 121 1 1 1 1 2
1 1 1 1 1 131 133 1 3
1 221 1 131 133 1 3
1 221 113 1 133 1 3
1 2 1 1 1 1 3 2 2 2 2 1 2
1 2 1 1 1 1 322 221 3
254
PAINTING
TABLE V, CHEMICAL RESISTANCE OF COATING MATERIAL
(continued)
u
.....u
Hydrofluoric acid, 75% .. 1
Hydrogen peroxide, 3% .. 1
Hydrogen perioxide, 30%. 2
Hydrogen sulphide ..... 1
Hypocholorous acid . . . . 1
Kerosene . . . . . . . . . . . 4
Lubricating oil . . . . . . . . 4
Magnesium sulphate .... 1
Methyl ethyl ketone .... 1
Mineral oil . . . . . . . . . . 4
Nitric acid, 5% . . . . . . . . 1
Nitric acid, 10% . . . . . . 2
Nitric acid, 40% . . . . . . . 2
Nitric acid, conc . . . . . . . 3
Nitrobenzene . . . . . . . . . 4
Oleic acid . . . . . . . . . . . 3
Oxalic acid . . . . . . . . . . 1
Phenol, 15-25% . . . . . . .
Phenol. . . . . . . . . . . . .
Phosphoric acid, 10% . . . 1
Phosphoric acid, 60% ... 1
Phosphoric acid, conc. . . 1
Potassium alum . . . . . . . 1
Potassium hydroxide, 20% 1
Potassium hydroxide, 95% 1
Potassium permanganate . 2
Potassium sulphate ..... 1
Sea water . . . . . . . . . . . 1
Sil ver ni tra te . . . . . . . . . 1
Sodium bisulphate ..... 1
Sodium carbonate. . . . . . 1
Sodium chloride. . . . . . . 1
Sodium hydroxide, 10% . 1
Sodium hydroxide, 20% . 1
Sodium hydroxide, 40% . 1
Sodium hypochlorite.... 1
Sodium nitrate . . . . . . . . 1
Sodium sulphate. . . . . . . 1
Sodium sulphite . . . . . . . 1
Sulphur dioxide . . . . . . . 1
Sulphuric acid, 10% .... 1
Sulphuric acid, 30% .... 1
Sulphuric acid, 60% .... 1
Sulphuric acid, conc .... 2
Toluene . . . . . . . . . . . . 4
Trichloroethylene ..... 4
2
1
2
1
2
4
4
1
1
4
1
2
2
3
4
3
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
4
4
1
1
1
1
1
1
1
1
2
1
1
1
2
2
4
2
1
3
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
4
4
1
3
3
1
4
1
1
1
1
1
4
4
4
4
1
1
1
I
1
2
2
1
3
1
1
1
1
1
2
2
3
3
1
1
1
1
1
2
2
1
3
1
1
1
1
1
2
2
3
3
1
1
1
1
32
3 1
3 2
2 1
4 1
2 1
2 1
2 1
4 4
2 1
4 1
4 2
4 2
4 2
3. 3
3 2
2 1
2
1
2
1
1
1
1
1
4
1
1
2
2
2
3
2
1
2
3
3
2
3
4
4
2
3
4
3
3
4
4
4
4
2
2
3
3
2
3
4
4
2
3
4
3
3
4
4
4
4
2
2
1
3
1
1
2
2
1
I
2
1
1
2
2
3
2
1
1
1
1
1
4
4
3
1
1
1
1
4
1
4
4
4
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
2
2
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
2
2
3
1
1
1
1
1
1
1
1
1
1
3
3
3
2
4
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
4
3
3
3
2
2
2
3
2
1
1
2
2
1
1
2
2
3
2
2
2
2
2
3
3
3
4
4
3
3
3
2
2
2
3
2
1
1
2
2
1
1
2
2
3
2
2
2
2
2
3
3
3
4
4
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
4
3
2
1
2
3
4
1
4
4
4
4
2
2
2
2
3
3
3
3
3
4
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
4
3
4
4
2
4
4
4
2
3
4
3
3
4
4
4
4
2
4
4
3
3
3
2
3
3
4
2
1
2
2
4
1
3
3
3
4
2
2
2
2
2
3
3
3
4
4
c<:t
.....
s:::
o
u
.....
u
...
:a
...o
~
.5
o
U
bll
I:
:a.!!l
:c::s
~
255
CHECK LIST FOR INSPECTORS
QC
I. Codes and Addenda ..............................................................................
2. Drawings:
a) All info & details required by QC Manual shown on drawing .......
b) Heads correctly identified ...............................................................
c) All metal correctly identified ..........................................................
d) Name plate facsimilie stamped correctly:
MAWP, MDMT and RT .................................................................
e) Approval by fabricator (on drawing) ..............................................
f) Revisions or metal substitution shown and approved .....................
3. Bill of Material:
a) All material identified as SA or SB ................................................
b) Requirements of UCS 79 (d) specified were applicable .................
c) Required material test reports specified .........................................
d) Shop order, serial number, andlor job number shown ....................
e) Material revision or substitution approved
and shown when applicable ............................................................
4. Calculations:
a) Dimensions used match drawing ....................................................
b) Correct stress values and joint efficiencies (S & E) used ...............
c) Correct formula & dimensions used for heads ...............................
d) Do nozzle necks comply with UG-45? ...........................................
e) Required reinforcement calculations available for all openings .....
f) Special flange or structural loading calculations available ............
g) Identification with S/O or SIN and approved by fabricator ............
h) External design pressure correct - template
calculations & template available ...................................................
i) MA WP & MDMT matches drawing and specifications.
MDMT correct for materials used (UCS-66, UHA-51) .................
5. Purchase Orders:
a) Is job number shown (when applicable)? .......................................
b) Correct specification (SA or SB) used ............................................
c) USC 79(d) & UG 81 requirements specified as applicable ............
d) Material Test Reports requested .....................................................
e) Is material ordered identical to Bill of Material
or drawing requirements? ...............................................................
6. Welding:
a) Are correct WPS(s) shown on drawings? .......................................
b) Are complete weld details for all welds shown on drawing? .........
c) Are copies ofWPS(s) available to shop
supervisor for instruction? ..............................................................
AI
256
CHECK LIST FOR INSPECTORS (continued)
QC
d) Is a Welder's Log and Qualification Directory
kept up-to-date and available? ........................................................
e) Are WPS, PQR, & WPQ forms correct and signed? ......................
f) Are welders properly qualified for thickness, position, pipe
diameter and welding with no backing (when required)? ...............
g) Is sub-arc flux, electrodes and shielding gas(es) used the
same as specified on applicable WPS? ...........................................
h) Do weld sizes (fillet & butt weld reinforcement)
comply with drawing and Code requirements? .............................. ,
i) Is welder identification stamped or recorded per
QC Manual and/or Code requirements? ..........................................
7.
Non-Destructive Examination & Calibration:
a) Are SNT-TC-I A qualification records with current visual
examination available for all RT technicians used? .......................
b) Do film reader sheets or check off records show film
intemretation by a SNT- t~· LevelIorIfexaminer or interpreter? ..................................................................................
c) Are the required number of film shots in the proper
locations for the joint efficiency and welders used
(UW-II, 12, & 52)? ........................................................................
d) Is an acceptable PT and/or MT procedure and personnel
qualified and certified in accordance with Sec. VIII,
Appendix 6 or 8 available? .............................................................
e) Is the PT material being used the same as
specified in the PT procedure? ........................................................
f) Do all radiographs comply with identification,
density, penetrameter, and acceptance requirements
of Sect. VIII and V? ........................................................................
g) For B31.1 fabrication, is a visual examination
procedure and certified personnel available? .................................
h) Are tested gases marked or identified and
calibrated as stated in QC Manual? ................................................
i) Is a calibrated gage size per UG-l 02 available
for demo vessel? ..............................................................................
ABBREVIA TIONS:
Authorized Inspector
AI
Maximum Allowable Working Pressure
MAWP
Maximum Design Metal Temperature
MDMT
Quality Control
QC
Radiographic Examination
RT
Serial Number
SIN
SIO
Shop Order
Welding Procedure Specification
WPS
Al
257
PART II.
GEOMETRY AND LAYOUT OF PRESSURE VESSELS
1.
Geometrical Formulas .................................................................................. 258
2.
Geometrical Problems and Construction ................................................... 268
3.
Solution of Right Triangles ........................................................................ 270
4.
Optimum Vessel Size ................................................................................... 272
5.
Flat Rings Made of Sectors...... .................. .................................. .............. 274
6.
Frustum of Concentric Cone...................................................................... 276
7.
Frustum of Eccentric Cone......................................................................... 278
8.
Bent and Mitered Pipes................ ................................................ .............. 280
9.
Intersections ............................................................................................... 281
10. Drop at the Intersection of Vessel and Nozzle .......................................... 291
11. Table for Locating Points on 2: 1 Ellipsodial Heads .................................. 293
12. Length of Arcs............................................................................................ 297
13. Circumferences and Areas of Circles ......................................................... 300
14. Appurtenances ........................................................................................... 312
258
GEOMETRICAL FORMULAS
(See examples on the facing page.)
SQUARE
A
Area
A
a2
d
1.414 a
2
d
A
a
2
0,7071 d or a=-fA
RECTANGLE
A
Area
A
axb
d
-Va2 +b2
a
-V d 2 - b2 or a =4
b
-V d 2
- a2 or b =..4.
a
PARALLELOGRAM
A
Area
A
axb
A
a
b
A
b
a
RIGHT-ANGLED TRIANGLE
Area
A
axb
A
-2-
a
b
c
-V c2 -b2
-Vc2 -a2
-Va2 +b2
ACUTE ANGLED TRIANGLE
A
Area
cxh
A
-2A
s
-V s (s - a) X (s - b)
\Ii (a + b + c)
X (s -
c)
OBTUSE ANGLED TRIANGLE
Area
A
bxh
A
2
A
-V s (s - a)
s
\Ii(a+b+c)
X (s - b) X (s -
c)
259
EXAMPLES
(See formulas on the facing page.)
SQUARE
Given:
Find:
Side
Area
Diagonal
Area
a = 8 in.
A·- a2 = 82 = 64 sq. in.
d = 1.414 a = 1.414 x 8 = 11.312 in.
A = ~ = 11.~122 = 64 sq. in.
Side a = 0.7071 d = 0.7071 x 11.312 = 8 in.
Side a =
RECfANGLE
Given:
Side
Area
Find:
Diagonal
a
=
{64 = 8 in.
a = 3 in., and b = 4 in.
A = a x b = 3 x 4 = 12 sq. in.
d = -Yal + b2 = -Y32 + 42 = -Y9 + 16 =
Side a =
t J
Side b=
~
=
=
m = 5 in.
= 3 in.
~2=
4 in.
PARALLEWGRAM
Given: Height a = 8 in., and the side b = 12 in.
Area A = a x b = 8 x 12 = 96 sq. in.
Find:
Height
-t = i~ = 8 in.
= 4= 9 6 = 12 in.
8
a =
Side b
RIGHT ANGLED TRIANGLE
Given:
Side a = 6 in., and side b = 121n.
axb
6x8
.
Find:
Area A = -2- = -2- = 24 sq, Ill.
Sidee=-Ya2+b2 = ~ = ~ = -VI00 = lOin.
Sidea=-Ve2 _b 2 = -YI02- 82 = -Y100-64 = -{36 =6in.
Side b = -Ye2 - a2 = -V102 - 62 = -Y100 - 36 =
-%4 = 8 in.
ACUTE ANGLED TRIANGLE
Side a = 6 in., side b = 8 in:; and side e = 10 in.
Given:
Area s = ~(a+b+e) = ~(o+8+ 10) = 12
Find:
A = -vs(s-a)x(s-b)x(s-e)=
-Y12 (12 - 6) x (12 - 8) x (12 -10) =24 sq. in.
OBTUSE ANGLED TRIANGLE
Given:
Find:
Side
Area
a = 3 in., side b = 4 in., and side e = 5 in.
s=~(a+b+e)=~(3+4+5)=6
A = -ys(s-a)x(s-b)x(s-e)=
-Y6 (6 - 3) x (6 - 4) x (6 - 5) =
f36 = 6 sq. in.
260
GEOMETRICAL FORMULAS
(See examples on the facing page.)
RIGHT TRIANGLE WITH 2 45° ANGLES
A = Area
A =a
2
2
A = 1.414a
h=0.7071a
a= 1.414h
EQUILATERAL TRIANGLE
A = Area
A=axh
2
h=0.886a
a=1.155h
TRAPEWID
A
=
Area
A = (a+b)h
2
REGULAR HEXAGON
A = Area
R = Radius of circumscribed circle
r = Radius of inscribed circle
A = 2.598 a 2 = 2.598 R2 = 3.464r2
R=a=1.155r
r = 0.866 a = 0.866R
a=R=1.155r
REGULAR OCTAGON
A = Area
R = Radius of circumscribed circle
r = Radius of inscribed circle
A = 4.828 a 2 = 2.828 R2 = 3.314r2
R = 1.307 a = 1.082r
r = 1.207 a = 0.924R
a = 0.765 R = 0.828r
REGULAR POLYAGON
A = Area
n = Number of sides
360 0
oc
13= 1800 = oc
n-
A
2
=n a
r
R = ...Jr2 + a
2
4
= ...JR2 - a; a = 2...JR2- r2
261
EXAMPLES
(See formulas on the facing page.)
RIGHT TRIANGLE WITH 2 45° ANGLES
Given:
Side
Find:
Area
8 in.
a2
A = 2=
Side
b= 1.414
a
=
"4
2- ="2
= 32 sq. in.
Q2
a=1.414x8=11.312in.
h = 0.7071 a=0.7071 x8 = 5.6568 in.
EQUILATERAL TRIANGLE
Given:
Side
Fine:
A = 8 in.
h = 0.866 x a = 0.866 x 8 = 6.928 in.
Area
= 27712
.
A = a 2x h = 8 x 26.928 = .5.5A24.
2
.
sq. m.
TRAPEZOID
Given:
Side
Find:
Area
= 4 in., b = 8 in., and height h = 6 in.
(a+b)h
(4+8)x6
.
A=
2
=
2
= 36 sq. m.
a
REGULAR HEXAGON
Given:
Side
a = 4 in.
Find:
Area
A = 2.598 x a = 2.598 x 4 = 41.568 sq. m.
2
2
•
r = 0.866 x a= 0.866 x 4 = 3.464 in.
R= a = 1.155r = 1.155 x 3.464 =4in.
REGULAR OCTAGON
Given:
Find:
R = 6 in., radius of circumscribed circle
2
2
Area
A = 2.8 28 R = 2.828 x 6 = 101.81 sq.
Side
a = 0.765
•
m.
R = 0.765 x 6 = 4.59 in.
REGULAR POLYGON
Given:
Number of sides n = 5, side a= 9.125 in.
Find:
Radius of circumscribed circle, R = 7.750
_12(ii _I
2 9.125 2
•
r = -'1R -"4 = -'17.750 --4- = 6.25 m.
Area
A= nra=
5x6.252 x9.125 = 14258
.
2
. sq. m.
262
GEOMETRICAL FORMULAS
(See examples on the facing page.)
CIRCLE
A
Area
A
r 2 n=r2 x3.1416=d2 x 0.7854
C = Circumference
C =dxn=dx3.1416
Length of arc for angle oc = 0.008727 d x ex:
a
CIRCULAR SECTOR
A
Area
a = Arc
ex: = Angle
2
A = r n x 360
a
r x oc x 3.1416
180
ex: = 57.297xa
r
r = 2A
a
CIRCULAR SEGMENT
A
Area
ex: = Angle
c = Cord
A
Area of sector minus area of triangle
h
see table on page 290
c
see table on page 290
ELLIPSE
A = Area
P = Perimeter
A = Jrxa)(b=3.1416xaxb
An approximate formula for perimeter:
a
P = 3.1416 -V2 (a 2 + b2)
ELLIPSE
Locating points on ellipse
a
C = Ratio of minor axis to major axis
b
-Va2 - 2C x y2)
x
a
y
N =
(lj-Y,
where
N = The required number of holes (diameter d) of which
total area equals area of circle diameter D.
263
EXAMPLES
(See formulas on the facing page.)
CIRCLE:
Given:
Radius r = 6 in.
Find Area:
A = r2 x n = 6 2 x 3.1416 = 113.10 sq. in. or
A = J2 x 0.7854 = 122 x 0.7854 = 113.10 sq. in.
Circumference C= d x n = 12 x 3.1416 = 37.6991 in.
The length of arc for an angle, if IX = 60°
Arc = 0.008727 d x IX = 0.008727 x 12 x 60 = 6.283 in.
CIRCULAR SECTOR:
Given:
Radius r = 6 in.
Angle = 60°
.
Find Area:
A = r2 n x ~
360 -- 62 n x 60
360 -- 18 .85 sq. m.
Arc a = r x ex 1~~·1416 = 6 x 60 1~03.1416 = 6.283 in.
Angle
ex = 57,296 x a = 57,296 x 6.283
CIRCLULAR SEGMENT:
Radius r = 6 in.
Given:
Find Area: A
Area of sector
r2
Jr
=
600
6
r
Angle ex = 90°
x360=6 2 x3.1416x
~~O
= 28.274 sq. in.
Minus area oftriangle = 18.000 sq. in.
Area of segment A = 10.274 sq. in.
Chord
c = 2r x sin ~ = 2 x 6 x sin 90= 2 x 6 x 0.7071 = 8.485 in.
2
ELLIPSE:
Given: Half axis,
a
Find:
A =
Area
Perimeter
=
8 in. and
b = 3 in.
a x b = 3.1416 x 8 x 3 = 75.398 in.
P = 3.1416"2(a2 +b 2 ) =3.1416"2(8 2 +3 2 ) =
7t X
3.1416 "146 = 37.96 in.
ELLIPSE:
Given: Half-axis,
Find:
y=
~~2
i
a = 8 in. and b = 4 in., then C = [;= = 2, x = 6 in.
2 2
= ...)8
6 = ~ =
~= 2.6457 in.
"9=
2
X= ~a2 - (2C xy2)
=..J8 2- (2 x 2 x 2.64572) = ~64 - 4 x 7 =....f36 =6 in.
EXAMPLE:
How many V4 in. ¢ holes have same areas as a 6 in. diam. pipe?
N= (D/d)2
(6/0.25)2 242 576 holes
Area of6 in. ¢pipe = 28,274 in. 2
Area of576, V4 in. ¢ holes = 28,276 in. 2
=
= =
264
GEOMETRICAL FORMULAS
(See examples on the facing page.)
CUBE
~
V= Volume
V= a 3
a =
,
,
tv
SQUARE PRISM
01;;>
V = Volume
V = axbxe
V
a
Q
V
a=liC
V
b=
ae
V
e=aJi
PRISM
V = Volume
A = Area of end surface
V = h x A
This formula can be applied for any shape of end surface if
h is perpendicular to end surface.
CYLINDER
V = Volume
S = Area of cylindrical surface
V = 3. 1416 x r2 x h = 0.785 x d 2 x h
S = 3.1416 x d x
h
CONE
V = Volume
2 S = Area of conical surface
V = 3. 1416 x r x h = 1.0472 x r2 x h
3
h
I
d
e
~r2
S
3.1416 re = 1.5708 de
x h2
FRUSTUM OF CONE
V = Volume
S = Area of conical surface
V = 0.2618h (D2 + Dd + d 2)
a = R-r
e = ~a2 + h2
S = 1.5708e(D+d)
265
EXAMPLES
(See formulas on the facing page.)
CUBE
Given:
Side
Find:
Volume V = a 3
a = 8 in.
= 83 = 512 cu. in.
a
=
~512
SQUARE PRISM
a
Given: Side
=
8 in., b = 6 in., and c
Side
Find:
Volume V = a x b x c x
Side
a =~
=
V
c =-axb
=--
bxc
PRISM
Given: End surface
Find:
=
=
4 in.
x 6 x 4 = 192 cu. in.
192 = 8 in.· b =~= 192 = 6 in.
6x4
' a x e 8x4
192 =
4 in.
8x6
and h
6 in.,
Volume V = 3.1416 x
r2
and h = 8 in.
= 8 x 12 = 96 cu. in.
V= h x A
r
=8
A = 12 sq. in.,
Volume
CYLINDER
Given:
Find:
8 in.
=
=
x h
12 in.
=
3.1416 x 6 2 x 12 = 1357.2 cu. in.
Area of Cylindrical Surface: S = 3.1416 x d x h=
CONE
Given:
Find:
r
=
3.1416 x 12 x 12 = 452.389 sq. in.
=
6 in.,
and h = 12 in.
Volume V = 1.0472 x
c
= ~r2 + h 2
Area of Conical Surface: S
=
r2
=
x h = 1.0472 x 6 2 x 12 = 452.4 cu. in.
-/36 + 144 = -V180
=
13.416 in.
3.1416 x r x c =
= 3.1416 x 6 x 13.416 = 252.887 sq. in.
FRUSTUM OF CONE
Given: Diameter D
=
24 in., and d= 12 in., h = 10.375 in.
Find:
=
0.2618 h (D2 + Dd = d2) =
Volume
V
= 0.2618 x 10.375 (242 + 24 x 12 + 122)
Surface:
=
2737.9 cu. in.
S = 1.5708 c (D + d) = 1.5708 x 12 (24 + 12) =678.586 sq. in.
266
GEOMETRICAL FORMULAS
(See examples on the facing page.)
SPHERE
V = Volume
A = Area of Surface
3
V= 4lrxr"3= lrxd
4.1888 r3 = O.5236d 3
3
6
A = 4lr x r2 = lrd2
SPHERICAL SEGMENT
V = Volume
A = Area of Spherical Surface
V = 3.1416 x m2(r-~)
A = 2lr x r x m
SPHERICAL ZONE
V = Volume
V = O.5236h
A = Area of Spherical Surface
(3C:
4
-t-
3C} + h 2 )
4
A = 2lr rh = 6.2832 rh
TORUS
R
r
V = Volume
A
Area of Surface
V = 19.739 Rr2
2.4674 Dd2
39.478Rr
A
9.8696Dd
See tables for volume and surface of cylindrical shell,
spherical, elliptical and flanged and dished heads, beginning
on page 416.
267
EXAMPLES
(See formulas on the facing page.)
SPHERE
Given: Radius
Find:
Volume
or
Area
or
r =
V =
V =
A =
A =
6 in.
4.1888 r3 = 4.1888 x 216 = 904.78 cu. in.
0.5236 d 3 = 0.5236 x 1728 = 904.78 cu. in.
4 lCr 2 = 4 x 3.1416 x 6 2 = 452.4 sq. in.
lCd 2 = 3.1416 x 122 = 452.4 sq. in.
SPHERICAL SEGMENT
Given:
Radius r = 6 in. and m = 3 in.
Find:
Volume V = 3.1416m 2 (r-'3)=3.1416x3 2
Area
(6-~)=141.37cu.in.
A = 2lC x r x m = 2 x 3.1416 x 6 x 3 = 113.10 sq. in.
SPHERICAL ZONE
Given:
Radius r = 6 in., C1 - 8 in., C2 = 11.625 in., and h = 3 in.
Find:
2
Volume V= 0.5236 x 3 x (3; 8 + 3 x ~1.6252 + 32) = 248.74 cu. in.
Area
A = 6.2832 x 6 x 3 = 113.10 sq. in.
TORUS
Given:
Radius R = 6 in. and r = 2 in.
Find:
Volume V= 19.739 R x r2 = 19.739 x 6 x 22 = 473.7 cu. in.
Area
A = 39.478 Rr = 39.748 x 6 x 2 = 473.7 sq. in.
268
GEOMETRICAL
PROBLEMS & CONSTRUCTIONS
A
LOCATING POINTS ON A CIRCLE
EXAMPLE
R = 5 in. X = 3 in.
Y = -VR2 - Xl
Find Y= ~ 52 - 3 2 =
X = -V R2 - y2
= ~ 25 - 9 =
116
=
=4 in.
LENGTH OF PLATE FOR CYLINDER
L = 7r X D
EXAMPLE
L
Length of
plate
D = Mean
diameter
Inside diameter = 24 in.
Thickness of plate: 1 in.
The length of plate =
L = 25 x 3.1416 = 78.5398 in.
=
TO FIND THE RADIUS OF A CIRCULAR ARC
(C/2)~ M2
EXAMPLE
R
2M
c = 6 in., M = 2 in.
( 6/2)2 + 22
Find: R=
2 x 2 = 3.25 in.
TO FIND THE CENTER OF A CIRCULAR ARC
When the radius, R, and chord, C, are known, strike
an arc from point A and from point B with the given
length of the adius. The intersecting point, 0, of the
two arcs is the center of the circular arc.
Y
=
~ R2 _ (C/2)2
TO FIND THE CENTER OF A CIRCULAR ARC
When the chord, C, and dimension, M, are known,
strike an arc from point A and from point B on both
sides of the arc. Connect the intersecting points with
straight lines. The intersecting point of the straight
lines, 0, is the center of the circular arc.
R = C2 + 4M2. Y = R _ M
8M
'
CONSTRUCTION OF A CIRCULAR ARC
The radius is known, but because of its extreme length it is impossible to draw the arc with a compass. Detennine the length ofchord,
C and dimension M. Draw at the center ofthe chord, C a perpendicular line. Measure on this line dimensionM. Connect points AD
and BD. Bisect lines AD and BD and measure MI4 dimension
perpendicular. Repeating this procedure to the requested accuracy,
M will be 4 times less at each bisection 4 times less. The vortices
ofthe trian les are the oints ofthe circular arc.
269
GEOMETRICAL PROBLEMS AND CONSTRUCTIONS
A
TO FIND THE FOCUS OF AN ELLIPSE
Given the minor and major axis of the ellipse.
Find the focus.
Strike an arc with radius, a (one half of the
major axis) with center at B. The intersecting points of the arc and major axis are
the two foci of the ellipse.
c = ~a2 - b2
THE CONSTRUCTION OF ELLIPSE
Place a looped string around points F 1, Band F 2 .
Draw the ellipse with a pencil moving it along the
maximum orbit of the string while it is kept taunt.
y= b
v'l-~
THE CONSTRUCTION OF ELLIPSE
Describe a circle of which diameter is equal to the
major axis of the ellipse and with the same center
a circle of which diameter is equal to the minor axis.
Draw a number of diameters. From the intersecting
points of the large circle draw perpendicular lines to
the major axis and from the intersections of the
small circle draw lines parallel with the minor axis.
The intersections of these parallel and perpendicular
lines are points of the elliptical curve.
PROPERTIES OF 2: 1 ELLIPTICAL HEAD
d
R
r
=
0.8 D (approx.)
0.9 D (approx.)
0.173 D (approx.)
The upper portion of the head within diameter, d
is a spherical segment with negligible deviation.
E
x
LOCATING POINTS ON A 2: 1 ELLIPTICAL HEAD
I X = V'R2
i
- 4 y:z
Y
= VR 2 - X2
2
Note: The curvature of an elliptical head on one side
only is a true ellipse (inside or outside). The opposite parallel curve is geometrically undetermined. To
locate points on this curve expecially in the case of a
heavy walled head is possible by means of layout
only. See tables on page 293.
270
SOLUTION OF RIGHT TRIANGLES
REQUIRED
KNOWN SIDE OR ANGLE
(ENCIRCLED)
a,b
@...L:J'
tan A
=...!..
b
a, b
~<;
b
b
tan B = a
b
a, b
~a
=~
c
@.£j.
a
sin A = c
a, c
~.
a
cos B = c
a, c
/'1
A, b
A~
b
=~
Find Angle B =~= 0.500
12
cos 0.500 = 60 0
Find side b =~ v'25-9
=V16 = 4 in.
b = a x cot A
Angle A = 25 0 , side a = 6 in.
Find side b = 6 x cot 25 0
= 6 x 2.1445 = 12.867 in.
~
a
c
= sin A
Angle A = 30 0 , side a = 6 in.
=_6_= 12 in.
Find side c = _6_ _
0.500
sin 30 0
a =- b x tan A
Angle A = 25 0 , side b = 12.867 in.
Find side a = 12.867 x tan 25 0
= ~ 2.867 x 0.4663 = 6 in.
c -
b
cos A
b
A, c
AL:::1<!l
a = cxsinA
A, c
;/1
b = c x cos A
A
= 12 in.
6
Find Angle A = - = 0.500
12
sin 0.500 = 30 0
lbJ
A.2::J·
A
=V
3 2 + 4 2 =-v'9+i6
=v'25 = 5 in.
Side a = 3 in. c = 5 in.
a
/1a
A, b
Find side c
Side a = 6 in. c = 12 in.
(I»
A, a
Side a = 6 in. b = 12.867 in.
12.867
Find Angle B = 2.1445
6
tan 2.1445 = 65 0
Side a = 6 in. c
a, c
A
Side a = 6 in. b = 12.867 in.
=_6_ _ =
Find Angle A
0.4663
12.867
tan 0.4663 = 25 0
Side a = 3 in. b = 4 in.
b
A, a
EXAMPLES
FORMULAS
C~
Angle A = 30 0 , side b = 12 in.
b
12
Find side c ="'CoSJO'O = 0.866
= 13.856 in.
Angle A = 30 0 , side c = 12 in.
Find side a = 12 x sin 30 0
= 12 x 0.500 = 6 in.
Angle A = 300 , side c = 12 in.
Find side b = 12 x cos 30 0
12 x 0.866 = 10.392 in.
271
Frustum of ECCENTRIC CONE
EXAMPLE
Given:
Mean diameter at the large end, 0 = 36 in.
Mean diameter at the small end, 01 = 24 in.
Height of frustum.
HI = 24 in.
Determine the Required Plate
Half of the Required Plate
Tan a =
_
0-01
36-24
H
= ~= 0.500 = 26 0 .34'
1
o
36
2. H = 'taii"Q. =0':500 = 72 in., H2 = H -H 1 =
72- 24 = 48 in.
3. Divide the base circle into 12 equal parts.
4. Draw chords Cl, C2, C3, etc. to the dividing points.
5. Calculate the length of the chords C \ ' C 2' C 3' etc. using Factor, C from table "Segments
of Circles for Radius = 1 on page 290 .
6. Calculate the lengths of SI, S2, etc. and Si, S2' etc.
At The Bottom
Factor c times
mean radius
=
30 0
60 0
Chords, CI C 2 ·· .
in.
9.317~
CI =
18.000~
VH2
At The Top
+
Factor c times
mean radius
=
=
C2
I, 2
S 1, 2 ... ft.-in.
SI =
6'-0
%
90 0
C2 =
C3 =
25.452"
6' - 2 0/16
S3 = 6'-4%
120 0
C4 =
31.176 "
S4 =
1500
C5
34.776"
S5 = 6' - 710/16
=
S6
S2 =
6'-6 7/16
=V H2 + 0 2 = 6' - 8Vl
v'H~
Chords, C I C 2 etc.
in.
Cl=
6.212 •
C2 = 12.000-
+
=
C'2
1,2 ...
•
SI,2 . . . ft.-in.
S ... = 4'-0 %
S2 = 4'-1 ~
= 4'-2'0/,6
53
C3 =,
16.968"
C4=
20.784 "
S4 = 4'-40/,6
C5 = 23.184 "
S5 = 4'-50/,6
S·6 =VHi + 0 2I
4'-5 11h6
272
OPTIMUM VESSEt SIZE*
To build a vessel of a certain capacity with the minimum material, the correct ratio of
length to diameter shall be determined.
The optimum ratio of length to the diameter can be found by the following procedure:
(The pressure is limited to 1000 psi and ellipsoidal heads are assumed)
F=
P
CSE
, where
p
C
S
E
DeSign pressure, psi.
Corrosion allowance, in.
Stress value of material, psi.
Joint efficiency
Enter chart on facing page at the left hand side at the desired capacity of the vessel.
Move horizontally to the line representing the value of F.
From the intersection move vertically and read the value of D.
The length of vessel
=
4 V 2 ,where V
D
D
1T
=
=
Volume of vessel, cu. ft.
Inside diameter of vessel, ft.
EXAMPLE
Design Data:
P = 100 psi, V = 1,000 cu. ft., S = 16,000 psi.,
Find the optimum diameter and length
F= _ _ _--"1:. .: 0-=.0 _ __
0.0625 x 16,000 x 0.8
E = 0.80,
C = 0.0625 in.
= 0.125 in.- 1
From chart D = 5.6 ft., say 5 ft. 6 in.
Length = 4 x 1,000
3.14 X 5.5 2
= 42.1, say 42 ft. 1 in.
·FROM:
" Nomographs Gives Optimum Vessel Size," by K. Abakians, Originally published in HYDROCARBON PROCESSING, Copyrighted Gulf Publishing Company, Houston. Used with permission.
273
100,000
80,000
60,000
50,000
40,000
30,000
20.000
t:
10,000
8,000
6.000
5.000
4,000
3.000
B2.000
uJ
:::;::
:l
:; 1,000
;;. 800
...I
600
uJ
Vl
500
Vl
uJ
400
;;.
300
200
100
80
60
SO
40
30
/
/
/ 1/
/
20
10
/
V
I.S
2
3
4
5
6
VESSEL DIAMETER, D FT.
8
910
15
CHART FOR DETERMINING THE OPTIMUM VESSEL SIZE
(See facing page for explanation)
20
274
FLAT RINGS MADE OF SECTORS
B
§
I~I
Making flat rings for base, stiffeners etc., by
dividing the ring into a number of sectors,
less plate will be required.
ONE
PIECE
The cost of the welding must be balanced
against the saving in plate cost.
2
SECTORS
3
SECTORS
0,7070
I~I
i"
~
6
SECTORS
=
Outside diameter of ring.
Inside diameter of ring.
1. Determine Df d and D2 (the area of square
plate would be required for the ring made
of one piece)
2. Read from chart (facing page) the percentage of the required area when the
ring divided into the desired number of
sectors
3. Determine the required area of plate
~
sr
D
d =
4
SECTORS
~
#
#
The chart on facing page shows the total
plate area required when a ring is to be
divided into sectors. This area is expressed
as a percentage of the square that is needed
to cut out the ring in one piece. The figures
at the left of this page show the width of
the required plate using different number of
sectors.
DETERMINATION OF THE REQUIRED
PLATE SIZE
0.3830
I;'
Since the sectors shall be welded to each
other, the welding will be increased by
increasing the number of sectors.
8
SECTORS
: it
THE REQUIRED WIDTH
OF PLATE FOR RINGS
MADE OF SECTORS
4. Divide the area by the required width of
plate as shown at the left of this page to
obtain the length of the plate.
5. Add allowance (max. 1 inch) for flame
cutting between sectors and at the edges
of the plate
See Example On Facing Page.
275
FLAT RINGS MADE OF SECTORS (cont.)
100r------.------.------.------,,------r-----~
0
N
0
d
I.l.
20
0
E-<
Z
70
~
60
~
~
18
16
~
CI')
-<
tZl
<
~
40
1.3
-<
30
12
1:4-
~
~
E-<
-<
.....l
20
1.1
~
10
0
2
EXAMPLE
3
4
5
6
7
8
NUMBER OF SECTORS
Determine the required plate size for a 168 in. 0.0., 120 in. I.D. ring made of
6 sectors
1. D/d = 1.4; 02 = 28,224 sq. in.
2. From chart (above) the required area of plate is 50% of the area that would
be required for the ring made of one piece.
3. Area required 28.224 x 0.50 = 14,112 sq. in.
4. Divide this area by the required width of plate (facing page). Width = 0.5
x 168 = 84 14,112/84 = 167.9 inches, the length of plate.
5. Add allowance for flame cut.
276
FRUSTUM OF
CONCENTRIC CONE
Given:
D = Mean diameter at the large end.
D J = Mean diameter at the small end.
H = Height of the frustum.
Determine the Required Plate.
The Required Plate
b
r
D
c= --.jH2 + b2
fJ= r.. x 360
D-D]
b=-2-'
e
R
=--.!;L
Sin a
tan a= Q
H
R = c+e
CONICAL TANK ROOF
D
R- r
-cos
r
jJ=L x 360
R
The Required Plate
r
D
=-]
] 2
277
FRUSTUM OF CONCENTRIC CONE
Made from two or more Plates
Given:
D
Mean diameter at the large end.
Mean diameter at the small end.
Height of the fustrum
Number of plates (sector)
DJ
H
n
Determine the Required Plate
b = D-D J
2
tan
D
Elevation
IX
12.
H
rJ
~b2 + H2
DJ 12
e
..!..) --
R
c+e
D x 1fX 57.296
2Rn
C
Z
=
sm
y
IX
X
Y
R x sin r + W'
R x sinr + I"
Z -=
e x sin
V = e x cos
One Sector of Plate
r
r
Width ofthe Required Plate = R - V + 1"
Length of the Required Plate if the Frustum made from:
2 Plates: 2X + Y + Z
x
IENGlH
y
Z
x
3 Plates: 2X + 2Y + 2Z
4 Plates: 2X+ 3Y+ 3Z
6 Plates: 2X + 5 Y + 5Z
-r--tt---t-t--::::=*=~=t- YJ" typical
~
cl_
Required Plate
278
THE FRUSTUM OF ECCENTRIC CONE
Determination of the Required Plate by Layout and by Calculation
Half of the plate
Symmetrical
LAYOUT
1.
2.
3.
Draw the side view and half
of the bottom view of the
cone.
Divide into equal parts the
base and the top circle.
Draw arcs from points 2 1,
3 1, 4 1, etc. with the center
]1.
4.
Side view
of cone
From the points /0, 2°, 3",
etc. strike arcs with center
O.
5.
Half of the
bottom view
Fig. A
o
- 6.
Starting from a point on arc 1 1,
(marked 1) measure the spacing of the
bottom circle of the cone and intersect arc 2°. From the point marked 2
measure again one space intersecting
arc 3°, etc. The points or intersections
are points on the curvature of the
plate at the bottom of the cone.
To determine the curvature of the
plate at the top of the cone, repeat
steps 4 and 5, but measure on the
arcs drawn with center 0 the spaces
of the top circle.
CALCULATION
To find the curvature of the plate by calculation,
the simensions ]1 - 2 1, ]1 _ 31, etc. and 0 - ]1, 0 _
21 , etc. shall be determined.
Fig. B shows as an example the calculation of 0-4 1
only (marked S, ).
If the bottom circle is divided into 12 equal spaces,
C3 = 2 R x sin 45°
S3
Fig.B
=
VH2 + C]
Where R denotes the mean radius of the base circle.
See example on the following page.
279
FRUSTUM OF ECCENTRIC CONE
EXAMPLE
Given: Mean diameter at the large end, D = 36 in.
Mean diameter at the small end, I?J = 24 in.
Height of frustum,
H / = 24 in.
Determine the required Plate.
s
Half of the Required Plate
il4 = 0.500=260-34'
Tana=D D 1 = 36
il/
=~ = 72 in. H =H-H =
tan a 0.500
'2
1
72 - 24 = 48 in.
Divide the base circle into equal parts.
H=.J2.
4.
Draw chords C 1 , C2 , C3 , etc. to the dividing points.
5.
Calculate the length of the chords C1 ' C2' C3' etc. using Factor C from table
"Segments of Circles for Radius = 1" on page 290.
6.
Calculate the lengths of S1' S2' etc. and Sj, Sj, etc.
At The Bottom
Factor c times
mean radius =
hords, c/ ' C2 ... in.
30°
60°
90°
150°
C]
=
C2 =
C3 =
C =
C5 =
9.137"
18.000"
25.452"
31.176"
34.776"
...f H2 + C2}, 2=
S}, 2 . . . [1. in,
S. = 6' - 6 7116
S5 = 6' - 7 15 116
At The To
Factor c times
mean radius =
Chords, C], C2 etc. in.
C] =
6.212"
C =
16.968"
20.784"
23.184"
C =
C5 =
...fH22 + C2],2 =...
S/*.2 . .. [1. in.
S]* =4' - 0 3/8
S = 4' - 2 15116
S,,* =4' - 4 5116
S5* =4' - 5 5116
S6 =V H } + Dl = 4' - 511 116
280
BENT AND MITERED PIPE
The length of a pipe bent to any shape is equal to the
length measured on the centerline of pipe. Example:
(The pipe bent as shown)
Given: R = 8 in., RI = 6 in.,
Find the length of pipe, L.
L = R It''x
ex
=
nO
~ = 36 0
1=
2 in.
~ + RI ". -'l- +
180
180
8x3.14 x 2L-+6x3.14 x
180
36 +2
180
25.13 x 0.40 + 18.85 x 0.20 + 2 =
15.82 in.
The Required Length of Pipe for Coil
L = V(n x D x".)2 + H2 Where
n
Number of turns
L = Length of required pipe
EXAMPLE
Given:
D = 10 in., H = 24 in., n = 12
L
=V (12 x 10 x 3.14)2 + 242
= 378 in.
The Required Length of Pipe for Coil
2
Where
L = r ".
c
d + C
Clearance between turns of pipe.
Outside disl!1eter of pipe.
(Approximation) d
L
Required length of pipe.
=
EXAMPLE
Given:
r
10 in. d = 2.375 in., c = 1 in.
L = 10 2 x 3.14 = 93.08 in.
2.375 + 1
Mitered Elbow
To find the angle of cut for any elbow, divide the total
number of degrees of the elbow by twice the number
of cuts.
EXAMPLES
90 0 : 6 = 15 0
3 cuts x 2
6
90 0 : 4 = 22V20
2 cuts x 2 = 4
2 cuts x 2 = 4
120 0 :4= 300
The length of pipe required to form any shapes by mitering is the sum of the centerline lengths of the pipe sections.
281
INTERSECTION OF
CYLINDER &
PLANE
When the intersecting plane is not
perpendicular to the axis of the
cylinder, the intersection is an
ellipse.
CONSTRUCTION OF THE INTERSECTING ELLIPSE
Divide the circumference of the
cylinder into equal parts and draw
an element at each division point.
The major axis of the ellipse is the
longest distance between the intersecting points and the minor axis is
the diameter of the cylinder. The
points of the ellipse can be determined by using the chords of the
cylinder spaced by projection as
shown or by calculations as exemplified below. With this method
may be laid out sloping trays, baffles, down-comers etc. The thickness of the plate and the required
clearance shall also be taken into
consideration.
DEVELOPMENT
The length, H is equal to the circumference of the cylinder. Divide
this line into the same number of
equal parts as the circumference of
the cylinder.
Draw an element
through each division perpendicular
to this line. Determine the length
. of each element as shown or by calculation. By connecting the end
points of the elements can be obtained the stretched-out line of the
intersection and may be used for
cutting out pattern for pipe mitering, etc.
la
EXAMPLE
11
(a 4 - a 3 ) cos 40 0
12
(a 4 - a 2 ) cos 40 0
for calculation of length of
elements.
The circumference of the cylinder
is divided into 16 equal parts.
The angle of a section = 22-1 /2
degrees.
The angle of the intersecting plane
to the axis of the cylinder = 40
degrees.
c 1 = r X cos 22-1/2 0
r X cos 45 0
r x sin 22-1/2 0
etc.
a1
=
hI
--=--~
~n 40 0
a
2
h2
= ----"'--,.....
0
~n 40
etc.
282
INTERSECTION OF CYLINDERS
of equal diameters with angle of intersection 90 0
I
I
!
I
L
/
-~--,~ f--
---
-+"\.
!'\
/
I
I
""
I
'"1"\ - 1/
I
/l
'.:Ie,
.......
I
j
.......
/'
./
~ C31 C4
........
./
./
1
I
I
!
~ ~"
t-
~
'/4 OF
f-
l-
~
L
w
~
C3
C2
z
w
~
I
~
ci\
C3 \
C4
~
~
~
~-~c, «
w
a:
Ll-
V
C1
V
(..)
\
'/40F
Divide the circumference of the cylinders
into equal parts and draw an element at
each division point. The intersecting
points of the elements determine the line
of intersection.
.......
\
OF
THE LINE OF INTERSECTION
I
I
lL'
'12
::)
(..)
a:
U
DEVELOPMENT OF PATTERNS
Draw straight line of equal length to the
circumference of the cylinders. Divide the
. lines into the same number of equal parts
as the circumference of the cylinders.
Draw an element through each division
perpendicular to these lines. Determine
the length of each element by projection
or calculation. (See example below). By
connecting the end point of the elements
the stretched out curve of the intersection
can be developed.
EXAMPLE
for calculation of length of elements
If the circumference of cylinders is divided
into 16 equal parts a = 22-1/2 0
c1
c2
c3
c4
=
=
=
=
r sin a
rsin2a
r cos a
r
283
INTERSECTION OF CYLINDERS
of unequal diameters with angle of intersection 90 0
+-+-+~.--.
c b
Q
Q
b c
THE LINE OF INTERSECTION
w
U
Z
w
c::
W
LL
~
;:)
u
c::
u
Divide the circumference of the small cylinder into as many equal parts as necessary
for the desired accuracy. Draw an element
at each division point. Project distances
C 1 ' c 2 etc. to the circumference of the
larger cylinder and draw elements at each
points. The intersecting points of the
elements of the large and small cylinder
determine the curve of intersection.
DEVELOPMENT OF PATTERNS
Draw a straight line of equal length to the
circumfer-ence of the cylinders. Divide the
line for the small cylinder into the same
number of equal parts as the circumference
of the small cylinder. Draw an element
thrsugh each division perpendicular to the
line. Determine the length of the elements
by projection or calculation. (See example
below). By connecting the end point of
the elements the stretched out curve of the
intersection can be developed.
The curvature of the hole in the large
cylinder is determined by the length of
elements c 1 ' c2 etc. spacing them at distances a, b, c etc., which are the length of
arcs on the partial view of the large cylinder.
EXAMPLE
for calculation of length of elements.
Dividing the circumference of the cylinder
into 12 equal parts, a = 300
c 1 = r sin 300 c2 = r cos 300 c 3 = r
284
INTERSECTION OF CYLINDERS
with non intersecting axes
abc
d
e
f
THE LINE OF INTERSECTION
Divide the circumference of the
branch cylinder on both views into
as many equal parts as necessary
for the intended accuracy. Draw
an element at each division point.
The points of intersection of the
corresponding elements determine
the line of intersection.
l
L
J
L
/
DEVELOPMENT OF PATTERN
Draw a straight line of equal length
to the circumference of the branch
cylinder and divide it into the same
number of equal parts as the circumference. Draw an element
through each division perpendicular
to the line. Determine the length
of the elements by projection or
calculation. (See example below).
By connecting the end point of the
elements the stretched out curve of
the intersection can be developed.
w
u
z
w
a:
w
V
lh
u..
~
:::>
12~
u
13 ' \
14
~
I~
Ie
1
1
a:
U
The curvature of the hole in the
main cylinder is determined by the
length of elements c 1 , c 2 etc. spacing them at distances a, b, c, etc.,
which are the length of arcs on the
main cylinder (see elevation).
EXAMPLE
for calculation of length of elements
Dividing the circumference of the
cylinder into 12 equal parts, a =30 0
C
1=
r
sin 300
c'2, = r cos
c3 = r
'6
R
30 0
11 = yR2_ (r + C2)2
=V R2_ (r + e l )2
1'2,
13 =
14=
15 =
V R2_ r2
VR2-(r -c l )2
v' R2_ (r - C2)2
285
INTERSECTION OF CONE AND CYLINDER
THE LINE OF INTERSECTION
Divide the circumference of the
cylinder on both views into as
many equal parts as necessary for
the desired accuracy.
Draw an
element at each division point.
Draw circles on plan view with
radius r l' r 2' etc. The line of intersection on the plan is determined
by the points of intersections of
elements and the corresponding
circles. Project these points to the
elevation. The intersecting points
of the projectors and elements will
determine the line of intersection
on the elevation. The stretched
out curvature of the hole in the
cone is to be determined by the
length of arcs a 2 , a 3 , etc. transferred from the plan view or calculated
as exemplified below. The spacing
of arcs a 2 , a 3' etc. may be obtained
as shown or may be calculated.
(See example below).
DEVELOPMENT OF PATTERN
Draw a straight line of length equal
to _the circumference of the cylinder and divide it into the same
number of equal parts as the circumference. Draw an element
through each division point perpendicular to the line. Determine
the length of the elements by projection or by calculating the length
of 1 1 , 12 , etc.(See example below).
w
U
Z
w
cr:
w
u.
~
::J
U
cr:
u
EXAMPLE
for calculation of length of elements
c 6 :::: r sin a:
radius, R6
h6 tan {3
arc a 6 :::: 2R6
16::::
JR~ - c~
11'
X -2JL
360
etc.
286
INTERSECTION OF CYLINDER AND SPHERE
.1
l
I
I
112
R
--------f--- - - - -7- - - - I
/
I
I
•
/
-Ii
""-V '
I
;,
\ \. "J\ -_~+_+
-
"""'-I
3
,
~
o
\ ,,'V"'
4
2
I
i
- ~b..-"J-..t- - - - - r - - +
03)(
5
/
I
1'-..,1;
~
R,
Y2 Y,
!J
-/
'/
V
-----
R2
0,
: '
:/
~
I
I
OJ w
THE LINE OF INTERSECTI ON
Divide the diameter of the cy linder into equal
spaces. The horizontal pIa nes through the
division points cut elements f rom the cylinder
and circles from the sphere. The intersections
of the elements with the corr esponding circles
are points on the curvature 0 f intersection.
u
z
w
J
II:
12
w
11
u.
I
~
::>
u
II:
-u
\
\
I
,r--........
i'
I
I
I
"
I
!
"
'23t567
v
1\
.K~>-+>-~-~
LJ
I
!J
I
I
\\,\
-H
DEVELOPMENT OF THE CYLINDER
Draw a straight line of eq ual length to the
circumference of the cylinde r and divide it in_ to the same number of parts as the cylinder.
The spacing of the division points are determined by the length of arc s of the cylinder.
Draw an element through ea ch division point
perpendicular to the line. Determine the
length of the elements by projection or by
calculation of the lengths 0 f I}, 12 , etc.
i
"i
34
~
T
EXAMPLE
for calculation
elements.
of
length
of
Calcula te the distances, x I ' x 2 , etc.
XI is given; x 2 = XI + r X sin 0/ ,etc.,
VR;- x;,
RI = VR2 - y;,
II =
etc_
etc_
Pipe in 2: 1 Ellipsoidal Head
The center portion of the head is approximately a spherical segmen t the radius of
which is equal 0.9 times th e diameter of the
head. When the pipe is wit hin a limit of 0.8
times the diameter of the head the line of
intersection and development of the cylinder
can be found in the above described manner.
Pipe in Flanged and Dished Head
Similar way the center portion of the head
within the knuckles is a spherical segment the
radius of which is equal to the radius of the
dish.
287
TRANSITION PIECES
connecting cylindrical and rectangular shapes
DEVELOPMENT
D~
______
~
Divide the circle into equal parts and
draw an element at each division
point.
Find the length of each element by
triangulation or by calculation. The
elements are the hypotenuse of the
triangles one side of which is
A-I', A-2', A-3' etc. and the other
side is the height of the transition
piece.
____- ,
A
A-3'
A-2'
A-4'
Begin the development on the line
I-S and draw the right triangle I-S-A,
whose base SA is equal to half the
side AD and whose hypotenuse A-I
found by triangulation or calculation. Find the points 1, 2, 3 etc.
The length of 1-2, 2-3, 3-4 etc. may
be taken equal to the cord of the
divisions of the top circle if they are
small enough for the desired accuracy. Strike an arc with 1 as center
and the chord of divisions as radius.
With A as center and A-2 as radius
draw arc at 2. The intersection of
these arcs give the point 2. The
points 3, 4 etc. in the curve can be
found in a similar manner.
EXAMPLE
for calculation of length of elements
c=r
X
e=b-c
D
~=
cos a
Vf2 + e 2
d=r
X
sin a
f=a-d
gr-:2-+-h-=-2
k
=V
LENGTH OF ELEMENTS
In the above described manner can
be found the development for transition pieces when:
1. one end is square
2. one or both sides of the rectangle are equal to the
diameter of the circle
3. the circular and rectangular
planes are eccentric
4. the circular and rectangular
planes are not parallel
288
TRANSITION PIECES
connecting cylindrical and rectangular shapes
DEVELOPMENT
Divide the circle into equal parts and
draw an element at each division
point.
Find the length of each element by
triangulation or by calculation. The
elements are the hypotenuse of the
triangles one side of which is
A-I', A-2', A-3' etc. and the other
side is the height of the transition
piece.
A-1
Begin the development on the line
I-S and draw the right triangle I-S-A,
whose base SA is equal to half the
side AD and whose hypotenuse A-I
found by triangulation or calculation. Find the points I, 2, 3 etc.
The length of 1-2, 2-3, 3-4 etc. may
be taken equal to the cord of the
divisions of the top circle if they are
small enough for the desired accuracy. Strike an arc with 1 as center
and the chord of divisions as radius.
With A as center and A-2 as radius
draw arc at 2. The intersection of
these arcs give the point 2. The
points 3, 4 etc. in the curve can be
found in a similar manner.
EXAMPLE
for calculation of length of elements
c = r X cos ex
d == r X sin ex
e = V(b-d)2+(c-a)2
k
= v' e2 + h2
In the above described manner can
be found the development for transition pieces when:
1. one end is square
2. one or both sides of the rectangle are equal to the
diameter of the circle
3. the circular and rectangular
planes are eccentric
4. the circular and rectangular
planes are not parallel
289
DIVISION OF CIRCLES INTO EQUAL PARTS
The best method for division of a circle into equal
parts is to find the length of the chord of a part and
measure this length with the divider on the circumference. The length of the chord, C = diameter of
+
circle x c, where c is a factor tabulated below.
EXAMPLE:
It is required to divide a 20 inch diameter circle into 8 equal spaces.
c for 8 spaces from the table: 0.38268
C
= Diameter
x 0.38268
= 20
X
= 7.6536 inches
0.38268
To find the length of chords for any desired number of spaces not shown in the
table:
180
C = Diameter X sin
number of spaces
EXAMPLE:
It is required to divide a 100 inch diameter circle into 120 equal parts
C
= 100
x sin
~
= 100
120
x sin 1° 30
1
= 100
X
0.0262
= 2.62 inches
Spaces
C
No. of
Spaces
C
No. of
Spaces
C
No. of
Spaces
1
2
3
4
0.00000
1.00000
0.86603
0.70711
26
27
28
29
0.12054
0.11609
0.11196
0.10812
51
52
53
54
0.06153
0.06038
0.05924
0.05814
76
77
78
79
0.04132
0.04079
0.04027
0.03976
5
6
7
8
0.58779
0.50000
0.43388
0.38268
30
31
32
33
0.10453
0.10117
0.09802
0.09506
55
56
57
58
0.05709
0.05607
0.05509
0.05414
80
81
82
83
0.03926
0.03878
0.03830
0.03784
9
10
11
12
0.34202
0.30902
0.28173
0.25882
34
35
36
37
0.09227
0.08964
008716
008481
59
60
61
62
0.05322
0.05234
0.05148
0.05065
84
85
86
87
0.03739
0.03695
0.03652
0.03610
13
14
15
16
0.23932
0.22252
0.20791
0.19509
38
39
40
41
0.08258
0.08047
0.07846
0.07655
63
64
65
66
0.04985
0.04907
0.04831
0.04758
88
89
90
91
0,03569
0.03529
0.03490
0.03452
17
18
19
20
0.18375
0.17365
0.16460
0.15643
42
43
44
45
0.07473
0.07300
0.07134
0.06976
67
68
69
70
0.04687
0.04618
0.04551
0.04487
92
93
94
95
0.03414
0.03377
0.03341
0.03306
21
22
23
24
25
0,14904
0.14232
0.13617
0.13053
0.12533
46
47
48
49
50
0.06824
0.06679
0.06540
0.06407
0.06279
71
72
73
74
75
0.04423
0.04362
0.04302
0.04244
0.04188
96
97
98
99
100
0.03272
0.03238
0.03205
0.03173
0.03141
No. of
C
290
1
,
V
~
e
De~
I
2
3
4
5
6
7
8
9
10
II
12
13
14
15
16
17
18
19
20
21
~~
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
SO
51
52
53
54
55
56
57
58
59
60
h
t
~
" ~aa.\\l.S
-c~
./
Area
I
h
C
0.017
0.034
0.052
0.069
0.087
0.104
0.122
0.139
0.157
0.174
0.191
0.209
0.226
0.244
0.261
0.279
0.;'96
0.314
0.331
0.349
0.366
0.383
0.401
0.418
0.436
0.453
0.471
0.488,
0.506
0.523
0.541
0.556
0.575
0.593
0.610
0.628
0.645
0.663
0.680
0.698
0.715
0.733
0.750
0.767
0.785
0.803
0.820
0.838
0.855
0.873
0.890
0.908
0.925
0.942
0.960
0.977
0.995
1.012
1.030
1.047
0.0000
0.0001
0.0003
0.0006
0.0009
0.0013
0.0018
0.0024
0.0030
0.017
0.034
0.052
0.069
0.087
0.104
0.122
0.13'l
0.156
0.174
0.191
0.209
0.226
0.243
0.261
0.27!!
0.295
0.312
0.330
0.347
0.364
0.381
0.398
0.415
0.432
0.449
0.466
0.483
0.500
0.51;
0.534
0.551
0.568
0.584
0.601
0.618
0.634
0.651
0.667
0.684
0.700
0.716
0.733
0.749
0.765
0.781
0.797
0.813
0.829
0.845
0.861
0.877
0.892
0.908
0.923
0.939
0.954
0.970
0.985
1.000
0.003~
0.0046
00054
0.0064
0.0074
O.O()85
0.0097
0.01 JO.
0.0123
0.0137
0.015 I
0.0167
0.0183
0.0200
0.0218
0.0237
0.0256
0.0276
0.0297
0.0318
0.0340
0.0363
0.0387
0.0411
0.0436
0.0462
0.0489
0.0516
0.0544
0.0573
0.0603
0.0633
0.0664
0.0695
0.0728
0.0761
0.0795
0.0829
0.0865
0.0900
0.0937
0.0974
0.1012
0.1051
0.1090
0.1130
0.1171
0.1212
0.1254
0.1296
0.1340
of Seg-
SEGMENTS OF CIRCLES FOR RADIUS = 1
Length of are, height of segment, length of chord,
and area of segment for angles from 1 to 180 degrees
and radius = 1. For other radii, multiply the values
of 1, hand c in the table by the given radius r, and
the values for areas, by r2, the square of the radius.
e
Deg
U.UWl
1.065
1.082
1.100
1.117
1.134
1.152
1.169
'1.187
U04
1.222
1.239
1.257
1.274
,1.291
1.309
1.326
77 1.344
78 1.361
79 1.379
80 1.396
81 1.414
82 1.431
83 1.449
84 1.466
85 1.483
86 1.501
87 1.518
88 :1.536
89 1.553
90 1.571
91 1.588
92 1.606
93 1.623
94 1.641
95 1.658
96 1.675
97 1.693
98 1.710
99 1.728
100 1.745
101 1.763
102 1.780
103 1.798
104 1.815
105 1.833
106 1.850
107 1.867
108 1.885
109 1.902
110 1.920
111 1.937
112 1.955
113 1.972
114 1.990
115 2.007
116 2.025
117 2.042
118 2.059
119 2.077
12012.094
0.0000
0.0000
0.0000
0.0000
0.0001
0.0001
0.0002
0.0003
0.0004
0.0005
0.0007
0.0009
0.0012
0.0014
0.0018
0.00;'1
0.0025
0.0030
0.0035
0.0040
0.0046
0.0053
0.0060
0.0068,
0.0077
0.0086
0.0096
0.0106
0.0118
0.0130
0.0142'
0.0156
0.0171
0.0186
0.0202
0.0219
0.0237
0.0256
0.0276
0.02'l7
0.0319.
0.0342
0.0366
0.0391
0.0417
0.0444
0.0473
0.0502
0.0533
0.0564
0.0597
0.0631
0.0667
0.0703
0.0741
0.0780
0.0821
0.0862
0.0905
h
C
of Seg-
e
men!
Deg
0.1384
0.1428
0.1474
0.1520
0.1566
0.1613
0.1661
0.1710
0.1759
0.1808
0.1859
0.1910
0.1961
0.2014
0.2066
0.2120
0.2174
0.2229
0.2284
0.2340
0.2396
0.2453
0.2510
0.2569
0.2627
0.2686
0.2746
0.2807
0.2867
0.2929
0.2991
0.3053
0.3116
0.3180
0.3244
0.3309
0.3374
0.3439
0.3506
0.3572
0.3639
0.3707
0.3775
0.3843
0.3912
0.3982
0.4052
0.4122
0.4193
0.4264
0.4336
0.4408
0.4481
0.4554
0.4627
0.4701
0.4775
0.4850
0.4925
0.5000
1.015
1.030
1.045
1.060
1.075
1.089
1.104
1.118
1.133
1.147
1.161
1.176
1.190
1.204
1.217
1.231
1.245
1.259
1.272
1.286
1.299
1.312
1.325
1.338
1.351
1.364
1.377
1.389
1.402
1.414
1.426
1.439
1.451
1.463
1.475
1.486
1.498
1.509
1.521
1.532
1.543
1.554
1.565
1.576
1.587
1.597
1.608
1.618
1.628
1.638
1.648
1.658
1.668
1.6 T7
1.687
1.696
1.705
1.714
1.723
1.732
0.0950
0.0995
0.1042
0.1091
0.1140
0.1191
0.1244
0.1298
0.1353
0.1410
0.1468
0.1527
0.1588
0.1651
0.1715
0.1780
0.1847
0.1916
0.1985
0.2057
0.2130
0.2204
0.2280
0.2357
0.2436
0.2517
0.2599
0.2682
0.2767
0.2854
0.2942
0.3032
0.3123
0.3215
0.3309
0.3405
0.3502
0.3601
0.3701
0.3803
0.3906
0.4010
0.4117
0.4224
0.4333
0.4444
0.4556
0.4669
0.4784
0.4901
0.5019
0.5138
0.5259
0.5381
0.5504
0.5629
0.5755
0.5883
0.6012
0.6142
Area
1
men!
A
Area
1
h
C
A
61
62
63
64
65
66
67
68
69
70
71
7;'
73
74
75
76
of Segmen!
A
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
2.112
2.129
2.147
2.164
2.182
2.199
2.217
2.234
2.251
2.269
2.286
2.304
2.321
2.339
2.356
2.374
2.391
2.409
2.426·
2.443
2.461
2.478
2.496
2.513
2.531
2.548
2.566
2.583
2.600
2.618
2.635
2.653
2.670
2.688
2.705
2.723
2.740
2.758
2.775
2.792
2.810
2.827
2.845
2.862
2.880
2.897
2.915
2.932
2.950
2.967
2.984
3.002
3.019
3.037
3.054
3.072
3.089
3.107
3.124
3.142
a.SOif!
0.5152
0.5228
0.5305
0.5383
0.5460
0.5538
0.5616
0.5695
0.5774
0.5853
0.5933
0.6013
0.6093
0.6173
0.6254
0.6335
0.6416
0.6498
0.6580
0.6662
0.6744
0.6827
0.6910
0.6993
0.7076
0.7160
0.7244
0.7328
0.7412
0.7496
0.7581
0.7666
0.7750
0.7836
0.7921
0.8006
0.8092
0.8178
0.8264
0.8350
0.8436
0.8522
0.8608
0.8695
0.8781
0.8868
0.8955
0.9042
0.9128
0.9215
0.9302
0.9390
0.9477
0.9564
0.9651
0.9738
0.9825
0.9913
1.000
1.741
1.749
1.758
1.766
1.774
1.782
1.790
1.798
1.805
1.813
1.820
1.827
1.834
1.841
1.848
1.854
1.861
1.867
1.873
1.879
1.885
1.891
1.897
1.902
1.907
1.913
1.918
1.922
1.927
1.932
1.936
1.941
1.945
1.949
1.953
1.956
1.960
1.963
1.%6
1.970
1.973
1.975
1.978
1.980
1.983
1.985
1.987
1.989
1.991
1.992
1.994
1:995
1.996
1.997
1.998
1.999
1.999
2.000
2.000
2.000
0.6273
0.6406
0.6540
0.6676
0.6812
0.6950
0.7090
0.7230
0.7372
0.7514
0.7658
0.7803
0.7950
0.8097
0.8245
0.8395
0.8545
0.8697
0.8850
0.9003
0.9158
0.9313
0.9470
0.9627
0.9786
0.9945
1.0105
1.0266
1.0427
1.0590
1.0753
1.0917
1.1082
1.1247
1.1413
1.1580
1.1747
1.1915
1.2083
1.2252
1.2422
1.2592
1.2763
1.2933
1.3105
1.3277
1.3449
1.3621
1.3794
1.3967
1.4140
1.4314
1.4488
1.4662
1.4836
1.5010
1.5185
1.5359
1.5533
1.5708
291
~
Shell
I. S.
Diam.
DROP AT THE INTERSECTION
OF SHELL AND NOZZLE
(Dimension,d Inches)
NOMINAL PIPE SIZE
1'/.t
IV2
2
2V2
3
3V2
4
5
6
8
12
0.0625
0.0625
0.1250
0.1875
0.2500
0.3750
0.4375
0.6875
1.0000
1.8125
14
0.0625
0.0625
0.1250
0.1250 0.2500
0.3125
0.3750
0.5625
0.8125
1.5000
16
0.0625
0.0625
0.0625
0.1250 0.1875
0.2500
0.3125
0.5000
0.6875
1.2500
0.1250 0.1875
0.2500
0.3125
0.4375
0.6250
1.1250
18
0.0625
0.0625
0.0625
20
0.0625
0.0625
0.0625
0.1250 0.1250
0.1875
0.2500
0.3750
0.5625
1.0000
0.1875
0.2500
0.3750
0.5000
0.8750
22
0.0625
0.0625
0.1250 0.1250
24
0.0625
0.0625
0.0625
0.1250
0.1875
0.1875
0.3125
0.4375
0.8125
0.1250
0.1875
0.3125
0.4375
0.7500
26
0.0625
0.0625
0.0625
0.1250
28
0.0625
0.0625
0.0625
0.1250
0.1250
0.1875
0.3125
0.3750
0.6875
0.1875
0.2500
0.3750
0.6250
30
0.0625
0.0625 0.1250
0.1250
32
0.0625
0.0625
0.1250
0.1250
0.1250 0.2500
0.3750
0.5625
34
0.0625
0.0625 0.0625
0.1250
0.1250 0.2500
0.3125
0.5625
36
0.0625
0.0625
0.0625
0.1250
0.1250 0.2500
0.3125
0.5000
0.3125
0.5000
38
0.0625
0.0625
0.0625
0.1250
0.1250 0.1875
40
0.0625
0.0625
0.0625
0.1250
0.1250 0.1875
0.2500
0.5000
0.2500
0.4375
42
48
0.0625
0.0625
0.0625
0.1250
0.1250 0.1875
0.0625
0.0625
0:0625
0.1250 0.1875
0.2500
0.3750
0.1875
0.3750
54
0.0625 0.0625
0.0625
0.1250 0.1250
60
0.0625
0.0625
0.0625
0.0625 0.1250
0.1875
0.3125
0.1875
0.3125
0.1250
0.2500
66
0.0625 0.0625
0.0625
0.0625 0.1250
72
0.0625
0.0625
0.0625 0.1250
78
0.0625
0.0625
0.0625 0.1250
0.1250
0.2500
84
0.0625
0.0625
0.0625 0.1250
0.1250
0.2500
90
0.0625
0.0625
0.0625 0.0625
0.1250
0.1875
96
0.0625
0.0625
0.0625 0.0625
0.1250
0.1875
102
0.0625
0.0625 0.0625
0.1250
0.1875
108
0.0625
0.0625 0.0625
0.1250
0.1875
114
0.0625
0.0625 0.0625
0.1250
0.1875
0.0625
0.1250
120
0.0625 0.0625
126
0.0625 0.0625
0.0625
0.1250
132
0.0625 0.0625
0.0625
0.1250
138
0.0625 0.0625
0.0625
0.1250
144
0.0625 0.0625
0.0625
0.1250
292
~
Shell
I. S.
Diam.
DROP AT THE INTERSECTION
OF SHELL AND NOZZLE
(Dimension d, Inches)
NOMINAL PIPE SIZE
10
12
3.0625
12
14
16
18
20
22
24
26
30
14
2.5000 4.1250
7.000
16
2.0625
3.1875
4.1250
8.000
18
1.7500 2.6250
3.3750
4.8750
9.0000
20
1.5625
2.3125
2.8750
4.0000
5.6250 10.0000
22
1.3750 2.0625
2 5000
3.4375
4.6875
6.4375
24
1.2500
1.8125
2.2500
3.0625
4.0625
5.3750
26
1.1875
1.6875
2.0625
2.7500
3.6250 4.6875
28
1.0625
1.5000
1.8750
2.5000
3.2500 4.1875
5.3125 6.8125
8.9125
30
1.0000
1.4375
1.7500
2.3125
3.0000
3.8125
4.8125
7.5000
15.0000
11.0000
7.1875 12.0000
I
6.0625 8.0000 13.0000
6.0000
32
0.9375
1.3125
1.6250
2.1250
2.7500
3.5000
4.3750 5.4375
6.6875
10.4375
34
0.8750
1.2500
1.5000
2.0000
2.5625
3.2500
4.0625 4.8125
6.0625
9.0000
36
0.8125 0.8125
1.4375
1.8750
2.4375
3.0625
3.7500 4.5625
5.5625
8.1250
38
0.7500
1.1250
1.3125
1.7500 2.2500
2.8750
3.5000 4.2500
5.1250
7.3125
40
0.7500
1.0625
1.2500
1.6875
2.1250
2.6875
3.3125 4.0000
4.8125
6.7500
42
0.6875
1.0000
1.1250
1.5675
2.0000
2.5625
3.1250 3.7500
4.5000
6.3125
48
0.3125
0.875
1.0625
1.1875
1.7500 2.1875
2.6875
3.1875
3.8125
5.2500
54
0.5625
0.7500
0.9375
1.1875
1.5625
1.9375
2.3125
2.8125
3.3125
4.5625
60
0.4375
0.6875
0.8125
1.0625
1.3750
1.6875
2.1250 2.5000
2.9375
4.0000
66
0.4375
0.6250
0.7500
1.0000
1.2500
1.5625
1.8750 2.2500
2.6875
3.6250
72
0.3750 0.5625
0.6875
0.8750
1.1250
1.4375
1.7500 2.0625
2.4375
3.2500
78
0.3750 0.5000
0.6250
0.8125
1.0625
1.3125
1.5625
1.8750
2.2500
3.0000
84
0.3750 0.5000
0.5625
0.7500
1.0000
1.1875
1.4375
1.7500
2.0625
2.7500
90
0.3125 0.4375
0.5625
0.6875
0.4375
1.1250
1.3750 1.8750
1.9375
2.5625
96
0.3125
0.5000
0.6875
0.8750
1.0625
1.2500 1.5000
1.8125
2.3750
1.1875
1.4375
1.6875
2.2500
1.1250 1.3750
1.5625
2.1250
0.4375
102
0.3125 0.3750
0.5000
0.6250
0.8125
1.0000
108
0.2500 0.3750
0.4375
0.6250
0.7500
0.9375
114
0.2500 0.1875
0.4375
0.5625
0.6875
0.8750
1.062<;
1.2500
1.5000
2.0000
120
0.2500 0.1875
0.4375
0.5625
0.6875
0.8125
1.0000 1.1875
1.4375
1.8750
0.9375
1.1250
1.3750
1.8125
0.9375
1.1250
1.3125
1.7500
126
0.2500 0.3125
0.3750
0.5000
0.6250
0.8125
132
0.2500 0.3125
0.3750
0.5000
0.6250
0.7500
138
0.1825 0.3125
0.3750
0.4375
0.5625
0.7500
0.8750 1.0625
1.2500
1.6250
144
0.1825
0.3125
0.4375
0.5625
0.6875
0.8750 1.0000
1.1875
1.5625
0.3125
293
TABLE FOR LOCATING POINTS
ON 2: 1 ELLIPSOIDAL HEADS
R
V'!
I
x
1
2
3
4
5
6
x
1
2
3
4
5
6
7
x
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
9
D= 12
Y
2.9580
2.8284
2.5980
2.2360
1.6583
0
D= 14
y
3.4641
3.3541
3.1622
2.8722
2.4494
1.8027
0
D= 16
y
3.9686
3.8729
3.7081
3.4641
3.1225
2.6457
1.9364
0
D= 18
y
4.4721
4.3878
4.2426
4.0311
3.7416
3.3541
2.8284
2.0615
0
!
x
1
2
3
4
5
6
7
8
9
10
x
1
2
3
4
5
6
7
8
9
10
11
x
1
2
3
4
5
6
7
8
9
10
11
x
~IC jy
T!lngent
Lme
From these tables the dimension
y can be found if the diameter,
D and dimension x are known,
or x can be determined if D and
yare given. The tables based on
the formula: _ 1 VRl
h
- x 2 ,were
y -2'
R = the radius of head.
D= 20
Y
4.9749
4.8989
4.7697
4.5825
4.3301
4
3.5707
3
2.1794
0
D= 22
Y
5.4772
5.4083
5.2915
5.1234
4.8989
4.6097
4.2426
3.7749
3.1622
2.2912
0
D= 24
y
5.9791
5.9160
5.8094
5.6568
5.4543
5.1961
4.8734
4.4721
3.9686
3.3166
2.3979
12
0
D= 26
y
x
1
6.4807
2
6.4226
3
6.3245
4
6.1846
5
6
6
5.7662
7
5.4772
8
5.1234
9
4.6904
10
4.1533
11
3.4641
12
2.5
13
0
D= 28
y
x
1
2
3
4
5
6
7
8
9
10
11
12
13
14
6.9821
6.9282
6.8374
6.7082
6.5383
6.3245
6.0621
5.7445
5.3619
4.8989
4.3301
3.6055
2.5980
0
D;;: 30
y
x
1
7.4833
2
7.4330
3
7.3484
7.2284
7.0710
6.8738
6.6332
6.3442
6
5.5901
11
5.0990
12
4.5
13
3.7416
14
2.6925
15
0
D-32
x
Y
1
7.9843
2
7.9372
3
7.8581
4
7.7459
5
7.5993
6
7.4162
7.1937
7
8
6.9282
6.6143
9
10
6.245
11
5.8094
12
5.2915
13
4.6636
14
3.8729
15
2.7838
16
0
D=34
x
Y
1
8.4852
8.4409
2
3
8.3666
4
8.2613
8.1240
5
7.9529
6
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
7.7459
7.5
7.2111
6.8738
6.4807
6.0208
5.4772
4.8218
4
2.8722
0
D= 36
Y
8.9861
8.9442
8.8741
8.7749
8.6458
8.4852
8.2915
8.0622
7.7942
7.4833
7.1239
6.7082
6.2249
5.6568
4.9749
4.1231
2.9580
0
x
1
2
3
4
5
D= 38
y
9.4868
9.4472
9.3808
9.2870
9.1651
7
8
9
10
11
12
13
14
15
16
17
x
294
TABLE FOR LOCATING POINTS
ON 2: 1 ELLIPSOIDAL HEADS (Cont.)
6
7
8
9
10
11
12
13
14
15
16
17
18
19
D=38
9.0138
8.8317
8.6168
8.3666
8.0777
7.7459
7.3654
6.9282
6.4226
5.8309
5.1234
4.2426
3.0413
0
D-40
x
y
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
9.9874
9.9498
9.8868
9.7979
9.6824
9.5393
9.3675
9.1651
8.9302
8.6602
8.3516
8
7.5993
7.1414
6.6143
6
5.2678
4.3589
3.1225
0
D=42
x
1
2
3
4
5
6
7
y
10.4881
10.4523
10.3923
10.3078
10.198
10.0623
9.8994
8
9
10
11
12
13
14
15
16
17
18
19
20
21
9.7082
9.4868
9.2330
8.9442
8.6168
8.2462
7.8262
7.3484
6.8007
6.1644
5.4083
4.4721
3.2015
0
D=48
x
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
y
x
1
2
3
4
5
11.9896
11.9583
11.9059
11.8322
11.7367
11.619
11.4782
11.3137
11.1243
10.9087
10.6654
10.3923
10.0871
9.7467
9.3675
8.9442
8.4705
7.9372
7.3314
6.6332
5.8094
4.7958
3.4278
0
D= 54
y
13.4907
13.4629
13.4164
13.351
13.2665
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
13.1624
13.0384
12.8939
12.7279
12.5399
12.3288
12.0934
11.8322
11.5434
11.225
10.8743
10.4881
10.0623
9.5916
9.0691
8.4852
7.8264
7.0710
6.1846
5.0990
3.6400
0
D=60
x
1
1
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
y
14.9917
14.9666
14.9248
14.8661
14.7902
14.6969
14.586
14.4568
14.3091
14.1421
13.9553
13.7477
13.5185
13.2665
12.9904
12.6886
12.3592
12
11.6082
11.1803
10.7121
10.198
9.6306
24
25
26
27
28
29
30
9
8.2915
7.4833
6.5383
5.3851
3.8405
0
D=66
x
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
y
16.4924
16.4697
16.4317
16.3783
16.3095
16.225
16.1245
16.0078
15.8745
15.7242
15.5563
15.3704
15.1658
14.9416
14.6969
14.4309
14.1421
13.8293
13.4907
13.1244
12.7279
12.2984
11.8322
11.3248
10.7703
10.1612
9.4868
8.7321
7.8740
6.8738
5.6558
4.0311
0
D= 72
x
1
2
y
17.9931
17.9722
3
4
5
6·
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
17.9374
17.8885
17.8255
17.7482
17.6564
17.5499
17.4284
17.2916
17.1391
16.9706
16.7854
16.5831
16.3631
16.1245
15.8666
15.5885
15.2889
14.9666
14.6202
14.2478
13.8474
13.4164
12.9518
12.4499
11.9059
11.3137
10.6654
9.9498
9.1515
8.2462
7.1937
5.9160
4.2130
0
D=78
x
1
2
3
4
5
6
7
8
9
10
11
Y
19.4936
19.4743
19.4422
19.3972
19.3391
19.2678
19.1833
19.0853
18.9737
18.8481
18.7083
I
295
TABLE FOR LOCATING POINTS
ON 2: 1 ELLIPSOIDAL HEADS (Cont.)
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
D=78
18.554
18.3848
18.2003
18
17.7834
17.5499
17.2988
17.0294
16.7407
16.4317
16.1012
15.748
15.3704
14.9666
14.5344
14.0712
13.5739
13.0384
12.4599
11.8322
11.1467
10.3923
9.5524
8.6023
7.5
6.1644
4.3874
0
D=84
x
y
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
20.994
20.9762
20.9464
20.9045
20.8507
20.7846
20.7063
20.6155
20.5122
20.3961
20.267
20.1246
19.9687
19.799
19.615
19.4165
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
19.2029
18.9737
18.7283
18.4662
18.1865
17.8885
17.5713
17.2337
16.8745
16.4924
16.0857
15.6525
15.1905
14.6969
14.1686
13.6015
12.9904
12.3288
11.6082
10.8167
9.9373
8.9442
7.7942
6.4031
4.5552
0
D=90
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
20.1556
19.8997
19.6278
19.3391
19.0329
18.7083
18.3644
18
17.6139
17.2047
16.7705
16.3095
15.8193
15.2971
14.7394
14.1421
13.5
12.8062
12.052
11.225
10.3078
9.2736
8.0777
6.6332
4.7169
0
D=96
y
x
y
x
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
22.4944
22.4778
22.4499
22.4109
22.3607
22.2991
22.2261
22.1416
22.0454
21.9374
21.8174
21.6852
21.5407
21.3834
21.2132
21.0297
20.8327
20.6216
20.3961
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
23.9948
23.9792
23.9531
23.9165
23.8694
23.8118
23.7434
23.6643
23.5744
23.4734
23.3613
23.2379
23.103
22.9565
22.798
22.6274
22.4444
22.2486
22.0397
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
21.8174
21.5812
21.3307
21.0654
20.7846
20.4878
20.1742
19.8431
19.4936
19.1246
18.735
18.3235
17.8885
17.4284
16.9411
16.4241
15.8745
15.2889
14.6629
13.9911
13.2665
12.48
11.619
10.6654
9.5916
8.3516
6.8556
4.8734
0
D= 108
x
y
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
26.9954
26.9815
26.9583
26.9258
26.884
26.8328
26.7722
26.7021
26.6224
26.533
26.4339
26.3249
26.2059
26.0768
25.9374
25.7876
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
x
1
2
3
4
5
6
7
25.6271
25.4558
25.2735
25.0799
24.8747
24.6577
24.4285
24.1868
23.9322
23.6643
23.3827
23.0868
22.7761
22.4499
22.1077
21.7486
21.3717
20.9762
20.5609
20.124f
19.666
19.1833
18.6748
18.1384
17.5713
16.9706
16.3325
15.6525
14.9248
14.1421
13.2947
12.3693
11.3468
10.198
8.8741
7.2801
5.1720
0
D= 120
I
y
29.9958
29.9833
29.9625
29.9333
29.8957
29.8496
29.7951
296
TABLE FOR LOCATING POINTS
ON 2: 1 ELLIPOIDAL HEADS (Cont.)
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
D=120
29.7321
29.6606
29.5804
29.4915
29.3939
29.2874
29.l719
29.0474
28.9137
28.7706
28.6182
28.4561
28.2843
28.1025
27.9106
27.7083
27.4955
27.2718
27.037
26.7909
26.533
26.2631
25.9808
25.6856
25.3772
25.0549
24.7184
24.367
24
23.6167
23.2164
22.798
22.3607
21.9032
21.4243
20.9225
20.3961
19.8431
19.2614
18.6481
18
17.3133
16.5831
15.8035
14.9666
14.0624
13.0767
55
56
57
58
59
60
x
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
10.9896
10.7703
9.3675
7.6811
5.4543
0
0= 132
y
32.9962
32.9848
32.9659
32.9393
32.9052
32.8634
32.8139
32.7567
32.6917
32.619
32.5384
32.45
32.3535
32.249
32.1364
32.0156
31.8865
31.749
31.603
31.4484
31.285
31.1127
30.9314
30.7409
30.541
30.3315
30.1123
29.8831
29.6437
29.3939
29.1333
28.8617
28.5788
28.2843
27.9777
27.6586
27.3267
26.9815
26.6224
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66X
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
26.2488
25.8602
25.4558
25.035
24.5967
24.1402
23.6643
23.1679
22.6495
22.1077
21.5407
20.9464
20.3224
19.666
18.9737
18.2414
17.4642
16.6358
15.748
14.7902
13.7477
12.5996
11.3137
9.8361
8.0622
5.7227
0
0= 144
Y
35.9965
35.9861
35.9687
35.9444
35.9131
35.8748
35.8295
35.7771
35.7176
35.6511
35.5774
35.4965
35.4083
35.3129
35.2101
35.0999
34.9821
34.8569
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
34.7239
34.5832
34.4347
34.2783
34.1138
33.9411
33.7602
33.5708
33.3729
33.1662
32.9507
32.7261
32.4923
32.249
31.9961
31.7333
31.4603
31.1769
30.8828
30.5778
30.2614
29.9333
29.5931
29.2404
28.8747
28.4956
28.1 025
27.6948
27.2718
26.8328
26.3771
25.9037
25.4116
24.8998
24.367
23.8118
23.2325
22.6274
21.9943
21.3307
20.6337
19.8997
19.1246
18.303
17.4284
16.4924
15.4839
14.3875
67
68
69
70
71
72
13.1814
11.8322
10.2835
8.4261
5.9791
0
NOTE:
The curvature
of an ellipsoidal
head either
inside or outside
is a true
ellipse.
The parallel
curve of the
opposite side
is not ellipse
and the
data of
this table
are not
applicable
to locate
points on
that geometrically undetermined
curve.
( especially
in the case
of heavy
walled heads)
297
LENGTH OF ARCS
1. These tables are for locating points on pipes and shells by measuring
the length of arcs.
2. The length of arcs are computed for the most commonly used pipe-
sizes and vessel diameters.
3. The length of arcs for any diameters and any degrees, not shown in the
table, can be obtained easily using the values given for diam. 1 or degree 1.
4. All dimensions are in inches.
EXAMPLES
A.
270"
90"
O.D. = 30"
Nozzle located @ 30°
From table the length of
arc = 7.8438 in.
180"
B.
O.D. = 30"
Nozzle located @ 60°
The arc to be measured from the
closest centerline
The nozzle is @ 30° from the 90°
<L. The length of this arc: 7.8438 in.
270"
180"
c.
270"
90"
I.D. = 30" Wall thickness = 3/8", than
O.D. = 30 %"
Nozzle located @ 300
From table length of 30° arc for
dia. 1 = 0.26180
0.26180 x 30.75 = 8.0503 in.
180"
D.
270"
90"
1800
O.D. = 30"
Nozzle located @ 22~0
From table length of 1° arc on
30" 0.0. Pipe =0.26180
0.26180 x 22.5 =5.890 in.
298
LENGTH OF ARCS
DEGREES
Diam.
1
~
N
t il
~
1
5
0.00873
0.04363
10
0.08727
15
20
25
0.13090
0.17453
0.21817
1
0.01148
0.0625
0.1250
0.1875
0.2188
1'h
0.01658
0.0938
0.1563
0.2500
0.3438
30
0.26180
0.2813
0.3438
0.4063
0.5000
2
0.02073
0.0938
0.2188
0.3125
0.4063
0.5313
0.6250
2'h
0.02509
0.1250
0.2500
0.3750
0.5000
0.6250
0.7500
0.9063
3
0.03054
0.1563
0.3125
0.4688
0.6250
0.7500
3'h
0.03491
0.1875
0.3438
0.5313
0.6875
0.8750
1.0625
-<
Z
4
0.03927
0.1875
0.4063
0.5938
0.7813
0.9688
1.1875
5
0.04855
0.2500
0.5000
0.7188
0.9688
1.2188
1.4688
~
6
0.05781
0.2813
0.5938
0.8750
1.1563
1.4375
1.7500
8
0.07527
0.3750
0.7500
1.1250
1.5000
1.8750
2.2500
10
0.09381
0.4688
0.9375
1.4063
1.8750
2.3488
2.8125
12
0.11126
0.5625
1.1250
1.6563
2.2188
2.7813
3.3438
12
0.10472
0.5313
1.0625
1.5625
2.0938
2.6250
3.1563
14
0.12217
0.6250
1.2188
1.8438
2.4375
3.0625
3.6563
16
0.13963
0.6875
1.4063
2.0938
2.7813
3.5000
4.1875
Q"
Q"
~
0
Z
18
0.15708
0.7813
1.5625
2.3438
3.1563
3.9375
4.7188
20
0.17453
0.8750
1.7500
2.6250
3.5000
4.3750
5.2500
22
0.19199
0.9688
1.9063
2.8750
3.8438
4.8125
5.7500
24
0.20944
1.0625
2.0938
3.1563
4.1875
5.2500
6.2813
26
0.22689
1.1250
2.2813
3.4063
4.5313
5.6875
6.8125
28
0.24435
1.2188
2.4375
3.6563
4.8750
6.0938
7.3488
30
0.26180
1.3125
2.6250
3.9375
5.2500
6.5313
7.8438
32
0.27925
1.6172
2.7813
4.1875
5.5938
6.9688
8.3750
34
0.29671
1.6224
5.9375
7.4063
8.9063
0.31416
1.5625
2.9688
3.1563-
4.4375
36
4.7188
6.2813
7.8438
9.4375
:x::
38
0.33161
1.6563
3.3125
4.9688
6.6250
8.2813
9.9375
Z
40
0.34907
1.7500
3.5000
5.2500
6.9688
8.7188
10.4688
~
~
~
42
0.36652
1.8438
3.6563
5.5000
7.3438
9.1563
11.0000
48
0.41888
2.0938
4.1875
6.2813
8.3750
12.5625
:x::
til
54
0.47124
2.3438
4.7188
7.0625
9.4375
10.4688
11.7813
~
60
0.57360
2.6250
5.2500
7.8438
10.4688
13.0938
15.7188
17.2813
til
~
U
0
14.1250
66
0.57596
2.8750
5.7500
8.6250
11.5313
14.4063
72
0.62832
3.1250
6.2813
9.4375
12.5625
15.7188
18.8438
~
78
0.68068
3.4063
6.8125
10.2188
13.6250
17.0313
20.4063
-<
84
0.73304
3.6563
7.3438
11.0000
14.6563
18.3125
22.0000
90
0.78540
3.9375
7.8438
11.7813
15.7188
19.6250
23.5625
96
102
0.83776
4.1875
8.3750
12.5625
16.7500
20.9375
25.1250
0.89012
4.4375
8.9063
13.3438
17.8125
22.2500
26.7188
108
0.94248
4.7188
9.4375
14.1250
18.8438
23.5625
28.9063
114
0.99484
4.9688
9.9375
14.9375
19.9063
24.8750
29.8438
120
1.04720
5.2500
10.4688
15.7188
20.9375
26.1875
31.5313
126
1.09956
5.5000
11.0000
16.5000
22.0000
27.5000
33.0000
132
1.15192
5.7500
11.5313
17.2813
23.0313
28.8125
34.5625
138
1.20428
6.0313
12.0313
18.0625
24.0938
30.0938
36.1250
144
1.25664
6.2813
12.5625
18.8438
25.1250
31.4063
37.6875
~
~
~
~
~
299
LENGTH OF ARCS
DEGREES
Diam.
"-l
N
r;;
"-l
i:I..
35
40
45
90
180
270
360
2.35619
3.14159
1
0.30543
0.78540
1.57080
1
1 V,
0.4063
0.4688
0.5313
1.0313
2.0625
3.0938
0.5938
0.6563
0.7500
1.5000
3.0000
4.4688
5.9688
2
0.7188
0.8438
0.9375
1.8750
3.7188
5.5938
7.4688
2V,
0.8750
1.0000
1.1250
2.2500
4.5313
6.7813
9.0313
3
1.0625
1.2188
1.3750
2.7500
5.5000
8.2500
11.0000
0.34907
0.39270
4.1250
Q:
3%
1.2188
1.4003
1.5625
9.4375
12.5625
4
1.3750
1.5625
1.7813
3.1563
3.5313
6.2813
.J
7.0625
10.5938
14.1250
5
1.6875
1.9375
2.1875
4.3750
8.7500
13.0938
17.4688
6
2.0313
2.3125
2.5938
5.2188
10.4063
15.6250
20.8125
27.0938
<
Z
i
0
Z
8
2.6250
3.0938
3.3750
6.7813
13.5625
20.3125
10
3.2813
3.7500
4.2188
8.4375
16.8750
25.3438
33.7813
12
3.9063
4.4375
5.0000
10.0000
20.0313
30.0313
40.0625
12
3.6563
4.1875
4.7188
9.4375
18.8438
29.2813
37.0625
14
4.2813
4.8750
5.5000
11.0000
22.0000
33.0000
43.9688
16
4.8750
5.5938
6.2813
12.5625
25.1250
37.6875
50.2500
18
5.5000
6.2813
7.0313
14.1250
28.2813
42.4063
56.5625
20
6.9688
7.8438
15.7188
31.4063
47.1250
62.8438
22
6.0938
6.7188
7.6875
8.6563
17.2813
34.5625
51.8438
69.1250
24
7.3438
8.3750
9.4375
18.8438
37.6875
56.5625
75.4063
26
7.9375
9.0625
10.2188
20.4063
40.8438
61.2500
81.6875
28
8.5625
9.7813
11.0000
22.0000
43.9688
65.9688
87.9688
30
9.1563
10.4688
11.7813
23.5625
47.1250
70.6875
94.2500
32
9.7813
11.1563
12.5625
25.1250
50.2500
75.4063
100.5313
34
10.3750
11.8750
13.3438
26.7188
53.4060
80.1250
106.8125
36
11.0000
12.5625
14.1250
28.2813
56.5625
84.8125
113.0938
38
11.5938
13.2500
14.9375
29.8438
59.6875
89.5313
119.3750
-
40
12.2188
13.9688
15.7188
31.4063
62.8438
94.2500
125.6563
42
12.8438
14.6563
16.5000
33.0000
65.9688
98.9688
131.9375
48
14.6563
16.7500
18.8438
37.6875
75.4063
113.0938
150.7813
"-l
54
16.5000
18.8438
21.2188
42.4063
84.8125
127.2500
169.6563
til
60
18.3125
20.9375
23.5625
47.1250
94.2500
141.3750
188.5000
0
'-
66
20.1563
23.0313
25.9065
51.8438
103.6875
155.5000
20~.3.~
~
72
22.0000
25.1250
28.2813
56.5625
113.0938
169.6563
226.1875
~
78
23.8125
27.2188
30.6250
61.2500
122.5313
183.7813
245.0313
84
25.6563
29.3125
33.0000
65.9688
131.9375
197.9063
263.9063
90
27.5000
31.4063
35.2438
70.6875
141.3750
212.0625
282.7500
96
29.3125
33.5000
37.6875
75.4063
150.7813
226.1875
301.5938
102
31.1563
35.5938 40.1250
80.1250
160.2188
240.3438
320.4375
til
"-l
::z::
U
Z
.J
.J
::z::
"-l
"-l
::!!
-<
Q
108
33.0000
37.6875
42.4063
84.8125
169.6563
354.4688
339.2813
114
34.8125
39.7813 49.7813
89.5313
179.0625
268.5938
358.1250
120
36.6563
41.8750 47.1250
94.2500
188.5000
282.7500
377.0000
126
38.5000
43.9688
49.4688
98.9688
197.9063
296.8750
395.8438
132
40.3125
46.0625
51.8438
103.6563
207.3438
311.0313
414.6875
138
42.1563
48.1563
54.1875
108.3750
216.7813
325.1563
433.5313
144
43.9688
50.2500
56.5625
113.0938
226.1875
339.2813
452.3750
300
CIRCUMFERENCES AND AREAS OF CIRCLES
Dia.
}(4
~2
;(4
~6
~2
VB
%2
~6
}{2
}i
%
Yi6
IJ{2
VB
lYa2
Ks
1%'2
Yz
IJ{2
Us
1~2
%
2J{2
IY(S
2Ya2
~
2%2
l~(S
2J{2
VB
2~2
l?{S
3}{2
Circum.
.04909
.09818
.14726
.19635
.29452
.39270
.49087
.58905
.68722
Area
.00019
.00077
.00173
.00307
.00690
.01227
.01917
.02761
.03758
.78540
.88357
.98175
1.0799
1.1781
l.2763
1.3744
1.4726
.04909
.06213
.07670
.09281
.11045
.12962
.15033
.17257
1.5708
1.6690
1.7671
1.8653
1.9635
2.0617
2.1598
2.2580
.19635
.22166
.24850
.276.88
.30680
.33824
.37122
.40574
2.3562
2.4544
2.5525
2.6507
2.7489
2.8471
2.9452
3.0434
.44179
.47937
.51849
.55914
.60132
.64504
.69029
.73708
Dia.
2.
~6
Va
~6
}i
~6
VB
J{6
Yz
Us
%
lY(6
~
I;J{S
VB
1?{6
3.
k6
VB
;J{s
7'4
~{6
%
J{s
Yz
Us
%
lY(s
~
Ws
VB
I%;
4.
k6
VB
--1.
k6
VB
~6
}i
?{6
%
J{6
Yz
Yt6
%
lk6
%
1;J{6
VB
1~6
3.1416
3.3379
3.5343
3.7306
3.9270
4.1233
4.3197
4.5160
4.7124
4.9087
5.1051
5.3014
5.4978
5.6941
5.8905
6.0868
.7854
.8866
.9940
1.1075
l.2272
1.3530
1.4849
1.6230
1.7671
1.9175
2.0739
2.2365
2.4053
2.5802
2.7612
2.9483
~6
}i
Yi6
VB
K6
Yz
Yt6
%
lY(S
~
1:l16
VB
lYis
5.
h'6
Va
I
Circum.
Area
Dia.
3.1416
3.3410
3.5466
3.7583
3.9761
4.2000
4.4301
4.6664
4.9087
5.1572
5.4119
5.6727
5.9396
6.2126
6.4918
6.7771
~6
}4
Yi6
\
6.2832
6.4795
6.6759
6.8722
7.0686
7.2649
7.4613
7.6576
7.8540
8.0503
8.2467
8.4430
8.6394
8.8357
9.0321
9.2284
9.4248
9.6211
9.8175
10.014
10.210
10.407
10.603
10.799
10.996
11.192
11.388
11.585
11.781
11.977
12.174
12.370
i
7.0686
7.3662
7.6699
7.9798
8.2958
8.6179
8.9462
9.2806
9.6211
9.9678
10.321
10.680
11.045
11.416
11. 793
12.177
12.566
12.763
12.959
13.155
13.352
13.548
13.744
13.941
14.137
14.334
14.530
14.726
14.923
15.119
15.315
15.512
12.566
12.962
13.364
13.772
14.186
14.607
15.033
15.466
15.904
16.349
16.800
17.257
17.728
18.190
18.665
19.147
15.708
15.904
16.101
19.635
20.129
20.629
VB
K6
Yz
Yt6
%
1!{6
~
W6
VB
1~i6
6.
Va
}4
VB
Yz
%
~
Ys
7.
VB
}i
VB
Yz
%
~
Ys
8.
VB
}i
VB
Yz
%
~
Ys
9.
Va
}i
VB
Yz
%
~
Ys
10.
Va
}i
I
Circum.
I
Area
16.297
16.493
16.690
16.886
17.082
17.279
17.475
17.671
17.868
18.064
18.261
18.457
18.653
21.135
21.648
22.166
22.691
23.221
23.758
24.301
24.850
25.406
25.967
26.535
27.109
27.688
18.850
19.242
19.63)
20.028
20.420
20.813
21.206
21.598
28.274
29.465
30.680
31.919
33.183
34.472
35.785
37.122
21.991
22.384
22.776
23.169
23.562
23.955
24.347
24.740
38.485
39.871
41.282
42.718
44.179
45.664
47.173
48.707
25.133
25.525
25.918
26.311
26.704
27.096
27.489
27.882
50.265
51.849
53.456
55.088
56.745
58.426
60.132
61.862
28.274
28.667
29.060
19.452
29.845
30.238
30.631
31.023
63.617
65.397
67.201
69.029
70.882
72.760
74.662
76.589
31.416
31.809
32.201
78.540
80.516
82.516
301
CIRCUMFERENCES AND AREAS OF CIRCLES
Dia.
10.
%
Circum.
Area
84.541
86.590
88.664
90.763
92.886
34.558
34.950
35.343
35.736
36.128
36.521
36.914
37.306
95.033
97.205
99.402
101.62
103.87
106.14
108.43
110.75
37.699
38.092
38.485
38.877
39.270
39.663
40.055
40.448
113.10
115.47
117.86
120.28
122.72
125.19
127.68
130.19
40.841
41.233
41.626
42.019
42.412
42.804
43.197
43.590
132.73
135.30
137.89
140.50
143.14
145.80
148.49
151.20
43.982
44.375
44.768
45.160
45.553
45.946
46.338
46.731
153.94
156.70
159.48
162.30
165.13
167.99
170.87
173.78
Y2
%
%:
VB
47.124
47.517
47.909
48.302
48.695
49.087
49.480
49.873
176.71
179.67
182.65
185.66
188.69
191. 75
194.83
197.93
VB
50.265
50.658
201.06
204.22
11.
VB
~
%
Y2
%
%:
VB
12.
VB
7.i
%
Y2
%
%:
VB
13.
VB
~
%
Y2
%
%:
VB
14.
VB
~
%
Y2
%
%:
VB
15.
VB
~
%
16.
Dia.
Circum.
Area
Dia.
Circum.
~
51.051
51.444
51.836
52.229
52.622
53.014
207.39
210.60
213.82
217.08
220.35
223.65
VB
69.508
69.900
70.293
70.686
71.079
71.471
71.864
384.46
388.82
393.20
397.61
402.04
406.49
410.97
53.407
53.800
54.192
54.585
54.978
55.371
55.763
56.156
226.98
230.33
233.71
237.10
240.53
243.98
247.45
250.95
72.257
72.649
73.042
73.435
73.827
74.220
74.613
75.006
415.48
420.00
424.56
429.13
433.74
438.36
443.01
447.69
56.549
56.941
57.334
57.727
58.119
58.512
58.905
59.298
254.47
258.02
261.59
265.18
268.80
272.45
276.12
279.81
75.398
75.791
76.184
76.576
76.969
77.362
77.754
78.147
452.39
457.11
461.86
466.64
471.44
476.26
481.11
485.98
59.690
60.083
60.476
60.868
61.261
61.654
62.046
62.439
283.53
287.27
291.04
.294.83
298.65
302.49
306.35
310.24
78.540
78.933
79.325
79.718
80.111
80 503
80.896
81.289
490.87
495.79
500.74
505.71
510.71
515.72
520.77
525.84
62.832
63.225
63.617
64.010
64.403
64.795
65.188
65.581
314.16
318.10
322.06
326.05
330.06
334.10
338.16
342.25
81.681
82.074
82.467
82.860
83.252
83.645
84.038
84.430
530.93
536.05
541.19
546.35
551.55
556.76
562.00
567.27
65.973
66.366
66.759
67.152
67.544
67.937
68.330
68.722
346.36
350.50
354.66
358.84
363.05
367.28
371.54
375.83
84.823
85.216
85.608
86.001
86.394
86.786
87.179
87.572
572.56
577.87
583.21
588.57
593.96
599.37
604.81
610.27
69.115
380.13
I
32.594
32.987
33.379
33.772
34.165
Y2
%
%
VB
(continued)
%
Y2
%
%
VB
17.
VB
~
%
Y2
%
%
VB
18.
VB
~
%
Y2
%
%:
VB
19.
VB
~
%
Y2
%
%
VB
20.
VB
~
%
Y2
%
%:
VB
21.
VB
~
%
Y2
%
%:
~
22.
~
%
Y2
%
%
Ys
23.
VB
~
%
Y2
%
%:
VB
24.
VB
~
%
Y2
%
%:
VB
25.
VB
~
%
Y2
%
%:
VB
26.
VB
~
%
Y2
%
%:
VB
27.
VB
~
%
Y2
%
%
VB
II
Area
302
CIRCUMFERENCES AND AREAS OF CIRCLES
Circum.
Area
87.965
88.357
88.750
89.143
89.535
89.928
90.321
90.713
615.75
621.26
626.80
632.36
637.94
643.55
649.18
654.84
34.
91.106
91.499
91.892
92.284
92.677
93.070
93.462
93.855
660.52
666.23
671.96
677.71
683.49
689.30
695.13
700.98
35.
706.86
712.76
718.69
724.64
730.62
736.62
742.64
748.69
36.
7.i
%
%
%
94.248
94.640
95.033
95.426
95.819
96.211
96.604
96.997
97.389
97.782
98.175
98.567
98.960
99.353
99.746
100.138
754.77
760.87
766.99
773.14
779.31
785.51
791.73
797.98
37.
Ys
7.i
%
%
%
100.531
100.924
101.316
101.709
102.102
102.494
102.887
103.280
804.25
810.54
816.86
823.21
829.58
835.97
842.39
848.83
38.
103.673
104.065
104.458
104.851
105.243
105.636
106.029
106.421
855.30
861.79
868.31
874.85
881.41
888.00
894.62
901.26
39.
Dia.
28.
%
7.i
%
%
%
~
~
29.
%
7.i
%
%
%
~
VB
30.
%
~
~
31.
~
~
32.
Ys
7.i
%
%
%
~
VB
Dia.
%
7.i
VB
%
%
~
~
%
7.i
VB
%
%
~
VB
Ys
7.i
VB
Y2
%
~
~
%
7.i
VB
Y2
%
~
Ys
Ys
7.i
%
Y2
%
~
~
Circum.
Area
106.814
107.207
107.600
107.992
108.385
108.778
109.170
109.563
907.92
914.61
921.32
928.06
934.82
941.61
948.42
955.25
40.
109.956
110.348
110.741
111.134
111.527
111.919
112.312
112.705
962.11
969.00
975.91
982.84
989.80
996.78
1003.8
1010.8
41.
113.097
113.490
113.883
114.275
114.668
115.061
115.454
115.846
1017.9
1025.0
1032.1
1039.2
1046.3
1053.5
1060.7
1068.0
42.
)16.239
116.632
117.024
117.417
117.810
118.202
118.596
118.988
1075.2
1082.5
1089.8
1097.1
1104.5
1111.8
1119.2
1126.7
43.
119.381
119.773
120.166
120.559
120.951
121.344
121.737
122.129
1134.1
1141.6
1149.1
1156.6
1164.2
1171.7
1179.3
1186.9
122.522
122.915
123.308
123.700
124.093
124.486
124.878
125.271
1194.6
1202.3
1210.6
1217.7
1225.4
1233.2
1241.0
1248.8
Dia.
%
7.i
VB
%
%
~
~
%
7.i
%
%
%
~
~
%
7.i
%
Y2
%
~
~
Ys
I
7.i
VB
~
%
~
Ys
44.
Ys
74
%
%
%
~
!
Ys
I
(continued)
Circum.
Area
125.664
126.056
126.449
126.842
127.235
127.627
128.020
128.413
1256.6
1264.5
1272.4
1280.3
1288.2
1296.2
1304.2
1312.2
128.805
129.198
129.591
129.983
130.376
130.769
131.161
131.554
1320.3
1328.3
1336.4
1344.5
1352.7
1360.8
1369.0
1377.2
131.947
132.340
132.732
133.125
133.518
133.910
134.303
134.696
1385.4
1393.7
1402.0
1410.3
1418.6
1427.0
1435.4
1443.8
135.088
135.481
135.874
136.267
136.659
137.052
137.445
137.837
1452.2
1460.7
1469.1
1477.6
1486.2
1494.7
1503.3
1511.9
138.230
138.623
139.015
139.408
139.801
140.194
140.586
140.979
1520.5
1529.2
1537.9
1546.6
1555.3
1564.0
1572.8
1581.6
141.372
141.764
142.157
142.550
142.942
143.335
143.728
144.121
1590.4
1599.3
1608.2
1617.0
1626.0
1634.9
1643.9
1652.9
I
33.
Ys
7.i
%
Y2
%
~
Ys
Ys
7.i
VB
Y2
%
~
Ys
45.
I
Ys
74
%
72
%
~
Ys
303
CIRCUMFERENCES AND AREAS OF CIRCLES
Dia.
Circum.
Area
Dia.
46.
144.513
144.906
145.299
145.691
146.084
146.477
146.869
147.262
1661.9
1670.9
1680.0
1689.1
1698.2
1707.4
1716.5
1725.7
52.
147.655
148.048
148.440
148.833
149.226
149.618
lSO.011
150.404
1734.9
1744.2
1753.5
1762.7
1772.1
1781.4
1790.8
1800.1
53.
lSO.796
151.189
151.582
151.975
152.367
152.760
153.153
153.545
1809.6
1819.0
1828.5
1837.9
1847.5
1857.0
1866.5
1876.1
54.
153.938
154.331
154.723
155.116
155.S09
155.902
156.294
156.687
1885.7
1895.4
1905.0
1914.7
1924.4
1934.2
1943.9
1953.7
55.
157.080
157.472
157.865
158.258
158.650
159.043
159.436
159.829
1963.5
1973.3
1983.2
1993.1
2003.0
2012.9
2022.8
2032.8
56.
160.221
160.614
161.007
161.399
161.792
162.185
162.577
162.970
2042.8
2052.8
2062.9
2073.0
2083.1
2093.2
2103.3
2113.5
57.
Va
~
%
%
%
%
Ys
47.
Va
~
%
72
%
%
Ys
48.
Ys
7.i
%
72
%
%
Ys
49.
Ys
~
%
%
%
%
Ys
SO.
Ys
7.i
%
%
%
%
Ys
51.
Ys
7.i
%
%
%
%
Ys
Va
~
%
%
%
%
Ys
Ys
7.i
%
}1
%
%
Ys
Ys
7.i
%
%
%
%
Ys
Ys
~
%
72
%
%
Ys
Ys
~
%
72
%
%
Ys
Ys
7.i
%
72
%
%
Ys
I
Area
Dia.
163.363
163.756
164.148
164.541
164.934
165.326
165.719
166.112
2123.7
2133.9
2144.2
2154.5
2164.8
2175.1
2185.4
2195.8
58.
166.504
166.897
167.290
167.683
168.075
168.468
168.861
169.253
2206.2
2216.6
2227.0
2237.5
2248.0
2258.5
2269.1
2279.6
59.
16~.646
2290.2
2300.8
2311.5
2322.1
2332.8
2343.5
2354.3
2365.0
60.
170.039
170.431
170.824
171.217
171.609
172.002
172.395
172.788
173.180.
173.573
173.966
174.358
174.751
175.144
175.536
2375.8
2386.6
2397.5
2408.3
2419.2
2430.1
2441.1
2452.0
61.
175.929
176.322
176.715
177.107
177.500
177.893
178.285
178.678
2463.0
2474.0
2485.0
2496.1
2507.2
2518.3
2529.4
2540.6
62.
179.071
179.463
179.856
180.249
180.642
181.034
181.427
181.820
2551.8
2563.0
2574.2
2585.4
2596.7
2608.0
2619.4
2630./
63.
Circum.
I
I
Va
~
VB
%
%
%
Ys
Ys
7.i
%
72
%
%
Ys
Ys
~
%
72
%
%
Ys
Ys
7.i
%
%
%
%
Ys
Ys
7.i
%
72
%
%
Ys
Ys
7.i
%
%
%
%
Ys
I
(continued)
Circum.
I
Area
182.212
182.605
182.998
183.390
183.783
184.176
184.569
184.961
2642.1
2653.5
2664.9
2676.4
2687.8
2699.3
2710.9
2722.4
185.354
185.747
186.139
186.532
186.925
187.317
187.710
188.103
2734.0
2745.6
2757.2
2768.8
2780.5
2792.2
2803.9
2815.7
188.496
188.888
189.281
189.674
190.066
190.459
190.852
191.244
2827.4
2839.2
2851.0
2862.9
2874.8
2886.6
2898.6
2910.5
191.637
192.030
192.423
192.815
193.208
193.601
193.993
194.386
2922.5
2934.5
2946.5
2958.5
2970.6
2982.7
2994.8
3006.9
194.779
195.171
195.564
195.957
196.350
196.742
197.135
197.528
3019.1
3031.3
3043.5
3055.7
3068.0
3080.3
3092.6
}l04.9
197.920
198.313
198.706
199.098
199.491
199.884
200.277
200.669
3117.2
3129.6
3142.0
3154.5
3166.9
3179.4
3191.9
3204.4
304
CIRCUMFERENCES AND AREAS OF CIRCLES
~I
64.
VB
~
%
Yz
%
%
Ys
65.
VB
}i
%
Yz
Ys
%
Ys
66.
VB
~
%
~1
Ys
%
Ys
67.
VB
3i
%
Yz
Ys
%
Ys
68.
VB
~
%
Yz
%
%
VB
69.
VB
~
%
Y2
%
%
Ys
Circum.
I
Area
Dia.
3217.0
3229.6
3242.2
3254.8
3267.5
3280.1
3292.8
3305.6
70.
204.204
204.596
204.989
205.382
205.774
206.167
206.560
206.952
3318.3
3331.1
3343.9
3356.7
3369.6
3382.4
3395.3
3408.2
7l.
207.345
207.738
208.131
208.523
208.916
209.309
209.701
2lO.094
3421.2
3434.2
3447.2
3460.2
3473.2
3486.3
3499.4
3512.5
72.
210.487
210.879
211.272
211.665
212.058
212.450
212.843
213.236
3525.7
3538.8
3552.0
3565.2
3578.5
3591.7
3605.0
3618.3
73.
213.628
214.021
214.414
214.806
215.199
215.592
215.984
216.377
3631.7
3645.0
3658.4
3671.8
3685.3
3698.7
3712.2
3725.7
74.
216.770
217.163
217.555
217.948
218.341
218.733
219.126
219.519
3739.3
3752.8
3766.4
3780.0
3793.7
3807.3
3821.0
3834.7
75.
201.062
201.455
201.847
202.240
202.633
203.025
203.418
203.811
VB
~
%
Yz
%
%
Ys
VB
~
%
Yz
Ys
%
Ys
VB
~
%
Yz
Ys
%
Ys
VB
~
%
~
Ys
%
Ys
VB
~
%
Yz
Ys
%
Ys
VB
~
%
Y2
Ys
%
VB
I
Area
Dia.
219.911
220.304
220.697
221.090
221.482
221.875
222.268
222.660
3848.5
3862.2
3876.0
3889.8
3903.6
3917.5
3931.4
3945.3
76.
223.053
223.446
223.838
224.231
224.624
225.017
225.409
225.802
3959.2
3973.1
3987.1
4001.1
4015.2
4029.2
4043.3
4057.4
77-
226.195
226.587
226.980
227.373
227.765
228.158
228.551
228.944
4071.5
4085.7
4099.8
4114.0
4128.2
4142.5
4156.8
4171.1
78.
229.336
.229.729
230.122
230.514
230.907
231.300
231.692
232.085
4185.4
4199.7
4214.1
4228.5
4242.9
4257.4
4271.8
4286.3
79.
232.478
232.871
233.263
233.656
234.049
234.441
234.834
235.227
4300.8
4315.4
4329.9
4344.5
4359.2
4373.8
4388.5
4403.1
80.
235.619
236.012
236.405
236.798
237.190
237.583
237.976
238.368
4417.9
4432.6
4447.4
4462.2
4477.0
4491.8
8l.
Circum.
I
4506.7
4521.5
(continued)
Circum.
Area
238.761
239.154
239.546
239.939
240.332
240.725
241.117
241.510
4536.5
4551.4
4566.4
4581.3
4596.3
4611.4
4626.4
4641.5
241.903
242.295
242.688
243.081
243.473
243.866
244.259
244.652
4656.6
4671.8
4686.9
4702.1
4717.3
4732.5
4747.8
4763.1
245.044
245.437
245.830
246.222
246.615
247.008
247.400
247.793
4778.4
4793.7
4809.0
4824.4
4839.8
4855.2
4870.7
4886.2
Yz
248.186
248.579
248.971
249.364
249.757
%
%
250.149
250.542
4901.7
4917.2
4932.7
4948.3
4963.9
4979.5
4995.2
5010.9
VB
~
%
Yz
%
%
Ys
VB
~
%
Yz
Ys
%
Ys
VB
~
3/
/8
Yz
Ys
%
Ys
VB
}i
%
Ys
Ys
~
%
Yz
Ys
%
VB
VB
~
%
Y2
%
%
VB
I
250.935
251.327
251.720
252.113
252.506
252.898
253.291
253.684
254.076
5026.5
5042.3
5058.0
5073.8
5089.6
5105.4
5121.2
5137.1
254.469
254.862
255.254
255.647
256.040
256.433
256.825
257.218
5153.0
5168.9
5184.9
5200.8
5216.8
5232.8
5248.9
5264.9
I
305
CIRCUMFERENCES AND AREAS OF CIRCLES
~1~cum·I~~_
Dia.
Circum.
82.
257.611
258.003
258.396
258.789
259.181
259.574
259.967
260.359
5281.0
5297.1
5313.3
5329.4
5345.6
5361.8
5378.1
5394.3
88.
260.752
261.145
261.538
261.930
262.323
262.716
263.108
263.501
5410.6
5426.9
5443.3
5459.6
5476.0
5492.4
5508.8
5525.3
89.
263.894
264.286
264.679
265.072
265.465
265.857
266.250
266.643
5541.8
5558.3
5574.8
5591.4
5607.9
5624.5
5641.2
5657.8
90.
267.035
267.428
267.821
268.213
268.606
268.999
269.392
269.784
5674.5
5691.2
5707.9
5724.7
5741.5
5758.3
5775.1
5791.9
91.
270.177
270.570
270.962
271.355
271. 748
272.140
272.533
272.926
5808.8
5825.7
5842.6
5859.6
5876.5
5893.5
5910.6
5927.6
92.
273.319
273.711
274.104
274.497
274.889
275.282
275.675
276.067
5944.7
5961.8
5978.9
5996.0
6013.2
6030.4
6047.6
6064.9
VB
34
%
Yz
%
%
:Va
Area
1- - - -
VB
74
%
Yz
%
%
:Va
---- - ---83.
Ys
74
%
Yz
%
%
:Va
--84.
VB
34
%
Yz
%
%
:Va
85.
VB
34
%
Yz
%
Ys
74
%
Yz
%
%
Ys
VB
74
%
Yz
%
%
:Va
VB
34
%
Yz
%
%
%
:Va
--- ---- ---86.
VB
74
%
7:!
%
%
:Va
87.
VB
34
%
Yz
%
%1
:Va
I
Ys
Ys
74
%
Yz
%
%
Dia.
Circum.
Are.
295.310
295.702
296.095
296.488
296.881
297.273
297.666
298.059
6939.8
6958.2
6976.7
6995.3
7013.8
7032.4
7051.0
7069.6
298.451
298.844
299.237
299.629
300.Q22
300.415
300.807
301.200
7088.2
7106.9
7125.6
7144.3
7163.0
7181.8
7200.6
7219.4
301.593
301.986
302.378
302.771
303.164
303.556
303.949
304.342
7238.2
7257.1
7276.0
7294.9
7313.8
7332.8
7351.8
7370.8
304.734
305.127
305.520
305.913
306.305
306.698
307.091
307.483
7389.8
7408.9
7428.0
7447.1
7466.2
7485.3
7504.5
7523.7
307.876
308.269
308.661
309.054
309.447
309.840
310.232
310.625
7543.0
7562.2
7581.5
7600.8
7620.1
7639.5
7658.9
7678.3
311.018
311.410
311.803
312.196
312.588
312.981
313.374
313.767
7697.7
7717.1
7736.6
7756.1
7775.6
7795.2
7814.8
7834.4
276.460
276.853
277.246
277.638
278.031
278.424
278.816
279.209
6082.1
6099.4
6116.7
6134.1
6151.4
6168.8
6186.2
6203.7
94.
279.602
279.994
280.387
280.780
281.173
281.565
281.958
282.351
6221.1
6238.6
6256.1
6273.7
6291.2
6308.8
6326.4
6344.1
95.
282.743
283.136
283.529
283.921
284.314
284.707
285.100
285.492
6361.7
6379.4
6397.1
6414.9
6432.6
6450.4
6468.2
6486.0
96.
285.885
286.278
286.670
287.063
287.456
287.848
288.241
288.634
6503.9
6521.8
6539.7
6557.6
6575.5
6593.5
6611.5
6629.6
97.
289.027
289.419
289.812
290.205
290.597
290.990
291.383
291.775
6647.6
6665.7
6683.8
6701.9
6720.1
6738.2
6756.4
6774.7
98.
292.168
292.561
292.954
293.346
293.739
294.132
294.524
294.917
6792.9
6811.2
6829.5
6847.8
6866.1
6884.5
6902.9
6921.3
99.
VB
34
%
Yz
%
%
:Va
Ys
74
%
Yz
%
%
Ys
VB
74
%
Yz
%
%
:Va
VB
74
%
Yz
%
%
Ys
Ys
34
%
7:!
%
%
Ys
- - - - - - - ----93.
VB
74
%
Yz
%
%
Ys
(continued)
Ys
Ys
74
%
Yz
%
%
Ys
306
CIRCUMFERENCES AND AREAS OF CIRCLES ( continued)
Dia.
100.
Ys
!4
%
Yz
%
%
:Va
101.
Ys
!4
%
Yz
%
%
:Va
102.
Ys
!4
%
Yz
%
%
:Va
103.
VB
!4
%
Yz
%
%
:Va
104.
Ys
!4
%
Yz
%
%
:Va
--lOS.
Ys
!4
%
Yz
%
%
:Va
Circum.
Area
Dia.
314.16
314.55
314.95
315.34
315.73
316.12
316.52
316.91
7854
7873
7893
7913
7933
7952
7972
7992
106.
317.30
317.69
318.09
318.48
318.87
319.27
319.66
320.05
8012
8032
8052
8071
8091
8111
8131
8151
107.
320.44
320.84
321.23
321.62
322.Dl
322.41
322.80
323.19
8171
8191
8211
8231
8252
8272
8292
8312
108.
323.59
323.98
324.37
324.76
325.16
325.55
325.94
326.33
8332
8352
8372
8393
8413
8434
8454
8474
109.
326.73
327.12
327.51
327.91
328.30
328.69
329.08
329.48
8495
8515
8536
8556
8577
8597
8618
8638
110.
329.87
330.26
330.65
331.05
331.44
331.83
332.22
332.62
8659
8679
8700
8721
8741
8762
8783
8804
111.
Circum.
I
Area
Dia.
333.01
333.40
333.80
334.19
334.58
334.97
335.37
335.76
8825
8845
8866
8887
8908
8929
8950
8971
112.
336.15
336.54
336.94
337.33
337.72
338.12
338.51
338.90
8992
9014
9035
9056
9077
9098
9119
9140
113.
339.29
339.69
340.08
340.47
340.86
341.26
341.65
342.04
9161
9183
114.
9225
9246
9268
9289
9310
342.43
}42.83
343.22
343.61
344.01
344.40
344.79
345.18
9331
9353
9374
9396
9417
9439
9460
9481
115.
9503
116.
%
%
Ys
345.58
345.97
346.36
346.75
347.15
347.54
347.93
348.33
9525
9546
9568
9589
9611
9633
9655
VB
348.72
349.11
Yz
349.90
350.29
Ys
351.Q7
351.47
Ys
!4
%
Yz
%
%
:Va
Ys
!4
%
Yz
%
%
:Va
Ys
!4
%
Yz
%
~4
Ys
VB
!4
%
Yz
%
%
:1
Ys
!4
%
Yz
~
~
%
%
I
349.50
350.68
9677
9698
9720
9742
9764
9786
9808
9830
Circum.
Area
351.86
352.25
352.65
~
353.04
%
%
:Va
353.43
353.82
354.22
354.61
9852
9874
9897
9919
9941
9963
9985
10007
355.00
355.39
355.79
356.18
356.57
356.96
357.36
357.75
10029
10052
10074
10097
10119
10141
10163
10185
358.14
358.54
358.93
359.32
359.71
360.11
360.50
360.89
10207
10230
10252
10275
10297
10320
10342
10365
361.28
361.68
362.07
362.46
362.86
363.25
363.64
364.03
10387
10410
10432
10455
364.43
364.82
365.21
365.60
366.00
366.39
366.78
367.18
10568
10590
106l}
10636
10659
10682
10705
10728
367.57
367.96
368.35
368.75
369.14
369.53
369.92
370.32
10751
10774
10798
10821
10844
10867
10890
10913
Ys
!4
Yz
VB
~
~
Yz
%
%
Ys
VB
~
~
9204
I
Yz
%
%
Ys
VB
~
~
Yz
%
%
Ys
VB
!4
%
Yz
%
%
Ys
117.
VB
!4
%
Yz
%
%
Ys
10477
10500
10522
10545
307
CIRCUMFERENCES AND AREAS OF CIRCLES
Dia.
118.
Ys
~
%
~
%
~
Ys
119.
Ys
~
%
~'2
%
~
Ys
120.
Ys
~
%
~
%
~
Ys
121.
Ys
~
%
~
%
~
Ys
122.
Ys
~
%
~
%
~.
Ys
123.
Ys
~
%
Y2
%
~
Ys
I
Circum.
Area
370.71
371.11
371.49
371.89
372.28
372.67
373.Q7
373.46
10936
10960
10983
11007
11030
11053
11076
11099
373.85
374.24
374.64
375.03
375.42
375.81
376.21
376.60
11122
11146
11169
11193
11216
11240
11263
11287
125.
376.99
377.39
377.78
378.17
378.56
378.96
379.35
379.74
11310
11334
11357
11381
11404
11428
11451
11475
126.
380.13
380.53
380.92
381.31
381.70
382.10
382.49
382.88
11499
11522
11546
11570
11594
11618
11642
11666
127.
383.28
383.67
384.06
384.45
384.85
385.24
385.63
386.02
11690
11714
11738
11762
11786
11810
11834
11858
128.
386.42
386.81
387.20
387.60
387.99
388.38
388.77
389.17
11882
11907
11931
11956
11980
12004
12028
12052
129.
Dia.
I Circum.
~I
Ys
~
%
~
%
~
Ys
Ys
~
%
Y2
%
~
Ys
Ys
~
%
~
%
~
Ys
.-
Ys
~
%
Y2
%
~
Ys
Ys
~
%
Y2
%
~
Ys
VB
~
%
Y2
%
~
Ys
Area
( continued)
~I Circum~j~_a_
389.56
389.95
390.34
390.74
391.13
391.52
391.92
392.31
12076
12101
12125
12150
12174
12199
12223
12248
130.
392.70
393.09
393.49
393.88
394.27
394.66
395.06
395.45
12272
12297
12321
12346
12370
12395
12419
12444
131.
395.84
396.23
396.63
397.02
397.41
397.81
398.20
398.59
12469
12494
12518
12543
12568
12593
12618
12643
132.
398.98
399.38
399.77
400.16
400.55
400.95
401.34
401.73
12668
12693
12718
12743
12768
12793
12818
12843
133.
402.13
402.52
402.91
403.30
403.70
404.09
404.48
404.87
12868
12893
12919
12944
12970
12995
13020
13045
134.
405.27
405.66
406.05
406.44
406.84
407.23
407.62
408.02
13070
13096
13121
13147
13172
13198
13223
13248
135.
Ys
~
%
Y2
YS
~
Ys
Ys
~
%
Y2
%
~
Ys
Ys
~
%
~
%
~
Ys
Ys
~
%
Y2
%
~
Ys
Ys
~
%
~
%
~
Ys
VB
~
VB
Y2
%
~
Ys
408.41
408.80
409.19
409.59
409.98
410.37
410.76
411.16
13273
13299
13324
13350
13375
13401
13426
13452
411.55
411.94
412.34
412.73
413.12
413.51
413.91
414.30
13478
13504
13529
13555
13581
13607
13633
13659
414.69
415.08
415.48
415.87
416.26
416.66
417.05
417.44
13685
13711
13737
13763
13789
13815
13841
13867
417.83
418.23
418.62
419.01
419.40
419.80
420.19
420.58
13893
13919
13946
13972
13999
14025
14051
14077
420.97
42l.37
421.76
422.15
422.55
422.94
423.33
423.72
14103
14130
14156
14183
14209
14236
14262
14288
424.12
424.51
424.90
425.29
425.69
426.08
426.47
426.87
14314
14341
14367
14394
14420
14447
14473
14500
308
CIRCUMFERENCES AND AREAS OF CIRCLES
Dia.
136.
VB
}i
%
Y2
%
%;
Ys
137.
VB
}i
%
Y2
%
%;
Ys
138.
VB
}i
%
Y2
%
%
Ys
13~.
~il
~4
3/
"8
H
%
%
Ys
140.
VB
~
~/8
Y2
%
%;
Ys
H.
Ys
~
%
Y2
%
%
Ys
I Circum. I
Area
427.26
427.65
428.04
428.44
428.83
429.22
429.61
430.01
14527
14553
14580
14607
14633
14660
14687
14714
142.
430.40
430.79
431.19
431.58
431.97
432.36
432.76
433.15
14741
14768
14795
14822
14849
14876
143.
Dia.
VB
~
%
H
%
%
Ys
Ys
~
%
H
%
14903
%;
14930
Ys
I Circum.
Area
Dia.
446.11
446.50
446.89
447.29
447.68
448.07
448.46
448.86
15837
15865
15893
15921
15949
15977
16005
16033
148.
449.25
449.64
450.03
450.43
450.82
451.21
451.61
452.00
16061
16089
16117
16145
16173
16201
16229
16258
149.
452.39
452.78
453.18
453.57
453.96
454.35
454.75
455.14
16286
16314
16342
16371
16399
16428
16456
16485
150.
455.53
-455.93
456.32
456.71
457.10
457.50
457.89
458.28
16513
16542
16570
16599
16627
16656
16684
16713
151.
458.67
459.07
459.46
459.85
460.24
460.64
461.03
461.42
16742
16770
16799
16827
16856
16885
16914
16943
152.
461.82
462.21
462.60
462.99
463.39
463.78
464.17
464.56
16972
17000
17029
17058
17087
17116
17145
17174
153.
VB
}i
%
Y2
%
%;
Ys
VB
~
%
Y2
%
%;
Ys
--144.
433.54
433.93
434.33
434.72
435.11
14957
14984
435.50
435.90
436.29
15094
15121
15148
436.68
437.08
437.47
437.86
438.25
438.65
439.04
439.43
15175
15203
15230
15258
15285
15313
15340
15367
145.
439.82
440.22
440.61
441.00
44l.40
441.79
442.18
442.57
15394
15422
15449
15477
15504
15532
15559
15587
146.
442.97
443.36
443.75
444.14
444.54
444.93
445.32
445.72
15615
15642
15670
15697
15725
15753
15781
15809
147.
VB
}i
15012
15039
15067
I
%
Y2
%
%
Ys
VB
}i
%
Y2
%
%
Ys
Ys
}i
%
H
%
%;
Ys
VB
}i
%
Y2
%
%
Ys
Ys
~
%
Y2
%
%
Ys
Ys
~
%
Y2
%
%
Ys
VB
}i
%
Y2
%
%;
Ys
VB
}i
%
Y2
%
%;
51
( &onl;nued)
Circum.
Area
464.96
465.35
465.74
466.14
466.53
466.92
467.31
467.71
17203
17232
17262
17291
17321
17350
17379
17408
468.10
468.49
468.88
469.28
469.67
470.06
470.46
470.85
17437
17466
17496
17525
17555
17584
17614
17643
471.24
471.63
472.03
472.42
472.81
473.20
473.60
473.99
17672
17702
17731
17761
17790
17820
17849
17879
474.38
474.77
475.17
475.56
475.95
476.35
476.74
477.13
17938
17967
17997
18026
18056
18086
18116
477.52
477.92
478.31
478.70
479.09
479.49
479.88
480.27
18146
18175
18205
18235
18265
18295
18325
18355
480.67
481.06
481.45
481.84
482.24
482.63
483.02
483.41
18385
18415'
18446
18476
18507
18537
18567
18597
17908
I
309
CIRCUMFERENCES AND AREAS OF CIRCLES
Dia.
154.
VB
!-i
%
Y2
%
%
VB
155.
VB
X
%
Y2
VB
%
VB
156.
VB
!-i
%
Y2
%
%
VB
157.
VB
X
%
Y2
%
%
VB
158.
VB
X
%
Y2
%
%
VB
159.
VB
X
%
Y2
%
%
VB
Circum.
Area
483.81
484.20
484.59
484.99
485.38
485.77
486.16
486.56
i8627
18658
18688
18719
18749
18779
18809
18839
160.
486.95
487.34
437.73
488.13
488.52
488.91
489.30
489.70
18869
18900
18930
18961
18991
19022
19052
19083
161.
490.09
490.48
490.88
491.27
491.66
492.05
492.45
492.84
19113
19144
19174
19205
19235
19266
19297
19328
162.
493.23
493.62
494.02
494.41
494.80
495.20
495.59
495.98
19359
19390
19421
19452
19483
19514
19545
19576
163.
496.37
496.77
497.16
497.55
497.94
498.34
498.73
499.12
19607
19638
19669
19701
19732
19763
19794
19825
164.
499.51
499.91
500.30
500.69
S01.09
S01.48
S01.87
S02.26
19856
19887
19919
19950
19982
20013
20044
20075
165.
Dia.
VB
!-i
%
Y2
%
%
:Va
VB
X
%
Y2
%
%
VB
VB
!-i
%
Y2
%
%
VB
VB
X
%
Y2
%
%
VB
VB
X
%
Y2
%
%
VB
VB
X
%
Y2
%
%
VB
I Circum.
I
Area
Dia.
S02.66
S03.05
S03.44
S03.83
S04.23
S04.62
505.01
S05.41
20106
20138
20169
20201
20232
20264
20295
20327
166.
S05.80
506.19
506.58
506.98
S07.37
507.76
508.15
508.55
20358
20390
20421
20453
20484
20516
20548
20580
167.
508.94
S09.33
S09.73
510.12
510.51
510.90
511.30
511.69
20612
20614
20675
20707
20739
20771
20803
20835
168.
512.08
512.47
512.87
513.26
513.65
514.04
514.44
514.83
20867
_ 20899
20931
20964
20996
21028
21060
21092
169.
515.22
515.62
516.01
516.40
516.79
517.19
517.58
517.97
21124
21157
21189
21222
21254
21287
21319
21351
170.
518.36
518.76
519.15
519.54
519.94
520.33
520.72
521.11
21383
21416
21448
21481
21513
21546
21578
21610
171.
Va
X
%
Y2
%
%
:Va
VB
X
%
Y2
VB
%
VB
VB
X
%
Y2
%
%
VB
VB
X
%
Y2
%
%
VB
VB
X
%
Y2
%
%
VB
VB
X
%
Y2
%
%
VB
I
(continued)
Circum.
I
Area
521.51
521.90
522.29
522.68
523.08
523.47
523.86
524.26
21642
21675
21707
21740
21772
21805
21838
21871
524.65
525.04
525.43
525.83
526.22
526.61
527.00
527.40
21904
21937
21969
22002
22035
22068
22101
22134
527.79
528.18
528.57
528.97
529.36
529.75
530.15
530.54
22167
22200
22233
22266
22299
22332
22366
22399
530.93
531.32
531.72
532.11
532.SO
532.89
533.29
533.68
22432
22465
22499
22532
22566
22599
22632
22665
534.07
534.47
534.86
535.25
535.64
536.04
536.43
536.82
22698
22731
22765
22798
22832
22865
22899
22932
537.21
537.61
538.00
538.39
538.78
539.18
539.57
539.96
22966
22999
23033
23066
23100
23133
23167
23201
310
CIRCUMFERENCES AND AREAS OF CIRCLES
Dia.
172-
Ys
~
%
Y2
%
~
Ys
173.
Ys
~
%
Y2
%
~
Ys
174.
Ys
~
%
Y2
%
~
Ys
175.
Ys
~
%
Yz
%
34
Ys
176.
Ys
~
%
Y2
%
~
Ys
177.
Ys
~
%
Y2
%
~
Ys
I Circum.
540.36
540.75
541.14
541.53
541.93
542.32
542.71
543.10
I
Area
23235
23268
23302
23336
23370
Dia.
178.
Ys
~
%
Y2
%
23404
~
23438
23472
Ys
543.50
543.89
544.28
544.68
545.Q7
545.46
545.85
546.25
23506
23540
546.64
547.03
547.42
547.82
548.21
548.60
549.00
549.39
23779
23813
23848
23882
23917
23951
23985
549.78
550.17
550.57
550.96
551.35
551.74
552.14
552.53
24053
24087
24122
24156
24191
24225
24260
24294
552.92
553.31
553.71
554.10
554.49
554.89
555.28
555.67
24329
24363
24398
24432
24467
24501
24536
24571
182.
556.06
556.46
556.85
557.24
557.63
558.03
558.42
558.81
24606
183.
179.
Ys
~
23575
23609
23643
23677
23711
23745
%
Y2
%
~
Ys
180.
Ys
~
%
Y2
%
~
Ys
24019
24640
24675
24710
24745
24780
24815
24850
181.
Ys
~
%
Y2
%
~
Ys
Ys
~
Vs
Y2
%
~
Ys
Ys
~
%
Y2
%
~
Ys
Circum.
Area
559.21
559.60
559.99
560.38
560.78
561.17
561.56
561.95
24885
24920
24955
24990
25025
25060
25095
25130
184.
562.35
562.74
563.13
563.53
563.92
564.31
564.70
565.10
25165
25200
25236
25271
25307
25342
25377
25412
185.
565.49
565.88
566.27
566.67
567.06
567.45
567.84
568.24
25447
25482
25518
25553
25589
25624
25660
25695
186.
568.63
-569.02
569.42
569.81
570.20
570.59
570.99
571.38
25730
25765
25801
25836
25872
25908
25944
25980
187.
571.77
572.16
572.56
572.95
573.34
573.74
574.13
574.52
26016
26051
26087
26122
26158
26194
26230
26266
188.
574.91
575.31
575.70
576.09
576.48
576.88
577.27
577.66
--
26302
26338
26374
26410
26446
26482
26518
26554
Dia.
Ys
~
%
Y2
%
~
Y8
Ys
~
%
Y2
%
~
Ys
Ys
~
%
Yz
%
~
Ys
Ys
~
%
Y2
%
~
Ys
Ys
~
Vs
Y2
%
~
Ys
189.
Ys
~
%
Y2
I
(continued)
Circum.
578.05
578.45
578.84
579.23
579.63
580.02
580.41
580.80
26590
26626
26663
26699
26736
26772
26808
26844
581.20
581.59
581.98
582.37
582.77
583.16
583.55
583.95
26880
26916
26953
26989
27026
27062
27099
27135
584.34
584.73
585.12
585.52
585.91
586.30
586.59
587.09
27172
27208
27245
27281
27318
27354
27391
27428
587.48
587.87
588.27
588.66
589.05
589.44
589.84
590.23
27465
27501
27538
27574
27611
27648
27685
27722
590.62
591.01
591.41
591.80
592.19
592.58
592.98
593.37
27759
27796
27833
27870
27907
27944
27981
28018
593.76
594.16
594.55
594.94
595.33
28055
28092
28130
28167
28205
28242
28279
28316
%
~5.73
Ys
596.12
596.51
~
Area
311
CIRCUMFERENCES AND AREAS OF CIRCLES
Dia.
190.
Ys
~4
%
Y2
%
:Ji
Ys
191.
Ys
Ii
%
Y2
%
:Ji
Ys
192.
Ys
~
%
Y2
%
:Ji
Ys
193.
VB
~
%
Yz
%
%
Ys
194.
Ys
!4
%
Yz
%
:Ji
Ys
195.
Ys
!4
%
Yz
%
%
Ys
Circum.
I
Area
Dia.
596.90
597.29
597.68
598.08
598.47
598.86
599.25
599.64
28353
28390
28428
28465
28503
28540
28578
28615
196.
600.04
600.44
600.83
601.22
601.62
602.01
602.40
602.79
28652
28689
28727
28764
28802
28839
28877
28915
197.
603.19
603.58
603.97
604.36
604.76
605.15
605.54
605.94
28953
28990
29028
29065
29103
29141
29179
29217
198.
606.33
606.72
607.11
607.51
607.90
608.29
608.58
609.08
29255
29293
29331
29369
29407
29445
29483
29521
199.
609.47
609.86
61026
610.65
61l.05
611.43
611.83
612.29
29559
29597
29636
29674
29713
29751
29789
29827
200.
612.61
613.00
613.40
613.79
614.18
614.57
614.97
615.36
29865
29903
29942
29980
30019
30057
201.
30096
30134
Ys
!4
%
Y2
%
%
Ys
Ys
U
%
Y2
%
:Ji
VB
Ys
!4
%
Y2
%
:Ji
Ys
Ys
!4
%
~2
%
:Ji
Ys
Ys
~
%
Y2
%
:Ji
Ys
Ys
!4
%
Yz
%
%
Ys
I Circum. I
Area
Dia.
( continued)
Circum.
I
Area
634.60
635.00
635.40
635.79
636.18
636.57
636.97
637.36
32047
32086
32126
32166
32206
32246
32286
32326
637.74
638.15
638.54
638.93
639.32
639.72
640.11
640.50
32366
32405
32445
32485
32525
32565
32605
32645
Ys
640.88
641.28
641.67
642.07
642.46
642.85
643.24
643.63
32685
32725
32766
32806
32846
32886
32926
32966
VB
!4
%
Y2
%
%
Ys
644.03
644.43
644.82
645.21
645.61
646.00
646.39
646.78
33006
33046
33087
33127
33168
33208
33249
33289
647.17
647.57
647.96
648.35
648.75
649.14
649.53
649.93
33329
33369
33410
33450
33491
33531
33572
33613
650.31
650.71
651.10
651.50
651.89
652.28
652.57
653.07
33654
33694
33735
33775
33816
33857
33898
33939
615.75
616.15
616.54
616.93
617.32
617.72
618.11
618.50
30172
30210
30249
30287
30326
30364
30403
30442
202.
618.89
619.29
619.68
620.08
620.47
620.86
621.25
621.64
30481
30519
30558
30596
30635
30674
203.
622.04
622.44
622.83
623.22
623.62
624.01
624.40
624.79
30791
30830
30869
30908
30947
30986
31025
31064
204.
625.18
625.58
625.97
626.36
626.76
627.15
627.54
627.94
31103
31142
31181
31220
31260
31299
31338
31377
205.
628.32
628.72
629.11
629.51
629.90
630.29
630.58
63l.08
31416
31455
31495
31534
31574
31613
31653
31692
206.
63l.46
631.86
632.26
632.65
633.05
633.43
633.83
634.29
31731
31770
31810
31849
31889
31928
31968
32007
207.
Ys
!4
%
Y2
%
%
Ys
Ys
~
%
Y2
%
%
Ys
30713
30752
Ys
!4
%
Yz
%
:Ji
Ys
!4
%
Yz
%
%
Ys
Ys
!4
%
Yz
%
%
Ys
312
DAVIT
l
I
3"
I
I __ -~3"
1~--+---4.\ ~~
I
! ~--
I
CENTER LINE
-4~~:.y-c~
I
4-_ _-4111......
~
FLANGE
1u--~
..0 ..
-tr
--,
-
".
'~,
~
-I
__
.~
EYE BOLT _ _ ,
/DAVITARM
,
1
I,
r-
,/""
..1
I
1
IVSLEEVE
Tt
I
STIFFENIN:'Ai"
n
U BAR-:tj
I
'
1/2 "
PLATE
\
i
-1
i
'\t
I
i
I
~5/8
I
====-
I : !!. . . .
if'
I
SLEEVE
=i
FOR VERTICAL OPENING
FOR HORIZONTAL OPENING
All material carbon steel
All welds 3/8" continuous filet weld
The davit has been tested against excessive deflection
Using davit less room is required than with the use of hinge
For frequently used opening, davit is preferred to hinge
FLANGE
RATING
SIZE
+
\
T
I.
2.
3.
4.
5.
PLATE
_+-+-_1-1/2"
H"D)~ ''"~-or~l~ht,;--4
NOTES:
'-IH+--
'I/~
OAVIT ARM
'\,
"
U'BAR-::Jj hSTIFFENING ..... ,
/' RING
.I'~
-HIt- , - _ .
1\
'::::-;:::
'\ ' l
i
,_'1'2"
EYE BOLT _ _
3"
300-
900 -
12 14 16 18 20 24 12 14 16 18 20 24 12 14 16 18 20 24 12 14 16 18 20 24
NO. OF
LIST
1 1 1 1 1 1 1 1 1 1 2 2 1 1 2 2 2 2
DAVIT ARM
SLEEVE
EYE-BOLT
V-BAR
LIST -I
1-1/2"-XH PIPE
2"-XH PIPE
5/8 q,
5/8 q,
RING
PLATE
HANDLE
5/8
5/8
5/8
STIFFENER
--
q,
LIST -2
2"-XXH PIPE
2-1/2" -STD PIPE
3/4
3/4
3/4
3/4
3/4
1 1 2 2 2
LIST - 3
2"-XXH PIPE
2-1/2"-STD PIPE
q,
q,
1"
I"
q,
1"
I"
q,
q,
I"
--
3/8"
q,
3
313
FIXED STAIR
Conforms to the requirements of
OCCUPATIONAL SAFETY AND HEALTH (OSHA) STANDARDS
Fixed stairs will be provided where operations necessitate regular travel between levels.
Fixed stairways shall be designed to carry a load of five times the normal live load anticipated
but never less than to carry a moving concentrated load of 1,000 pounds.
Minimum width: 22 inches
Angle of stairway rise to the horizontal: 30 to 50 degrees.
Railings shall be provided on the open sides of all exposed stairways. Handrails shall be
provided on at least once side of closed stairways, preferably on the right side descending.
Each tread and nosing shall be reasonably slip-resistant.
Stairs having treads of less than nine-inch width should have open risers. Open ,rating type
treads are desirable for outside stairs.
See figure for minimum dimensions. Bolts Y2
1<1
Bolt holes
9/16 1<1
All burrs and sharp edges shall be removed.
Dimensions of rises (R) and tread runs (T) tabulated below:
Ansle to
Horizontal
30 0
32 0
33 0
35 0
3S o
3S o
40 0
41 0
43 0
45 0
4S o
4S o
49 0
35'
OS'
41'
lS'
52'
29'
OS'
44'
22'
00'
3S'
lS'
54'
Riee
(in inches)
S~
Tread Run
(in inches)
~
11
lOy'
7
7~
7~
7Y.
10
9y'
10~
10~
9~
9~
S
S~
S~
9
Sy.
Sy.
9
S~
S~
9~
9~
S
5
'"
MIDRAIL
BAR 2xl/4
HANDRAIL POST
ANGLE 2x2.3/8
_
ANGLE 10 HORIZONTAL
314
HINGE
NOTE
LUG-A
WELDED TO BLIND FLANGE
Fit lugs and pin so that pin is loose
when cover is bolted up. Weld lugs
to flanges with full penetration weld.
Th~_~e_ordavit
preferred to hinge, especially
for frequently used openings.
A ==
VR2 - (R/2)2
B ==
VR2 -
(R/2+ 1/16+ t)2
C
R + 2% - A
o
R + 2% - B
R = Radius of flange
r = 1.5 times diameter of hole
Diameter of hole ::.
Pin diameter + 1/16 in.
LUG-B
WELDED TO FLANGE
THICKNESS, t OF LUGS AND DIAMETER OF PINS
RATING
FLG. DIAM.
RATING
3/4
3/4
3/4
3/4
3/4
3/4
3/4
3/4
3/4
3/4
3/4
12
14
16
18
20
24
12
14
16
18
20
3/4
3/4
3/4
3/4
24
1 1/2
315
LADDER
Conforms to the requirements of
STANDARD ANSI A14.3-1974 SAFETY REQUIREMENTS FOR FIXED LADDERS.
OUTSIDE OF
SHELL OR
INSULATION
SIDE STEP
.>"""'1".......=---'-
THROUGH STEP
24 in. min.
30 in. max.
n
SIDE RAIL
(note 5)
P=
RUNG
314 II BAR
NOTES
1. Cage is not required where the length of climb is 20 feet or less above ground
level.
2. Horizontally offset landing platform shall be provided at least every 30 ft. of
climbing length. Where safety devices are used, rest platforms shall be provided
at maximum interwalls of 250 feet.
3. All material: steel conforming to ASTM A 36
4. Instead of the above specified structural shapes any other structural steel of
equivalent strength may be used. To avoid damages during shipping or galvanizing, structural angles are widely used for side rail and vertical members of the
cage.
5. The recommended minimum size of side rails under normal atmospheric condition 2 1/2 x 3/8 in. flat bar,although 2 x 1/4 bars are frequently used in practice.
6. All burrs and sharp edges shall be removed.
7. Protective Coating: one shop coat primer and one field coat of paint or hot dip
galvanizing.
316
MIST
EXTRACTOR
Mist extractors by separating mist, undesirable liquids from vapor, steam, liquids,
etc. improve the performance of various process equipments. They are manufactured from metal or plastic mesh and available in any required size and shape.
~II~
detail· A or B
TYPES OF MIST EXTRACTORS
'ANGLE 1Klxl/8
DETAIL - A
DETAIL -
DETAIL - B
c
SUPPORT OF MIST EXTRACTORS
Use 6 I 12.5 beam support in center of mist extractor, when the diameter is greater
than 6 ft.
SPECIFICATION
THICKNESS OF PAD
WIRE
MESH
THICKNESS OF WIRE
MATERIAL OF WIRE
DENSITY Ib./Cu. ft.
PRESSURE DROP
MA TERIAL CARBON STEEL
GRID
4"
6"
.011 "
.011 "
TYPE 304 S.S. TYPE 304 S.S.
9.0
5.0
0.5" TO 1" WATER GAGE
BEARING BAR
l"x3/16"
CROSS BAR
BEARING BAR SPACING
CROSS BAR SPACING
WEIGHT Ib./sq.ft.
~ if>
lx3/16"
y.. if>
3-9/16
4"
3-9/16
4"
5.7
7.4
WIDTH OF ONE SECTION
12"
12"
317
NAME PLATE
Pressure vessels built in accordance with the requirements of the Code may be stamped
with the official symbol "U" to denote The American Society of Mechanical Engineers' standard. (Code UG-11S and 116)
Pressure vessels stamped with the Code-symbol shall be marked with the following:
1. manufacturer's name; preceded with the words: "certified by";
maximum allowable working pressure, (MA WP) psi at temperature, of;
maximum design metal temperature at maximum allowable working pressure,
psi (MDMT);
manufacturer's serial number; (SIN);
year built
Abbreviations may be used as shown in parenthesis.
2. the appropriate abbreviations indicating the type of construction, service, etc.,
as tabulated:
When inspected by a user's inspector
USER
Arc or gas welded
W
Lethal service
L
Unfired steam boiler
US
Direct firing
OF
Fully radiographed and UW-II (a)(S) not applied
Rfl
Joints A & D fully radiographed; UW-Il(a)(5)(b) applied
R12
Spot radiographed
RTI
When RTl, RT2 or RT3 are not applicable
Rf4
Post weld heat treated
ill
Part of the vessel post weld heat treated
PHT
Nonstationary Pressure Vessel
NPV
1. Symbol "UM" shall be used when the vessel is exemptedfrom inspection [Code U-l (k)].
2.
For vessels made of5%, 8% and 9% nickel sheets, the use afnameplates is mandatory
for shell thickness below ~ in.; name plates are preferred on all thicknesses.
Code ULT-1l5(c)
USER
CERTIFIED BY
OMEGA TANK CO.
MA WP 250 psi II 650'F
MDMT 6S0'F It 250 psi
S/N-19560
Year built: 1996
W-L
RT 1
NAME PLATE EXAMPLE
(The vessel was inspected by user's inspector, arc welded, used in lethal service, fully
radiographed and post weld heat treated.)
Additional data shall be below the code
reauired marking.
HT
The name plate shall be affixed directly to the shell. Ifadditional name plate is used on
skirts, supports, etc., it shall be marked: "Duplicate."
Lettering shall be not less than 5/32 in. high. The Code-symbol and serial number shall
be stamped, the other data may be stamped, etched, cast or impressed.
Commonly used material for name plate 0.32 in. stainless steel or '/s in carbon steel.
The name plate shall be seal welded to uninsulated vessel or mounted on bracket if
the vessel is insulated, and located in some conspicuous place; near manways, liquid
level control, level gage, about S ft. above ground, etc.
318
PLATFORM
Conforms to the requirements of
OCCUPATIONAL SAFETY AND HEALTH (OSHA) STANDARDS
3 ft 6
In
ma)(
MIDRAIL
BAR 2x1/4
i
/ANGLE 5x3xY.
1/
Platforms shall be fabricated in sections
if necessary suitable for shipping and
field erection.
Platforms fabricated in sections shall
SECTION
be shop fitted, marked and knocked
down for shipping.
All field connections are to be bolted.
Manufacturer shall furnish 10% extra
bolts of each sizes for spare.
All burrs and sharp edges shall be removed.
Paint:
one shop coat primer, except
walking surfaces.
Max. spacing of supports 6 ft.
Max. spacing of handrail posts 6 ft.
Drill one 9/16 ¢J drain hole in checkered
CHANNEL 6x8.2
plate for each 10 sq. ft. area of floor.
Bolts 1/2 ¢J
Bolt holes 9/16 ¢J
ALTERNATIVE SUPPORTS
319
SKIRT
OPENINGS
1/4 IN. CONTINUOUS
FILLET WELD
VENT HOLES
In service of hydrocarbons or other
combustible liquids or gases the
skirts shall be provided with minimum of two 2 inch vent holes located as high as possible 180 degrees
apart. The vent holes shall clear
head insulation. For sleeve may be
used coupling or pipe.
ACCESS OPENINGS
The shape of access openings may
be circular or any other shapes.
Circular access openings are used
most frequently with pipe or bent
plate sleeves. The projection of
sleeve equals to the thickness of
fireproofing or minimum 2 inches.
_The projection of sleeves shall be
increased when necessary for reinforcing the skirt under certain loading conditions.
Diameter (D) = 16 - 24 inches
PIPE OPENINGS
The shape of pipe openings are circular with a diameter of 1 inch larger than the diameter of flange.
Sleeves should be provided as for
access openings.
TYPES OF SKIRT ACCESSES
320
VORTEX BREAKER
The purpose of vortex breakers is to eliminate the undesirable vortexing of
liquids.
Cross and flat-plate baffles are frequently used with a wipth of two times the
nozzle diameter.
For a high degree of effectiveness under severe swirling conditions the width of
the baffle should be four times the nozzle diameter. The height above the outlet
should be about half the nozzle diameter but may be several inches if required
larger clearance for other reasons.
R11'1
~.-~
~
VORTEXING OF LIQUIDS
0= DIAMETER OF PIPE
c...
GRATING
GRATING BAFFLE
FLAT AND CROSS PLATE BAFFLES
Material: 1/4 carbon steel plate or grating with 1 x 1-1/8 bars.
Reference: F. M. Patterson "Vortexing can be prevented" The Oil and Gas
Journal, August 4, 1969.
321
PART III.
MEASURES AND WEIGHTS
1.
Table of Properties of Pipes, Tubes. '" ....................................... ........ ... 322
2.
Dimensions ............................................................................................ 334
of Heads, Flanges, Long Welding Necks, Welding Fittings,
Screwed Couplings.
3.
Weight ................................................................................................... 374
of Shells and Heads, Pipes and Fittings, Flanges, Openings,
Packing and Insulation, Plates, Circular Plates, Bolts.
4.
Volume .................................................................................................. 416
of Shells and Heads, Partial Volumes in Horizontal Cylinders,
Partial Volumes in Ellipsoidal and Spherical Heads.
5.
Area of Surfaces of Shells and Heads ...................... .............. ............... 425
6.
Conversion Tables ................................................................................ 426
Decimals of an Inch, Decimals ofa Foot, Metric System, Inches
to Millimeters, Millimeters to Iriches, Square Feet to Square
Meters, Square Meters to Square Feet, Pounds to Kilograms,
Kilograms to Pounds, U.S. Gallon to Liters, Liters to U.S.
Gallons, Pounds per Square Inches to Kilogram per Centimeter,
Kilogram per Centimeter to Pounds per Square Inch, Degrees to
Radius, Minutes and Seconds to Decimals of a Degree, Centigrade to Fahrenheit, Fahrenheit to Centigrade.
322
PROPERTIES OF PIPE
Schedule numbers and weight designations are in agreement with ANSI B36.1 0 for
carbon and alloy steel pipe and ANSI B36.19 for stainless steel pipe.
Nom
pipe
size
1
i
Schedule No.
Carbon
& alloy
steels
10~
.065
.088
.119
.330
.424
.535
.0570
.0451
.0310
.141
.141
.141
.1073
.0955
.0794
.1320
.1041
.0716
40
80
10S
405
80S
....
Sid.
X-Stg.
.675
.675
.675
.545
.493
.423
.065
.091
.126
.423
.567
.738
.1010
.0827
.0609
.171
.171
.177
.1427
.1295
.1106
.2333
.1910
.1405
...
40
105
40S
Sid.
.840
.840
.670
.622
.083
.109
.671
.850
.1550
.1316
.220
.220
.1764
.1637
.3568
.3040
80
160
80S
...
X-Slg.
...
. ..
XX·Stg.
.840
.840
.840
.546
.466
.252
.147
.187
.:294
1.087
1.310
1.714
.1013
.0740
.0216
.220
.220
.220
.1433
.1220
.0660
.2340
.1706
.0499
...
40
80
10S
405
80S
Std.
X-Stg.
1.050
1.050
1.050
.834
.824
.742
.083
.113
.154
.857
1.130
1.473
.2660
.2301
.1875
.275
.275
.275
.2314
.2168
.1948
.6138
.5330
.4330
160
...
1.050
1.050
XX·SIg. 1.050
.675
.614
.434
.188
.218
.308
1.727
1.940
2.440
.1514
.1280
.0633
.275
.275
.275
.1759
.1607
.1137
.3570
.2961
.1479
..
40
80
105
40S
80S
..
Std.
X.SIg.
1.315
1.315
1.315
1.097
1.049
.957
.109
.133
.179
1.404
1.678
2.171
.4090
.3740
.3112
.344
.344
.344
.2872
.2740
.2520
.9448
.8640
.7190
.. .
160
.. .
.. .
....
1.315
1.315
1.315
.877
.815
.599
.219
.250
.358
2.561
2.850
3.659
.2614
.2261
.1221
.344
.344
.344
.2290
.2134
.1570
.6040
.5217
.2818
1.660
1.660
1.442
1.380
.109
.140
1.806
2.272
.7080
.6471
.434
.434
.3775
.3620
1.633
1.495
1.278
1.160
.896
.191
.250
.382
2.996
3.764
5.214
.5553
.4575
.2732
.434
.434
.434
.3356
.3029
.2331
1.283
1.057
.6305
40
80
160
...
.. .
40
80
160
...
2
.0740
.0568
.0364
.0-49
.068
.095
.410
.364
.302
.. .
1~
.0804
.0705
.0563
.307
.269
.215
.540
.540
.540
.. .
1~
.106
.106
.106
.405
.405
.405
Sid.
X.SIg.
.. .
1
.0320
.0246
.0157
Weight
per
foot
lb.
. ...
3
3
.186
.244
.314
Wall
thickness
in.
105
405
80S
40
80
..
Trans·
verse
area
sq. in.
Inside
diam.
in.
Std.
X.SIg.
...
i
Wt. of Outsidt Inside
water surface surface
per ft. per ft. per ft.
pipe
sq. ft.
sq. ft.
lb.
Outside
diam.
in.
40S
80S
1
1
Weight
Designation
40
80
4
i
Stainless
steels
.. .
40
.. .
....
...
XX.Stg.
10S
40S
....
80S
X·SIg.
Std.
. ..
XX-Stg.
1.660
1.660
1.660
lOS
40S
....
Std.
1.900
1.900
1.682
1.610
.109
.145
2.085
2.717
.9630
.8820
.497
.497
.4403
.4213
2.221
2.036
80S
X·Stg.
1.900
1.900
XX·Stg. 1.900
1.500
1.337
1.100
.200
.281
.400
3.631
4.862
6.408
.7648
.6082
.4117
.497
.497
.497
.3927
.3519
.2903
1.767
1.405
.950
2.157
2.067
2.041
.109
.154
.167
2.638
3.652
3.938
1.583
1.452
1.420
.622
.622
.622
.5647
.5401
.5360
3.654
3.355
3.280
...
...
. ..
10S
40S
....
Std.
...
2.375
2.375
2.375
323
PROPERTIES OF PIPE (con't.)
Schedule No.
NomCarbon Staininal
& alloy less
pipe
steels
steels
size
2
(CONT.)
80
...
. ..
80S
. ..
.. .
160
...
...
., .
...
...
2~
40
..
80
160
.. .
...
.. .
...
...
40
3
.. .
...
80
.. .
.. .
160
...
...
. ..
10S
40S
80S
...
...
Weight Outside Inside
diam.
designa - diam.
in.
in.
tion
..
X.Stg.
'"
.
Wt. of
water
per ft.
pipe lb.
Outside
surface
per ft.
sq. ft.
Inside
surface
per ft.
sq. ft.
Transverse
area
sq. in.
2.375
2.375
2.375
2.000
1.939
1.875
.188
.218
.250
4.380
5.022
5.673
1.363
1.279
1.196
.622
.622
.l:22
.5237
.5074
.4920
3.142
2.953
2.761
2.375
2.375
2.375
1.150
1.689
1.503
.312
.343
.436
6.883
7.450
9.029
1.041
.767
.769
.622
.622
.622
.4581
.4422
.3929
2.405
2.240
1.714
.
Std.
2.875
2.875
2.875
2.635
2.469
2.441
.120
.203
.217
3.53
5.79
6.16
2.360
2.072
2.026
.753
.753
.753
.6900
.6462
.6381
5.453
4.788
4.680
X.Stg.
2.875
2.875
2.875
2.323
2.125
1.771
.276
.375
.552
7.66
10.01
13.69
1.834
1.535
1.067
.753
.753
.753
.6095
.5564
.4627
4.238
3.547
2.464
.
'"
...
XX·Stg.
.
'"
XX-Stg.
. ...
. ...
3.500
3.500
3.500
3.260
3.250
3.204
.120
.125
.148
4.33
4.52
5.30
3.62
3.60
3.52
.916
.916
.916
.853
.851
.940
8.346
8.300
8.100
. ..
40S
. ..
Std.
3.500
3.500
3.500
3.124
3.068
3.018
.188
.2.6
.241
6.65
7.57
8.39
3.34
3.20
3.10
.916
.916
.916
.819
.802
.790
7.700
7.393
7.155
...
. ..
80S
. ...
1.500
3.500
3.500
2.992
2.922
2.900
254
.289
.300
8.80
9.91
10.25
3.06
2.91
2.86
.916
.916
.916
.785
.765
.761
7.050
6.700
6.605
3.500
3.500
3.500
3.500
2.875
2.687
2.624
2.300
.312
.406
.438
.600
10.64
13.42
14.32
18.58
2.81
2.46
2.34
1.80
.916
.916
.916
.916
.753
.704
.687
.601
6.492
5.673
5.407
4.155
4.000
4.000
3.760
3.744
.120
.128
4.97
5.38
4.81
4.78
1.047
1.047
.984
.981
11.10
11.01
3.732
3.704
3.624
3.548
3.438
3.364
.134
.148
.188
.226
.281
.318
5.58
6.26
1.11
9.11
11.17
12.51
4.75
4.66
4.48
4.28
4.02
3.85
1.047
1.047
1.047
1.047
1.047
1.047
.978
.971
.950
.929
.900
.880
10.95
10.75
10.32
...
...
...
., .
10S
. ..
..
. ..
.
'"
X.Stg.
. ...
. ...
..
XX-Stg.
. ...
.,
..
. ...
40
405
Sid.
80
80S
X.Slg.
4.000
4.000
4.000
4.000
4.000
4.000
XX-Slg.
4.00u
4.000
4.000
3.312
3.062
2 728
.344
.469
.636
13.42
17.68
22.85
3.73
3.19
2.53
1.047
1.047
1.047
.867
.802
.716
8.62
7.37
5.84
4.500
4.500
4.500
4.260
4.244
4232
.120
.128
.134
5.61
5.99
6.26
6.18
6.14
611
.1.178
1.178
1.178
1.115
1.111
1.110
14.25
14.15
14.10
4.500
4.500
4.500
4.216
4.110
4.124
.142
.165
.188
6.61
7.64
8.56
6.06
5.92
5.80
1.178
1.178
1.178
1.105
1.093
1.082
13.98
13.6J
13.39
...
. ...
...
4
Weight
per
foot
lb.
...
10S
...
.. .
3i
Wall
thickness
in.
. .
'
...
...
...
. ..
. ..
...
105
.. .
..
...
.. .
...
.. .
..
.. .
...
9.89
9.28
8.89
324
PROPERTIES OF PIPE (con't.)
Schedule No.
Nom·
inal
Carbon Stain·
pipe & alloy less
size
steels
steels
o","d'i diam.
""d,
Weight
designa diam·
tion
in.
in.
Wall
thick·
ness
in.
Weight Wt. of
per
water
foot
per ft.
pipe Ib
lb.
4.500
4.090
4026
4.000
.205
.237
.250
9.39
10.79
11 35
5.71
5.51
5.45
1.178
1.178
1.178
1.071
1.055
1.049
13.15
12.73
12.57
4.500
4.500
4.500
3.958
3.938
3.900
.271
.281
.300
12.24
12.67
13.42
5.35
5.27
5.19
1.178
1.178
1.178
1.038
1.031
1.023
12.31
12.17
11.96
4.500
4.500
4.500
3.876
3.826
3.750
.312
.337
.375
14.00
14.98
16.52
5.12
4.98
4.78
1.178
1.17B
1.178
1.013
1.002
.982
11.80
11.50
11.04
4.500
4.500
4.500
4.500
3.624
3.500
3.438
3.152
.438
.500
.531
.674
1900
21.36
2260
27.54
4.47
4.16
4.02
3.38
1.178
1.178
1.178
1.178
.949
.916
.900
.826
10.32
9.62
9.28
7.80
5.295
5.047
4.859
4.813
.134
.258
.352
.375
7.770
14.62
19.59
20.78
9.54
8.66
8.06
7.87
1.456
1.456
1.456
1.456
1.386
1.321
1.272
1.260
22.02
20.01
18.60
18.19
4.500
40
405
Std.
4
ICQNT.J
.. .
...
80
80S
X.Stg.
120
.. .
.. .
160
.. .
...
. ..
·.
·.. .
XX.Stg .
105
405
Std.
80S
X·Stg.
5.563
5.563
5.563
5.503
XX·Stg .
5.563
5.563
5.563
5.563
4.688
4.563
4.313
4.063
.437
.500
.625
.750
23.95
27.10
3296
38.55
7.47
7.08
6.32
5.62
1.456
1.456
1.456
1.456
1.227
1.195
1.129
1.064
17.26
16.35
14.61
12.97
6625
6.625
6.625
6.3-57
6.287
6.265
.134
.169
.180
9.29
11.56
12.50
13.70
13.45
13.38
1.735
1.735
1.735
1.660
1.650
1.640
31.75
31.00
30.81
6.625
6.625
.6.625
6.249
6.187
6.125
.188
.219
.250
12.93
15.02
17.02
13.31
13.05
12.80
1.735
1.735
1.735
1.639
1.620
1.606
30.70
30.10
29.50
6.625
6.625
6.625
6.625
6.071
6.065
5.875
5.761
.277
.280
.375
.432
18.86
18.97
25.10
28.57
12.55
12.51
11.75
11.29
1.735
1.735
1.735
1.735
1.591
1.587
1.540
1.510
28.95
28.99
27.10
26.07
6.625
6.f\25
6.625
6.625
5.625
5501
.500
.562
.71 R
.864
32.79
36.40
45.30
53.16
10.85
10.30
9.16
8.14
1.735
1.735
1.735
1.735
1.475
1.470
1.359
1.280
24.85
23.77
21.15
18.83
13.40
14.26
14.91
23.6
23.6
2.26
2.26
2.26
2.180
2.178
2.175
54.5
54.3
54.1
16.90
18.30
19.64
23.2
23.1
22.9
2.26
2.26
2.161
2.152
53.5
53.1
2.26
2.148
52.7
.. .
.,
.
40
·.
5
80
.
'
.
...
.
120
160
...
.. .
. ..
·..
105
. ...
. ..
...
.. .
..
...
...
"
. ...
. ..
. ..
·.
40S
Std.
80
80S
X-Stg.
.. .
120
160
...
...
...
...
...
6
·.
40
...
·.
XX-Stg
...
.. .
8
4.~00
OutsidJ Inside Trans·
surtal:e surface verse
per ft. per ft.
area
sq. ft.
sq. ft.
sq. in.
lOS
. ...
.. .
....
5.18'1
4.897
.. .
.. .
....
8.625
8.295
.148
.158
.165
.. .
.. .
...
...
. ...
...
. ..
. ...
8.625
8.625
8.625
8.249
8.219
8.187
.188
.203
.219
. ...
8.625
8.625
8.329
8.309
23.5
325
PROPERTIES OF PIPE (con't.)
Schedule No.
NomCarbon Staininal
pipe & alloy less
steels
size
steels
..
20
30
8
ICONT.)
'"
'"
21.43
22.40
24.70
22.7
22.5
22.2
2.26
2.26
2.26
2.136
2.127
2.115
52.2
51.8
51.2
8.625
8.625
8.625
7.981
7.937
7.921
.322
.344
.352
28.55
30.40
31.00
21.6
21.4
21.3
2.26
2.26
2.26
2.090
2.078
2.072
50.0
49.5
49.3
8.625
8.625
8.625
7.875
7.813
7.687
.375
.406
.469
33.10
35.70
40.83
21.1
20.8
20.1
2.26
2.26
2.26
2.062
2.045
2.013
48.7
47.9
46.4
8.625
8.625
8.625
7.625
7.439
7.375
.500
.593
.625
43.39
50.90
53.40
19.8
18.8
18.5
2.26
2.26
2.26
2.006
1.947
1.931
45.6
43.5
42.7
8.625
8.625
8.625
8.625
7.189
7.001
6.875
6.813
.718
.812
.875
.906
60.70
67.80
72.42
74.70
17.6
16.7
16.1
15.8
2.26
2.26
2.26
2.26
1.882
1.833
1.800
1.784
40.6
38.5
37.1
36.4
Std.
. ...
...
.. .
60
...
...
. ...
. ...
80
100
80S
120
140
.,
.
..
X-Stg.
'"
Inside Transsurface verse
area
per ft.
sq. ft.
sq. in.
.238
.250
.277
...
...
'
Outside
surface
per ft.
sq. ft.
8.149
8.125
8.071
405
...
Weight Wt. of
per
water
foot
per ft.
pipe Ib
lb .
8.625
8.625
8.625
.
.
"
Wall
thickness
in.
.
.
40
"
I
...
...
Weight Outside Inside
designa diamdiam.
in.
tion
in.
.
...
...
...
XX-Stg.
160
"
.
105
"
.
"
.
...
...
'"
.
. ...
..
10.750 10.420
10.750 10.374
10.750 10.344
.165
.188
.203
18.65
21.12
22.86
36.9
36.7
36.5
2.81
2.81
2.81
2.73
2.72
2.71
85.3
84.5
84.0
10.750 10.310
10.750 10.250
10.750 10.192
.219
.250
.279-
2H'O
28.03
31.20
36.2
35.9
35.3
2.81
2.81
2.81
2.70
2.68
2.66
83.4
82.6
81.6
10.750 10.136
10.750 10.054
10.750 10.020
.307
.348
.365
34.24
38.66
40.48
35.0
34.4
34.1
2.81
2.81
2.81
2.65
2.64
2.62
80.7
79.3
78.9
10.750
10.750
10.750
9.960
9.750
9.687
.395
.500
.531
43.68
54.74
57.98
33.7
32.3
31.9
2.S1
2.81
2.81
2.61
2.55
2.54
77.9
74.7
73.7
10.750
10.750
10.750
9.564
9.314
9.250
.593
.718
.750
64.40
77.00
SO.10
31.1
29.5
29.1
2.81
2.81
2.81
2.50
2.44
2.42
71.8
68.1
67.2
10.750
10.750
10.750
10.750
9.064
8.750
8.625
8.500
.843
1.000
1.063
1.125
89.20
104.20
109.90
116.00
27.9
26.1
25.3
24.6
2.81
2.81
2.81
2.81
2.37
2.29
2.26
2.22
64.5
60.1
58.4
56.7
12.750 12.390
12.750 12344
.180
.203
24.16
27.2
52.2
52.0
3.34
3.34
3.24
3.23
120.6
119.9
12.750 12.312
12.750 12.274
12.750 12.250
.219
.238
.250
29.3
31.8
33.4
51.7
51.5
j13
3.34
3.34
3.34
3.22
3.22
3.12
119.1
118.5
118.0
.
"
'"
.
.
...
20
...
. ...
.
...
. ...
..
....
.
40
405
Std.
60
80S
X-Stg.
...
. ..
...
'"
"
"
30
..
'"
10
"
.
80
100
.
., ..
.. .
...
...
...
160
...
120
140
.. .
"
.
'" .
. ...
lOS
.. .
....
.
...
20
...
..
. ..
..
.
12 .. .
"
'"
. ...
'"
.
326
PROPERTIES OF PIPE (con't.)
Schedule No.
Nom·
inal
Carbon Stain·
pipe & alloy less
steels
steels
size
..
30
40S
Weight Outside Inside
designa diam·
diam.
tion
in.
in.
12
.279
37.2
50.7
3.34
3.19
.300
40.0
50.5
3.34
3.18
116.1
...
12.750 12.090
.330
43.8
49.7
3.34
3.16
114.8
12.750 12.062
.344
45.5
49.7
3.34
3.16
114.5
Std.
12.750 12.000
.375
49.6
48.9
3.34
3.14
113.1
12.750 11.938
.406
53.6
48.5
3.34
3.13
111.9
12.750 11.874
.438
57.5
48.2
3.34
3.11
111.0
12.750 11.750
.500
65.4
46.9
3.34
3.08
108.4
12.750 11.626
.562
73.2
46.0
3.34
3.04
106.2
12.750 11.500
.625
80.9
44.9
3.34
3.01
103.8
12.750 11.376
.687
88.6
44.0
3.34
2.98
101.6
12.750 11.064
12.750 11.000
.843
108.0
41.6
3.34
2.90
96.1
.875
110.9
41.1
3.34
2.88
95.0
12.750 10.750 1.000
12.750 10.500 1.125
125.5
39.3
3.)4
2.81
90.8
140.0
37.5
3.34
2.75
86.6
12.750 10.313
1.219
150.1
36.3
3.34
2.70
83.8
10.126 1.312
161.0
34.9
3.34
2.65
80.5
146.0
X.Stg.
80
.,
.
100
.,
.
. ...
....
..
Trans·
Inside
surface verse
area
per ft.
sq. in.
sq. ft.
12.750 12.150
·.
. ...
120
Outside
surface
per ft.
sq. ft.
12.750 12.192
60
(CONT.)
Weight Wt. of
water
per
foot
per ft.
pipe lb
IbJ
. ...
40
80S
Wall
thick·
ness
in.
116.9
.,
.
·.
. ...
.,
.
. ...
12.750
.,
.
. ...
14.000 13.624
14.000 13.560
14.000 13'.524
.188
28
63.4
3.67
3.57
.220
32
63.0
3.67
3.55
145.0
.238
35
62.5
3.67
3.54
144.0
.250
37
62.1
3.67
3.54
143.0
.312
46
60.8
3.67
3.50
140.5
Std.
14.000 13.500
14.000 13.375
14.000 13.250
.375
55
59.7
3.67
3.47
137.9
.406
58
59.5
3.67
3.45
137.0
....
14.000 13.188
14.000 13.124
.438
63
58.5
3.67
3.44
135.3
14.000 13.062
.469
68
58.1
3.67
3.42
134.0
14.000 13.000
14.000 12.814
.500
72
57.4
3.67
3.40
132.7
.593
85
55.9
3.67
3.35
129.0
14.000 12.750
.625
89
55.3
3.67
3.34
127.7
14.000 12.688
14.000 12.500
.656
94
54.7
3.67
3.32
126.4
80
.750
107
51.2
3.67
3.27
122.7
100
14.000 12.125
.937
131
50.0
3.67
3.17
115.5
120
14.000
1.093
151
47.5
3.67
3.09
109.6
103.9
140
160
.. .
..
10
20
30
40
14
X.Stg.
60
·.
11.814
14.000 11.500
14.000 11.313
. ...
14.000 11.188
140
160
.' .
1.250
171
45.0
3.67
3.01
1.344
182
43.5
3.67
2.96
100.5
190
42.6
3.67
2.93
98.3
1.406
327
PROPERTIES OF PIPE (con't.)
Schedule No.
Nom·
inal
Carbon Stain·
pipe & alloy less
size
steels
steels
Weight Outsid e Inside
design a diam· diam.
tion
in.
in.
...
. ..
. ...
...
. ..
10
..
. ...
..
20
.. .
...
. ..
...
...
. ..
40
...
30
...
16
. ...
. ..
X.SIg.
...
. ..
60
.. .
...
...
.., .
. ...
.. .
...
. ...
80
100
...
. ...
120
.
...
. ...
140.
...
. ..
...
...
.., .
....
...
. ...
...
.,
160
10
20
"
..
. ...
..
Std.
\Veight WI. of
per
water
per ft.
foot
lb)
pipe lb
Ou tsi de
surface
per fl.
sq. ft.
Inside
Trans·
surface verse
per ft.
area
sq. in.
sq. ft.
.188
32
4.09
192.0
4.20
4.06
190.0
.250
40
42
83.3
82.5
4.20
.238
82.1
4.20
4.06
189.0
16.000 15.438
16.000 15.375
16.000 15.31-2
.281
47
81.2
4.20
4.04
.312
344
52
57
80.1
4.20
4.03
187.0
185.6
80.0
4.20
4.01
184.1
16.000 15.250
16.000 15.188
16.000 15.124
.375
.406
.438
63
68
73
79.1
78.6
78.2
4.20
182.6
181.0
4.20
4.00
3.98
3.96
180.0
16.000 15.062
16.000 15.000
16.000 14.938
.469
.500
.531
78
83
88
77.5
76.5
75.8
4.20
4.20
4.20
3.94
3.93
3.91
178.5
176.7
175.2
16.000 14.688
16.000 14.625
16.000 14.500
.656
.687
.750
108
112
122
73.4
72.7
71.5
4.20
4.20
4.20
3.85
3.83
3.80
169.4
168.0
165.1
16.000 14.314
16.000 13.938
16.000 13.564
.843
1.031
1.218
137
165
193
69.7
66.0
62.6
4.20
4.20
4.20
3.75
3.65
3.55
160.9
152.6
144.5
16.000 13.124
16.000 13.000
16.000 12.814
1.438
1.500
1.593
224
23~
4.20
4.20
4.20
3.44
3.40
335
135.3
132.7
245
58.6
57.4
55.9
18.000 17.500
18.000 17.375
18.000 17.250
.250
.312
.375
47
59
71
104.6
102.5
101.2
4.71
4.71
4.71
4.58
4.55
4.51
Ul.0
237.1
233.7
18.000 17.124
18.000 17.000
18.000 16.876
.438
.500
.562
82
93
105
99.5
98.2
97.2
4.71
4.71
4.71
4.48
4.45
4.42
229.5
227.0
224.0
16.000 15.624
16.000 15.524
16.000 15.500
4.20
1~9.Q
30
...
X.SIg
40
...
...
...
. ...
., ..
..
18.000 16.813
18.000 16.750
18.000 16.500
.594
.625
.750
110
116
138
96.1
95.8
92.5
4.71
4.71
4.71
4.40
4.39
4.32
222.0
. ..
...
. ...
. ...
. ...
18.000 16.375
18.000 16.126
18.000 15.688
.812
.937
1.156
149
171
208
91.2
88.5
83.7
4.71
4.71
4.71
4.29
4.22
4.11
210.6
204.2
193.3
.. , .
. ...
18.000
18.000
18.000
18.000
15.250
...
1.375
1.562
1.687
1.781
244
275
294
309
79.2
75.3
72.7
71.0
4.71
4.71
4.71
4.71
3.99
3.89
3.83
3.78
182.7
173.8
168.0
163.7
.
...
60
..
18
Sid.
Wall
thick·
ness
in.
...
80
100
..
...
120
140
...
160
. ..
...
'0' •
. .. .
14.876
14.625
14.438
220.5
213.8
328
PROPERTIES OF PIPE (con't.)
Schedule No.
Nominal
Carbon Stainpipe & alloy less
size
steels
steels
10
.. .
20
.. .
30
.. .
20
'"
· ..
..
'
· ..
...
.
....
. ...
Std.
X-Stg.
"
· ..
.. .
...
. ...
. ...
60
.. .
· ..
. ...
40
.. .
80
100
120
140
· ..
"
"
"
'"
'"
22
Weight Outside Inside
designa diam- diam.
in.
in.
tion
.
.
.
. .0.
,.0 .
..0.
. ...
.
.
....
· ...
Weight WI. of
water
per
foot
per flpipe lb
lb.
Outside
surface
per ft.
sq. ft.
TransInside
surface verse
area
per flsq. ft.
sq. in.
20.000 19.500
20.000 19.374
20.000 19.250
.250
.313
.375
53
66
79
130.0
128.1
126.0
5.24
5.24
5.24
5.11
5.08
5.04
299.0
295.0
291.1
20.000 19.124
20.000 19.000
20.000 18.875
.438
.500
.562
92
105
117
125.1
122.8
121.1
5.24
5.24
5.24
5.01
4.97
4.94
28S.0
283.5
279.8
20.000
20.000
20.000
20.000
18.814
18.750
18.376
18.250
.593
.625
.812
.875
123
129
167
179
120.4
119.5
114.9
113.2
5.24
5.24
5.24
5.24
4.93
4.91
4.81
4.78
278.0
276.1
265.2
261.6
20.000
20.000
20.000
20.000
18.188
17.938
17.438
17.000
.906
1.031
1.281
1.500
20.000 16.500
20.000 16.313
20.000 16.064
1.750
1.S44
1.968
185
209
256
297
342
357
379
112.7
109.4
103.4
9S.3
92.6
90.5
87.9
5.24
5.24
5.24
5.24
5.24
5.24
5.24
4.76
4.80
4.56
4.45
4.32
4.27
4.21
259.S
252.7
238.8
227.0
213.8
209.0
202.7
160
. '"
.. .
.. ..
.. .
'"
.
·.
22.000 21.500
22.000 21.376
22.000 21.250
.250
.312
.375
58
72
87
157.4
155.6
153.7
5.76
5.76
5.76
5.63
5.60
5.56
363.1
358.9
354.7
.. .
'"
.
.. , .
22.000 21.126
22.000 2LOOO
22.000 20.876
.437
.500
.562
103
115
129
152.0
150.2
148.4
5.76
5.76
5.76
5.53
5.50
5.47
350.5
346.4
342.3
22.000 20.750
22.000 20.624
22.000 20.500
.625
.688
.750
143
157
170
146.6
144.8
143.1
5.76
5.76
5.76
5.43
5.40
5.37
338.2
334.1
330.1
24.000 23.500
24.000 23.376
24.000 23.250
.250
.312
.375
63
79
95
189.0
186.9
183.8
6.28
6.28
6.28
6.15
6.12
6.09
435.0
430.0
424.6
24.000 23.125
24.000 23.000
24.000 22.876
.437
.500
.562
110
125
141
181.8
181.0
178.5
6.28
6.28
6.28
6.05
6.02
5.99
420.0
416.0
411.0
24.000 22.750
24.000 22.626
24.000 22.500
.625
.687
.750
156
171
186
175.9
174.2
172.1
6.28
6.28
6.28
5.96
5.92
5.89
406.5
402.1
397.6
.968
1.031
1.218
1.531
238
253
297
367
165.8
163.6
158.2
149.3
6.28
6.28
6.28
6.28
5.78
5.74
5.65
5.48
382.3
378.0
365.2
344.3
.. .
.. .
.. .
10
.. .
....
'"
.
0"
•
·...
,0 ••
....
. ...
... .
....
'"
.
Std.
20
X-Stg.
30
24
Wall
thickness
in.
40
'"
.
'"
.
60
...
SO
100
·.
'"
.
....
'"
.
....
24.000
24.000
24.000
24.000
22.064
21.938
21.564
20.938
329
PROPERTIES OF PIPE (con't.)
Schedule No.
Nominal
Carbon Stainpipe & alloy less
steels
size
steels
24
iCONT.)
120
140
.. .
160
.. .
.. .
.. .
26
...
.. .
.. .
.. .
.. .
.. .
30
Weight Outside Inside
designa diam- diam.
lion
in.
in.
... .
....
. , ..
....
... .
'0' •
....
....
Weight WI. of Outsid~ Inside Transper
water surface surface verse
foot
per ft. per ft. per ft.
area
lb.
pipe lb sq. ft.
sq. ft.
sq. in.
20.376
19.876
19.625
19.314
1.812
2.062
2.187
2.343
429
484
510
542
141.4
134.4
130.9
127.0
6.28
6.28
6.28
6.28
5.33
5.20
5.14
5.06
326.1
310.3
302.0
293.1
.250
.312
.375
67
84
103
221.4
219.2
217.1
6.81
6.81
6.81
6.68
6.64
6.61
510.7
505.8
500.7
'0' •
....
... .
.....
... .
... .
....
26.000 25.500
26_000 25.376
26.000 25.250
...
....
....
26.000 25.126
26.000 25.000
26.000 24.876
.437
.500
.562
119
136
153
215.0
212.8
210.7
6.81
6.81
6.81
6.58
6.54
6.51
495.8
490.9
486.0
26.000 24.750
26.000 24.624
26.000 24.500
.625
.688
.750
169
186
202
208.6
206.4
204.4
6.81
6.81
6.81
0.48
6.45
6.41
481.1
476.2
471.4
30.000 29.376
30.000 29.250
30.000 29.125
.312
.375
.437
99
119
138
293.7
291.2
288.7
7_85
7.85
7.85
7.69
7.66
7.62
677.8
672.0
666.2
30.000 29.000
30.000 28.875
30.00C 28.750
.500
.562
.625
158
177
196
286.2
283.7
281.3
7.85
7.85
7.85
7.59
7.56
7.53
660.5
654.8
649.2
•
0'
•
... .
•
0'
•
.0
••
.. , .
....
'0' •
....
10
,0' •
....
.. .
.. .
.. , .
....
... .
....
20
....
....
...
10
24.000
24.000
24.000
24.000
Wall
thickness
in.
w
w
ANSI B 36.10
DIMENSIONS OF PIPE
o
1. All Dimensions are in inches
2. The Nominal Wall Thicknesses shown are subject to a 12.5% Mill Tolerance
3. Not included in standard ANSI B 36.10
Nominal Outside
Pipe
Diameter
Size
V.
v..
%
-~
%
1
0.405
0.540
0.675
--0.8-40
1.050
1.315
- - ---
Iv..
1.660
1~
1.900
2
2.375
--- --2.875
2~
3
3.500
3~
4.000
--- --4
4.500
5.563
5
6
6.625
- - --8
8.625
10
10.750
12
12.750
- - --14
14.000
16
16.000
18
18.000
- - --20
20.000
24
24.000
303
30.000
NOMINAL WALL THICKNESS
Sched.
10
Schad.
20
Sched.
30
Std.
Weight
Sched.
40
-----------------------
---
------------------
0.068
0.088
0.091
0.068
0.088
0.091
-0.109
0.113
0.133
--
-.
..
-------
0.250
0.250
0.250
-- ,_....
0.250
0.250
0.312
-------.----.-----.
--
0.109
0.113
0.133
-0.140
0.145
0.154
-0.203
0.216
0.226
--
0.312
0.312
0.312
0.375
0.375
0.438
0.237
0.258
0.280
-_._-0.322
0.365
0.375
-----0.375
0.375
0.375
------
------
------
0.375
0.375
0.500
0.500
0.562
0.625
0.375
0.375
0.375 3
--
-0.250
0.250
0.250
-0.277
0.307
0.330
~-.--
-------
0.140
0.145
0.154
-0.203
0.216
0.226
-0.237
0.258
0.280
-0.322
0.365
0.406
---- ._--
0.438
0.500
0.562
--.---0.593
0.687
--
Schad.
60
..
--.
--
---
-------------
--0.406
0.500
0.562
---_ .. 0.593
0.656
0.750
---0.812
0.968
--
Extra
Strong
Sched.
80
0.095
0.119
0.126
0.095
0.119
0.126
--
--
0.147
0.154
0.179
0.147
0.154
0.179
-0.191
0.200
0.218
--0.276
0.300
0.318
--0.337
0.375
0.432
---0.500
0.593
0.687
-0.191
0.200
0.218
-0.276
0.300
0.318
-0.337
0.375
0.432
-.-~-
-
0.500
0.500
0.500
.-_ .. __ ... --0.500
0.500
0.500
~---
0.500
0.500
0.500 3
-------
0.750
0.843
0.937
----.~
1.031
1.218
--
Sched.
100
Sched.
120
.-------------------
---------
--
-.-----0.438
0.500
0.562
--
0.593
0.718
0.843
--0.937
1.031
1.156
-1.281
1.531
--
------
0.718
0.843
1.000
----1.093
,1.218
1.375
--1.500
1.812
-
--
Sched.
140
--
--
--
--
----------------
Sched.
160
.---0.187
0.218
0.250
~--
0.250
0.281
0.343
--0.375
0.438
--
--
0.531
0.625
0.718
XX
Strong
.--
--
--
0.294
0.308
0.358
-0.382
0.400
0.436
--
0.552
0.600
0.636 3
-0.674
0.750
0.864
~-
------
0.812
1.000
1.125
-1.250
1.438
1.562
--
0.906
1.125
1.312
---1.406
1.593
1.781
0.875
--
--
1.750
2.062
1.968
2.343
--
.-
Nomina
Pipe
Size
--.
-----.---
V.
v..
¥a
-~
%
1
--
Iv..
1~
2
-2V2
3
3~
-4
5
6
-8
10
12
-14
16
18
-20
24
30
331
332
PROPERTIES OF STEEL TUBING
Internal
Area
Sq. In.
Sq. Ft.
External
Surface
Per Ft.
Length
Sq. Ft.
Internal
Surface
Per Ft.
Length
Theoretical
Weight Per
Ft. Length
ID
Tubing
Inches
.125
.110
.105
.095
.085
.1104
.1288
.1353
.1486
.1626
.1636
.1636
.1636
.1636
.1636
.0982
.1060
.1086
.1139
.1191
.668
.605
.583
.538
.490
5/8
5/8
5/8
5/8
5/8
.075
.065
.060
.055
.050
.1772
.1924
.2003
.2083
.2165
.1636
.1636
.1636
.1636
.1636
.1244
.1296
.1322
.1348
.1374
3/4
3/4
3/4
3/4
3/4
3/4
.150
.135
.125
.1 IO
.105
.095
.1590
.1810
.1964
.2206
.2290
.2463
.1963
.1963
.1963
.1963
.1963
.1963
3/4
3/4
3/4
3/4
3/4
3/4
.085
.075
.065
.060
.055
.050
.2642
.2827
.3019
.3117
.3217
.3318
7/8
7/8
7/8
7/8
7/8
7/8
.150
.135
.125
.IIQ
.105
.095
7/8
7/8
7/8
7/8
7/8
7/8
D of
Tubing
Inches
Wall
Thickness
Inches
5/8
5/8
5/8
5/8
5/8
Constant
C·
OD
-ID-
Metal Area
(Transver.;c
Metal Area)
Sq. In.
.375
.405
.415
.435
.455
172
201
211
232
254
1.667
1.543
1.506
1.437
1.374
.1964
.1780
.1715
.1582
.1442
.441
.389
.362
.335
.307
.475
.495
.505
.515
.525
276
300
312
325
338
1.316
1.263
1.238
1.214
1.190
.1296
.1144
.1065
.0985
.0903
.1178
.1257
.1309
.1388
.1414
.1466
.961
.887
.834
.752
.723
.665
.450
.480
.500
.530
.540
.560
248
282
306
344
357
384
1.667
1.563
1.500
1.415
1.389
1.339
.2STT
.1963
.1963
.1963
.1963
.1963
.1963
.1518
.1571
.1623
.1649
.1676
.1702
.604
.541
.476
.442
.408
.374
.580
.600
.620
.630
.640
.650
412
441
471
486
502
518
1.293
1.250
1.210
1.190
1.172
1.154
.1776
.1590
.1399
.1301
.1201
.1100
.2597
.2875
.3068
.3370
.3473
.3685
.2291
.2291
.2291
.2291
.2291
.2291
.1505
.1584
.1636
.1715
.1741
.1793
1.I61
1.067
1.001
.899
.863
.791
.575
.605
.625
.655
.665
.685
405
448
478
526
542
575
1.522
1.446
1.400
1.336
1.316
1.277
.3416
.3138
.2945
.2p44
.2540
.2328
.085
.075
.065
.060
.055
.050
.3904
.4128
.4359
.4477
.4596
.4717
.2291
.2291
.2291
.2291
.2291
.2291
.1846
.1898
.1950
.705
.725
.745
.755
.765
.775
609
.2003
.2029
.717
.641
.562
.522
.482
.441
680
698
717
736
1.241
1.207
1.174
1.159
1.144
1.129
.2110
.1885
.1654
.1536
.1417
.1296
I
.ISO
I
I
I
I
.135
.125
.110
.105
.095
.3848
.4185
.4418
.4778
.4902
.5153
.2618
.2618
.2618
.2618
.2618
.2618
.1833
.1911
.1964
.2042
.2068
.2121
1.362
1.247
1.168
1.046
1.004
.918
.700
.730
.750
.780
.790
.810
600
653
689
745
764
804
1.429
1.370
1.333
1.282
1.266
1.235
.4006
.3669
.3436
.3076
.2952
.2701
I
I
I
I
I
I
.085
.075
.065
.060
.055
.050
.5411
.5675
.5945
.6082
.6221
.6362
.2618
.2618
.2618
.2618
.2618
.2618
.2173
.2225
.2278
.2304
.2330
.2356
.831
.741
.649
.602
.555
.507
.830
.850
.870
.880
.890
.900
844
885
927
949
970
992
1.205
1.176
1.149
r.136
1.124
1.111
.2443
.2179
.1909
.1772
.1633
.1492
= pounds
per tube per hour
o
I
• Liquid velocity in feet/second
.1~77
644
.2608
.2454
.2212
.2128
.1955
C x specific gravity of liquid
Specific gravity of water at 60 deg. F
= 1.0
Courtesy of HEAT EXCHANGE INSTITUTE
333
PROPERTIES OF TUBING
Area
Metal
Sq. Fe
Sq. Ft. Weight
Weight Weight
(TransExternal Internal per Fe
per Ft. per Ft.
0.0.
Thick- Internal Surface Surface Length
Length Length
1.0.
0 0
verse
of
BWG
ness
Area
per Ft.
per Ft.
Adm.
Copper Steel Tubing Constant _ _ Metal
Tubing Gage Inches Sq. In.
Length
Length
Lbs.
Lbs.
Lbs.
Inches
C"
[ 0
Area)
--~-~-------------~----~-----------------
5/8
5/8
5/8
5/8
5/8
5/8
10
II
12
13
14
15
.134
.120
.109
.095
.083
.072
.[001
.1164
.1301
.1486
.1655
.1817
.1636
.1636
.1636
.1636
.1636
.1636
.0935
.1008
.1066
.1139
.1202
.1259
.766
.705
.655
.586
.524
.464
.801
.738
.685
.613
.548
.485
.703
.647
.601
.538
.480
.425
.357
.385
.407
.435
.459
.481
156
182
203
232
258
283
l.751
1.623
1.536
1.437
1.362
1.299
5/8
5/8
5/8
5/8
5/8
5/8
3/4
3/4
3/4
3/4
3/4
3/4
16
17
18
19
20
22
.065
.058
.049
.042
.035
.028
.1924
.2035
.2181
.2299
.2419
.2543
.1636
.1636
.1636
.1636
.1636
.1636
.1296.424
.1333
.383
.1380
.329
.1416
.285
.1453
.240
.1490
.195
.443
.400
.344
.298
.251
.204
.389
.351
.30 I
.262
.221
.179
.495
.509
.527
.541
.555
.569
300
317
340
359
377
397
1.263.1144
1.228 .1033
1.186 .0887
1.155 .0769
1.126 .0649
1.098 .0525
10
11
12
13
14
15
.134
.120
.109
.095
.083
.072
.1825
.2043
.2223
.2463
.2679
.2884
.1963
.1963
.1963
.1963
.1963
.1963
.1262
.1335
.1393
.1466
.1529
.1587
1.005
.920
.851
.758
.674
.594
.882
.807
.746
.665
.591
.521
.482
.510
.532
.560
.584
.606
285
JI9
347
384
418
450
1.556
1.471
1.410
1.339
1.284
1.238
.961
.880
.813
.724
.644
.568
.2067
.1904
.1767
.1582
.1413
.1251
.2593
.2375
.2195
.1955
.1739
.1534
1-.:...-...-------------------------------·-------------3/4
16
.065
.3019
.1963
.1623
.518
.542
.476
.620
471
1.210 .1399
3/4
17
.058
.3157
.1963
.1660
.467
.489
.429
.634
492
1.183 .1261
3/4
18
.049
.3339
.1963
.1707
.400
.418
.367
.652
521
1.150 .1079
3/4
19
.042
.3484
.1963
.1744
.346
.362
.318
.666
543 .1.126 .0934
3/4
20
.035
.3632
.1963
.1780
.291
.305
.267
.680
566
1.103 .0786
3/4
22
.028
.3783
.1963
.1817
.235
.246
.216
.694
590
1.081
.0635
1......:...:...-...-------------....:...:.;...;.;;.-...:..;:..-=------------------·-.:..:..:...:- - - - - - - - - - - - - 1.442
.3119
7/8
10
.134
.2894
.2291
.15891.156
1.2091.060
451
.607
1.378 .2846
494
7/8
11
.120
.3167
.2291
.1662 1.055
1.103
.968
.635
1.332 .2623
7/8
12
.109
.3390
.2291
.1720
.972
1.017
.892
529
.657
1.277 .2328
7/8
13
.095
.3685
.2291
.1793
.863
.902
.791
575
.685
1.234 .2065
7/8
14.083.3948.2291
.1856.765
.-800.702
616
.709
1.197 .1816
7/8
15
.072
.4197
.2291
.1914
.673
.704
.617
655
.731
1.174 .1654
7/8
16
.065
.4359
.2291
.1950
.613
.641
.562
.745
680
l.l53 .1489
.759
7/8
17
.058
.4525
.2291
.1987
.552
.577
.506
706
1.126 .1272
IS
.049
.4742
.2291
.2034
.471
.493
.432
.777
7/S
740
1.106 .1099
766
7/8
19
.042
.4914
.2291
.2071
.407
.426
.374
.791
•. 087 .0924
794
7/S
20
.035
.5090
.2291
.2107
.342
.358
.314
.805
1.068 .0745
822
22
.028
.5268
.2291
.2144
.276
.289
.253
.819
7/8
1
1
I
I
I
I
I
1
I
1
I
I
10
II
12
13
14
15
.134
.4208
.120.4536
.109
.4803
.095
.5153
.083
.5463
.072 .5755
.261S
.2618
.2618
.261S
.2618
.2618
.1916 1.351
.19901.229
.2047 1.131
.2121 1.001
.2183
.886
.2241
.778
16
17
18
19
20
22
.065
.058
.049
.042
.035
.028
.2618
.2618
.2618
.2618
.2618
.2618
.2278
.2314
.2361
.2398
.2435
.2471
.5945
.6138
.6390
.6590
.6793
.6999
"Liquid velocity in feetl second
=
.740
.665
.567
.490
.411
.331
pounds per tube per hour
C x specific gravity of liquid
Specific gravity of water at 60 deg. F
Courtesy of
.708
.636
.542
.468
.393
.317
1.413 1.239
1.2861.128
1.182 1.037
1.047
.918
.927
.813
.814
.714
= 1.0
HEAT EXCHANGE INSTITUTE
.649
.584
.498
.430
.361
.291
.732
.760
.782
.810
.834
.856
656
707
749
804
852
898
1.366
1.316
1.279
1.235
1.199
1.168
.3646
.3318
.3051
.2701
.2391
.2099
.870
.S84
.902
.916
.930
.944
927
957
997
1028
1059
1092
1.149
1.131
1.109
1.092
1.075
1.059
.1909
.1716
.1464
.1264
.1061
.0855
Weights of other materials - Multiply carbon
steel weights by the following factors:
90-10 Cu. Ni. Alloy 706 - 1.140
70-30 Cu. Ni. Alloy 715 • 1.140
70-30 Ni. Cu. Alloy 400 - 1.126
TP304 Stainless Steel·
1.013
334
HEADS
For vessels of small and medium diameters ellipsoidal heads are used most
commonly, while large diameter vessels are usually built with hemispherical or
flanged and dished heads.
Heads may be of seamless or welded construction.
STRAIGHT FLANGE
Formed heads butt-welded to the shell need not have straight flange when the
head is not thicker than the shell according to the Code Par. UG-32 & 33, but
in practice heads except hemisphericals are used with straight flanges.
The usual length of straight flanges: 2 inches for ellipsoidal, I 1/2 inches for
flanged and dished and 0 inches for hemispherical heads.
Formed heads thicker than the shell and butt-welded to it shall have straight
flange.
On the following pages the data of the most commonly used heads are listed.
The dimensions offlanged and dished heads meet the requirements of ASME Code.
WEIGHT OF HEADS See tables beginning on page 374
VOLUME OF HEADS See page 4116
SURF ACE OF HEADS See page 425
335
DIMENSIONS
~.1
D= inside diameter of hemispherical and ellipsoidal
heads, outside diameter of ASME flanged &
dished heads.
D
HEMISPHERICAL
I..
h = inside depth of dish of F & D heads
"
L(R) = inside radius of dish of ASME flanged &
dished heads as used in formulas for internal
or external pressure.
.1
D
ELLIPSOIDAL
ET
M= factor used in formulas for internal pressure.
~r
I.
L(R)7
D
ASME FLANGED & DISHED
.I
r
=
inside knuckle radius of ASME flanged & dished
heads.
t
=
wall thickness, nominal or minimum.
ALL DIMENSIONS IN INCHES
WALL THICKNESS
DIAM
ETER
D
14
16
18
20 '
22
L (R)
r
h
M
L (R)
r
h
M
L (R)
r
h
M
L (R)
r
h
M
L (R)
r
h
M
L (R)
24
HEADS
SYMBOLS USED IN THE TABLES
14
,-
OF
r
h
M
Ys
Y2
%
~
VB
1
lYs
1~
12
1.125
2.625
1.56
15
1.125
2.750
1.65
18
1.125
2.875
1.75
18
1.250
3.500
1.69
21
1.375
3.688
1.72
24
1.500
3.875
1.75
12
1.500
2.750
1.46
15
1.500
2.875
1.54
16
1.500
3.313
1.56
18
1.500
3.563
1.62
20
1.500
3.813
1.65
24
1.500
3.813
1.75
12
1.875
2.938
1.39
14
1.875
3.188
1.44
15
1.875
3.563
1.46
18
1.875
3.750
1.52
20
1.875
4.000
1.56
24
1.875
4.000
1.65
14
2.250
3.375
1.36
15
2.250
3.750
1.39
18
2.250
3.875
1.46
20
2.250
4.188
1.50
24
2.250
4.188
1.58
18
2.625
3.625
l.41
18
2.625
4.063
1.41
20
2.625
4.313
1.44
24
2.625
4.375
1.50
18
3.000
4.250
1.36
20
3.000
4.500
1.39
24
3.000
4.563
1.46
20
3.375
4.688
1.36
24
3.375
4.813
1.41
24
3.750
5.000
l.39
336
DIMENSIONS
OF
HEADS
ALL DIMENSIONS IN INCHES
DlAM
WALL THICKNESS
ETER
D
26
28
L(R).
r
h
M
L (R)
r
h
M
30
L (R)
r
h
32
L (R)
r
h
M
M
34
L(R)
r
h
36
L (R)
r
h
38
L (R)
r
h
M
M
M
40
42
L (R)
r
h
M
L (R)
r
h
M
48
54
L (R)
r
h
M
L (R)
r
h
M
60
L (R)
r
h
M
VB
Y2
%
24
1.625
4.500
1.72
26
1.750
4.813
1.72
30
1.875
4.875
1.75
30
2.000
5.563
1.72
24
1.625
4.438
1.72
26
1.750
4.750
1.72
30
1.875
4.813
1.75
30
2.000
5.500
1.72
24
1.875
4.500
1.65
26
1.875
4.750
1.69
30
1.875
4.813
1.75
30
2.000
5.375
1.72
34
2.125
5.563
1.75
36
2.250
5.938
1.75
36
2.375
6.500
1.72
40
2.500
6.625
1.69
40
2.625
7.188
1.72
42
3.000
8.000
1.69
54
3.250
8.938
1.77
60
3.625
10.000
1.77
34
30
2.125 2.125
5.500 6.000
1.75
1.69
36
36
2.250 2.250
5.875 5.813
1.75
1.75
36
36
2.375 2.375
6.438 6.375
1.72
1.72
40
36
2.500 2.500
6.563 6.938
1.69
1.69
40
40
2.625 2.625
7.125 7.063
1.72
1.72
42
42
3.000 3.000
8.750 8.688
1.69
1.69
48
48
3.250 3.250
9.750 9.750
1.72
1.72
60
54
3.625 3.625
9.875 10.688
1.77
1.72
%
Ys
1
178
I%;
1%
24
24
24
24
24
24
2.250 2.625 3.000 3.375 3.750 4.125
4.688 4.875 5.000 5.188 5.375 5.625
1.50
1.46
1.39
1.41
1.56
1.36
24
24
24
24
24
26
2.250 2.625 3.000 3.375 3.750 4.125
4.938 5.375 5.563 5.688 5.875 6.063
1.46
1.39
1.36
1.50
1.41
1.60
30
30
30
30
30
30
2.250 2.625 3.000 3.375 3.750 4.125
5.000 5.125 5.375 5.500 5.750 5.938
1.60
1.65
1.54
1.50
1.46
1.44
30
30
30
30
30
30
2.250 2.625 3.000 3.375 3.750 4.125
5.500 5.625 5.813 6.000 6.188 6.375
1.60
1.54
1.50
1.44
1.65
1.50
30
30
30
30
30
30
2.250 2.625 3.000 3.375 3.750 4.125
6.063 6.188 6.313 6.438 6.625 6.813
1.46
1.44
1.60
1.65
1.54
1.54
36
36
36
36
36
36
2.250 2.625 3.000 3.375 3.750 4.125
5.750 5.938 6.125 6.313 6.500 6.688
1.69
1.52
1.52
1.75
1.62
1.58
36
36
36
36
36
36
-2.375 2.625 3.000 3.375 3.750 4.125
6.375 6.438 6.563 6.750 6.938 7.125
1.69
1.48
1.52
1.72
1.62
1.60
36
36
36
36
36
36
2.500 2.625 3.000 3.375 3.750 4.125
7.000 7.000 7.125 7.313 7.438 7.625
1.48
1.69
1.52
1.69
1.62
1.58
40
40
40
36
36
36
2.625 2.625 3.000 3.375 3.750 4.125
7.000 7.000 7.125 7.125 8.000 8.125
1.72
1.48
1.72
1.65
1.52
1.56
42
42
42
42
42
42·
3.000 3.000 3.000 3.375 3.750 4.125
8.625 8.563 8.500 8.625 8.813 9.000
1.69
1.58
1.54
1.69
1.69
1.62
48
48
48
48
48
48
3.250 3.250 3.250 3.375 3.750 4.125
9.625 9.500 9.375 9.438 9.625 9.750
1.72
1.72
1.65
1.60
1.72
1.69
54
54
54
54
54
54
3.625 3.625 3.625 3.625 3.750 4.125
10.625 10.563 10.500 10.438 10.438 10.563
1.69
1.65
1.72
1.72
1.72
1.72
337
DIMENSIONS
OF
HEADS
ALL DIMENSIONS IN INCHES
WALL THICKNESS
DIAM
ETER
D
lYz
1%
l~
30
4.500
6.125
1.39
30
4.500
6.563
1.39
30
4.875
6.375
1.36
30
4.875
6.750
1.36
30
5.250
6.938
1.34
1%
2
2~
2Yz
2~
3
L(R)
26
r
28
r
30
L (R)
r
h
M
32
L (R)
r
h
M
34
L (R)
r
h
M
36
L (R)
r
h
M
38
L (R)
r
h
M
40
L (R)
r
h
M
h
M
L (R)
42
h
M
L (R)
r
h
M
48
L(R)
r
h
M
54
L (R)
r
h
M
60
L(R)
r
h
M
30
30
30
4.500 4.875 5.250
7.000 7.188 7.375
1.39
l.36
1.34
36
36
36
36
4.500 4.875 5.250 5.625
6.875 7.063 7.313 7.500
1.46
1.44
1.41
1.39
36
36
36
36
36
4.500 4.875 5.250 5.625 6.000
7.313 7.500 7.813 7.875 8.063
1.46
1.44
1.41
1.39
1.36
36
36
36
36
36
4.500 4.875 5.250 5.625 6.000
7.813 8.000 8.125 8.313 8.500
1.46
1.44
1.41
1.39
1.36
36
36
36
36
36
4.500 4.875 5.250 5.625 6.000
8.313 8.438 8.625 8.813 8.938
1.46
1.44
1.41
1.39
1.36
42
42
42
42
42
42
42
4.500 4.875 5.250 5.625 6.000 6.750 7.500
9.188 9.250 9.438 9.563 9.750 10.125 10.500
1.52
1.48
1.46
1.44
1.41
1.34
1.36
48
48
48
48
48
48
48
48
4.500 4.875 5.250 5.625 6.000 6.750 7.500 8.250
9.875 10.063 10.188 10.375 10.563 10.875 11.250 11.625
1.56
l.54
1.48
1.50
1.46
1.36
1.41
1.39
54
54
54
54
54
54
54
54
54
4.500 4.875 5.250 5.625 6.000 6.750 7.500 8.250 9.000
10.688 10.875 11.000 11.188 11.313 11.688 12.000 12.375 12.750
l.62
1.58
1.54
1.52
1.50
1.46
1.39
1.41
1.36
338
DIMENSIONS
OF
HEADS
ALL DIMENSIONS IN INCHES
WALL THICK.NESS
DIAM
ETER
%
D
66
L (R)
r
h
72
L (R)
r
h
M
M
78
L (R)
r
h
M
84
L (R)
r
h
M
90
L (R)
r
h
M
L (R)
96
r
h
M
L (R)
r
102
h
108
L (R)
r
h
M
M
L (R)
114
r
h
M
L (R)
r
120
h
126
L (R)
r
h
M
M
132
L (R)
r
h
M
66
4.000
11.000
l.77
72
4.375
12.000
1.77
78
4.750
13.000
l.77
84
5.125
14.000
1.77
90
5.500
15.125
1.77
96
5.875
16.125
1.77
96
6.125
17.938
1. 75
102
6.500
18.938
1.75
Y2
66
4.000
10.938
1.77
72
4.375
11.938
1.77
72
4.750
13.813
1.72
84
5.125
13.938
1.77
84
5.500
15.813
1.72
90
5.875
16.875
1.72
96
6.125
17.875
1.75
102
6.500
18.875
1.75
108
6.875
19.875
1.75
114
7.250
20.875
1.75
120
7.625
21.875
1.75
%
60
4.000
1l.750
1.72
72
4.375
11.875
1.77
72
4.750
13.750
1.72
84
5.125
13.875
1.77
84
5.500
15.750
1.72
90
5.875
16.813
1.72
96
6.125
17.750
1.75
102
6.500
18.750
1.75
108
6.875
19.813
1.75
114
7.250
20.813
1.75
120
7.625
21.813
1.75
126
8.000
22.875
1.75
%
60
4.000
11.625
l.72
72
4.375
11.875
1.77
72
4.750
13.688
1.72
84
5.125
13.813
1.77
84
5.500
15.688
1.72
90
5.875
16.750
l.72
96
_6.125
17.688
1.75
102
6.500
18.750
1.75
108
6.875
19.750
1.75
114
7.250
20.750
1.75
120
7.625
21.750
1.75
126
8.000
22.813
1.75
VB
60
4.000
11.563
1.72
66
4.375
12.625
1.72
72
4.750
13.563
1.72
84
5.125
13.750
1.77
84
5.500
15.625
1.72
90
5.875
16.625
1.72
Y6
6.125
17.625
1.75
102
6.500
18.688
1.75
108
6.875
19.685
1.75
114
7.250
20.688
1.75
120
7.625
21.688
l.75
120
8.000
23.688
1.72
1
60
4.000
1l.500
1.72
66
4.375
12.500
1.72
72
4.750
13.500
1.72
84
5.125
13.688
1.77
84
5.500
15.563
1.72
90
5.875
16.563
1.72
96
6.125
17.563
1.75
102
6.500
18.563
1.75
108
6.875
19.625
1.75
114
7.250
20.625
1.75
120
7.625
21.625
1.75
120
8.000
23.563
1.72
lYs
60
4.000
11.438
l.72
66
4.375
12.438
1.72
72
4.750
13.438
1.72
78
5.125
14.438
1.72
84
5.500
15.500
1.72
90
5.875
16.500
1.72
90
6.125
18.500
1.72
96
6.500
19.438
1.72
108
6.875
19.563
1.75
108
7.250
21.500
l.72
120
7.625
21.563
1.75
120
8.000
23.500
l.72
1~
J%
60
4.000
1l.375
l.72
66
4.375
12.375
1.72
72
4.750
13.375
1.72
78
5.125
14.375
1.72
84
5.500
15.438
1.72
90
5.875
16.438
l.72
90
6.125
18.375
1.72
96
6.500
19.375
1.72
108
6.875
19.500
1.75
108
7.250
21.438
1.72
120
7.625
21.500
1.75
120
8.000
23.438
l.72
60
4.125
11.375
l.72
66
4.375
12.313
1.72
72
4.750
13.313
1.72
78
5.125
14.313
1.72
84
5.500
15.313
1.72
84
5.875
17.313
1.72
90
6.125
18.250
1.72
96
6.500
19.313
1.72
108
6.875
19.438
1.75
108
7.250
21.375
l.72
114
7.625
22.313
1.72
120
8.000
23.750
1.72
339
DIMENSIONS
OF
HEADS
ALL DIMENSIONS IN INCHES
WALL THICKNESS
DIAM
ETER
iY2 1%
D
I%;
1%
2
2~
2~
2.~
3
66
60
60
60
60
60
60
60
60
L(R) 60
4.500 4.875 5.250 5.625 6.000 6.750 7.500 8.250 9.000
r
h
11.500 11.688 11.813 12.000 12.125 12.438 12.813 13.125 13.500
M
1.58
1.54
1.65
1.50
1.46
1.58
1.41
1.39
1.62
72
66
66
66
66
66
66
66
66
L (R) 66
4.500 4.875 5.250 5.625 6.000 6.750 7.500 8.250 9.000
r
12.313 12.500 12.625 12.750 12.938 13.250 13.563 13.938 14.313
h
1.60
1.44
M
1.54
1.65
1.72
1.50
1.46
1.58
1.69
78
72
72
72
72
72
72
72
72
L (R) 72
4.875 5.250 5.625 6.000 6.750 , 7.500 8.250 9.000
4.75
r
13.250 13.250 13.438 13.563 13.750 14.063 14.375 14.750 15.063
h
M
l.65
1.62
1.56
1.52
1.48
1.46
1.72
1.69
1.72
84
78
78
78
78
78
78
78
78
78
L (R)
5.250 5.625 6.000 6.750 7.500 8.250 9.000
5.125
5.125
r
14.250 14.188 14.250 14.375 14.500 14.875 15.188 15.500 15.875
h
1.72
M
1.60
1.48
1.69
1.56
1.72
1.65
1.72
1.52
90
~4
~4
M4
~4
84
84
84
84
84
L(R)
5.500 5.500 5.500 5.625 6.000 6.750 7.500 8.250 9.000
r
h
15.250 15.188 15.125 15.188 15.313 15.625 16.000 16.313 16.625
M
l.58
1.52
1.69
1.62
1.54
1.72
1.72
1.72
1.72
L (R)
96
r
h
M
L (R)
102
108
r
h
M
L (R)
r
h
M
L (R)
114
120
r
h
M
L(R)
r
h
M
L (R)
126
r
h
M
L(R)
132
r
h
M
84
5.875
17.250
1.69
90
6.125
18.125
1.72
96
6.500
19.250
1.72
108
6.875
19.313
1.75
108
7.250
21.313
1.72
114
7.625
22.250
l.72
120
8.000
23.313
1.72
84
5.875
17.125
1.69
90
6.125
18.125
1.72
96
6.500
19.125
1.72
102
6.875
20.125
1.72
108
7.250
21.250
1.72
114
7.625
22.188
1.72
120
8.000
23.250
1.72
84
5.875
17.063
1.69
90
6.125
18.063
1.72
96
6.500
19.063
1.72
102
6.875
20.063
1.72
108
7.250
2l.188
1.72
114
7.625
22.125
1.72
120
8.000
23.125
1.72
84
5.875
17.000
1.69
90
6.125
18.000
1.72
96
6.500
19.000
1.72
102
6.875
20.000
1.72
108
7.250
2l.063
1.72
114
7.625
22.063
1.72
120
8.000
23.063
1.72
84
6.000
17.063
1.69
90
6.125
17.938
1.72
96
6.500
18.938
1.72
102
6.875
19.938
1.72
108
7.250
20.938
1.72
114
7.625
21.938
1.72
120
8.000
23.000
1.72
84
6.750
17.313
1.62
90
6.750
18.125
1.65
96
6.750
18.938
1.69
102
6.875
19.813
1.72
108
7.250
20.813
l.72
114
7.625
21.813
1.72
120
8.000
22.875
1.72
84
7.500
17.625
l.58
90
7.50
18.375
1.62
96
7.500
19.188
1.65
102
7.500
20.000
1.69
108
7.500
20.813
1.72
114
7.625
21.625
1.72
120
8.000
22.750
1.72
84
8.250
17.875
1.54
90
8.250
18.688
1.58
96
8.250
19.500
1.60
102
8.250
20.312
1.62
108
8.250
21.125
1.65
114
8.250
21.938
1.69
120
8.250
22.750
1.72
84
9.000
18.188
1.52
90
9.000
19.000
1.54
96
9.000
19.813
1.56
102
9.000
20.563
1.60
108
9.000
21.438
1.62
114
9.000
22.188
1.65
120
9.000
23.000
l.65
340
DIMENSIONS
OF
HEADS
ALL DIMENSIONS IN INCHES
WALL THICKNESS
DIAM
ETER
138
144
DIAM
SEE
PAGE
138
144
lyg
1
l;i
1% lY2
132
132
L (R)
132
132
132
132
132
132
8.375 8.375 8.375 8.375 8.375 8.375 8.375 8.375
r
23.938 23.875 23.813 23.750 23.688 23.625 23.563 23.500
h
1.75
1.75
1.75
l.75
M
1.75
1.75
1.75
l.75
L (R) 132
132
132
132
132
132
132
132
r
8.750 8.750 8.750 8.750 8.750 8.750 8.750 8.750
h
25.875 25.813 25.750 25.625 25.563 25.500 25.438 25.313
M
l.72
l.72
1.72
l.72
l.72
l.72
l.72
1.72
ETER
D
Y8
%
%
D
325
WALL THICKNESS
1%
1%
1%
2~
2
2Y2 2%
3
-
L (R) 132
130
130
130
130
132
132
130
r
8.375
8.375 8.375 8.375 8.375 8.375 8.375 9.000
23.438 23.375 23.313 23.500 23.375 23.250 23.125 23.250
h
1.69
M
1.75
1.72
1.72
1.75
1.75
l.72
l.72
132
132
132
132
L (R)
132
132
132
132
r
8.750 8.750 8.750 8.750 8.750 8.750 8.750 9.000
25.250 25.188 25.125 25.063 24.938 24.813 24.625 l4.625
h
l.72
1.72
1.72
1.72
1.72
M
1.72
1.72
1.72
TOLERANCES
WALL THICKNESS (APPROXIMATION)
MINIMUM
REQ'D. THICKNESS
*
OTHER TYPES
HEMISPHERICAL
UP TO 150" I.D. inc!.
OVER 150" J.D.
To 1"
1" To 2"
2" To 3"
excl.
"
"
0.1875
0.3750
0.6250
0.0625
0.1250
0.2500
0.1250
0.1250
0.2500
3" To 3.5"
3.5" To 4"
4" To 4.5"
"
"
0.7500
1.1250
1.5000
0.3750
0.500
0.6250
0.3750
0.5000
0.6250
4.5" To 5"
5" To 5.5"
5.5" & Over
"
"
1.7500
2.0000
2.0000
0.7500
0.8750
1.0000
0.7500
0.8750
1.0000
"
* Specify minimum thickness (if required) when ordering.
INSIDE DEPTH OF DISH (h)
48" O.D. and under plus 0.5" minus 0"
Over 48" O.D. to 96" O.D. incl. plus 0.75", minus 0" Over 96" O.D. plus 1 ", minus 0"
OUT OF ROUNDNESS
Within the limits permitted by the Code.
341
FLANGES
FLANGE FACING FINISH
In pressure vessel construction only gasket seats of flanges, studded openings, etc.
require special finish beyond that afforded by turning, grinding or milling.
.
The surface finish for flange facing shall have certain roughness regulated by
Standard ANSI B16.5. The roughness is repetitive deviation from the nominal
surface having specified depth and width.
Raised faced flange shall have serrated finish having 24 to 40 grooves per inch. The
cutting tool shall have an approximate 0.06 in. or larger radius resulting 500
microinch approximate roughness IANSI B16.5, 6.3.4.1.1
The side wall surface of gasket groove of ring joint flange shall not exceed 63
microinch roughness. IANSI B16.5-6.3.4.3./
Other finishes may be furnished by agreement between user and manufacturer.
The finish of contact faces shall be judged by visual comparison with Standard ANSI
B46-1.
The center part of blind flanges need not to be finished within a diameter which equals
or less than the bore minus one inch of the joining flange. IANSI B16.5-6.3.31
Surface symbol used to designate roughness r is placed either on the line indicating
the surface or on a leader pointing to the surface as shown below. The numbers: 500
and 63 indicate the height of roughness; letter "c" the direction of surface pattern:
"concentric-serrated" .
CONCENTRIC SERRATED FINISH
SYMBOL USED IN PAST PRACTICE
342
I SO lb. FLANGES
STANDARD ANSI B16.5
1. All dimensions are in inches.
2. Material most commonly used, forged
steel SA 105. Available also in stainless
steel, alloy steel and non-ferrous metal.
3. The 1/16 in. raised face is included in
dimensions C, D and J.
4. The lengths of stud bolts do not include
the height of crown.
5. Bolt holes are 1/8 in. larger than bolt
diameters.
6. Flanges bored to dimensions shown unless otherwise specified.
7. Flanges for pipe sizes 22, 26, 28 and 30
are not covered by ANSI BI6.S.
SEE FACING PAGE FOR DIMENSION K
AND DATA ON BOLTING.
Diameter
of
Bore
Nominal
Pipe
Size
A
Length
Through
Hub
c
B
D
SLIp· ON
J~
aW?tW4@J .H=tI
I
~
I.
I .1
Ua
BLIND
Diameter
of Hub
at Point
of
Welding
Diameter
of
Hub
at
Base
Outside
Diameter
of
Flange
Thickness
of
Flange
E
G
H
J
.62
.82
1.05
.88
1.09
1.36
1~
2~6
2~6
.84
1.05
1.32
1~,
3Y2
1 V2
3%
11~6
4~
1.38
1.61
2.07
1.70
1.95
2.44
2~
2~
1.66
1.90
2.38
2~6
2~6
3~6
5
6
3Y.r
2.47
3.07
3.55
2.94
3.57
4.07
2.88
3.50
4.00
4~
4
5
6
4.03
5.05
6.07
4.57
5.66
6.72
4.50
5.56
6.63
5~
6~6
7~6
9
10
11
8
8.72
10.88
12.88
91~6
13Y2
16
19
1 V.
12
7.98
10.02
12.00
14
16
18
13.25
15.25
17.25
21
23V2
25
1%
20
Y.r
%
1
,Yo.
1Y.r
2
2Y.r
3
10
22
24
26
28
30
2V2
2~
2~
21~6
lV.
1~6
1~
1~6
Hi6
1~6
3~6
41~6
4%
7
7VJ
8V2
4
1~
4
11~6
4V2
2~6
14.14
16.16
18.18
5
5
5Y2
2V2
2 1!ti6
14.00
16.00
18.00
19.25
21.25
23.25
20.20
22.22
24.25
5Y.
2~
3~
3~
20.00
22.00
24.00
22
To be
specified
26.25
28.25
30.25
3~
26.00
28.00
30.00
28V2
34~
30~
32~
36V2
51~6
6
5
5 1..i6
5~
2~
3 7ti6
3V2
8.63
10.75
12.75
12
14%
15~
18
19~
24~
26Y.
27V2
29Y2
32
38~
¥a
I¥.6
1~6
1~6
1~6
1
1~
1~
1~
1~6
11~6
11~6
1 ¥.
343
150 lb.
LONG WELDING NECK
H
I- I'
K
I
~,
Il~
I. All dimensions are in inches.
2. Material most commonly used, forged
steel SA 105 . Available also in stainless
steel, alloy steel and non-ferrous metal.
3. The 1/16 in. raised face is included in
dimensions J and M.
4. The length of bolts do not include the
height of crown.
5. Bolt holes are 1/8 in. larger than bolt
diameters.
6. Dimensions, M (length of welding necks)
are based on data of major manufacturers. Long welding necks with necks
longer than listed are available on special
order.
~,
~~
~
~
J
~
~r-N-
~
~
~
~~
~
~
Ll~
SEE FACING PAGE FOR DIMENSION J.
Outside
Diameter
of
Raised
Face
Lel!gth of Bolts
No.
of
Holes
Diam.
of
Bolts
-Bolt
Circle
K
1~
l' Yi6
4
4
2
A
2Y2
2Y.
4
4
4
3%
AY.
5
5Y2
A
67i6
8
8
8
7~6
8Y2
10%
12%
15
8
12
12
Y2
Y2
Y2
2~
2)1
23A
3Va
2~
Y2
Y2
%
%
%
4
8
~
Raised
Face
0/.
%
L
M
Diameter Nominal
of
Pipe
Bore
Size
N
~
%
3Y.
2
1
3Y2
3Y.
2~
3l7.
3Yz
2~
4%
3~
1~
1~
3
5Y2
3)1
6
7
3~
%
%
%
11%
31.
---
Length
2~
7Y2
8Y2
9Y2
Y.
Ring
Joint
Outside
Diameter
3~
'"
4Y.
20/.
3~
2
9
d)
3%
.~
4~
CIl
Q)
2~
3
3~
4~
4%
3~
.s.
3~
4~
4
4Yz
4J1
5Y2
6Y2
<;
s:::
4
7%
0
6
4~
9~
4
14~
4.~
4~
17
4~
5~
5~
12
0.
·s
12
c:
CIl
'"
11)
E
14~
~
5
8
10
12
12
16
16
1
1
18%
5~
5~
21~
1~
22%
5Yz
6
6
6).1
16
18
20
1Y.
25
6Y.
6~
1~
1~
27~
22
27~
20
20
20
29Y2
6Y2
7
7
7J1
26~
20
22
24
29~
31 ~
33~
24
28
28
1~
1~
1~
31%
34
36
7
7
---.
28Y2
30Yz
32Y2
26
28
30
16~
18Y2
21
23
7~
14
16
18
10-14
344
eEl
300 lb. FLANGES
STANDARD ANSI B16.5
1. All dimensions are in inches.
2. Material most commonly used, forged
steel SA 105. Available also in stainless
steel, alloy steel and non-ferrous metal.
3. The 1/16 in. raised face is included in
dimensions C, D and J.
4. The lengths of stud bolts do not include
the height of crown.
5. Bolt holes are 1/8 in. larger than bolt
diameters.
6. Flanges bored to dimensions shown unless otherwise specified.
7. Flanges for pipe sizes 22, 26, 28 and 30
are not covered by ANSI BI6.5.
SEE FACING PAGE FOR DIMENSION K
AND DATA ON BOLTING.
Diameter
of
Bore
Nominal
Pipe
Size
Length
Through
Hub
nt:ln~l
~~
1,1.
WELDING NECK
H
~.
,~ 9--;t ¥
:
~~
I
I
U6
SLIP· ON
J
a~HII
I. I~ : I I ~.
BLIND
Diameter
of Hub
at Point
of
Welding
Diameter
of
Hub
at
Base
Outside
Diameter
of
Flange
Thickness
of
Flange
A
B
C
D
E
G
H
J
.62
.82
1.05
.88
1.09
1.36
2116
2JA
27i6
VI
1
1116
.84
1.05
1.32
1 Y2
1 V.
2Y.
33A
4%
~6
4V.
%
' 116
1114
1Y2
2
1.38
1.61
2.07
1.70
1.95
2.44
2'116
2 3,4
1116
1¥!6
HI6
1.66
1.90
2.38
2Y2
2 3,4
3t16
5JA
6Y.
6Y2
3A
'¥!6
V.
2Y2
3
3Y2
2.47
3.07
3.55
2.94
3.57
4.07
3
3Y.
3¥!6
1 Y2
1'116
1~
2.88
3.50
4.00
3 15
7Y2
8JA
9
1
1 Y.
1 ¥!6
4
5
6
4.03
5.05
6.07
4.57
5.66
6.72
3¥a
3Ye
3V.
1 V.
2
2116
4.50
5.56
6.63
10
11
12Y2
lJA
l¥a
17i6
8
10
12
7.98
10.02
12.00
8.72
10.88
12.88
4¥a
4%
5Y.
27i6
2Y.
2V.
8.63
10.75
12.75
15
17Y2
20Y2
1 V.
2
14
16
18
13.25
15.25
17.25
14.14
16.16
18.18
5%
6JA
3
3JA
3Y2
14.00
16.00
18.00
19
21
23
25Y2
28
2Y.
2JA
2¥a
20
22
24
19.25
21.25
23.25
20.20
22.22
24.25
6¥a
6Y2
6%
3~
4Y1,
20.00
22.00
24.00
23Y.
25JA
27%
30Y2
33
36
2Y2
2Y.
26
28
30
To be
spedfled
26.25
28.25
30.25
7JA
7JA
7~
7~
8~
28¥a
30Y2
38~
40~
8JA
26JA
28 JA
30JA
32~6
43
3Y.
3¥a
3%
Y2
1
¥..
2~6
5~
4
i
116
4%
5JA
5~
7
8Y.
10JA
12%
14~
16~
IV.
2~
345
300 lb.
LONG WELDING NECK
1. All dimensions are in inches.
2. Material most commonly used, forged
steel SA 105. Available also in stainless
steel, alloy steel and non-ferrous metal.
3. The 1/16 in. raised face is included in
dimensions J and M.
4. The length of bolts do not include the
height of crown.
5. Bolt holes are 1/8 in. larger than bolt
diameters.
6. Dimensions, M (length of welding necks)
are based on data of major manufacturers. Long welding necks with necks
longer than listed are available on special
order.
SEE FACING PAGE FOR DIMENSION J.
Outside
Diameter
of
Raised
Face
Length of Bolts
No.
of
Holes
Diam.
of
Bolts
Bolt
Circle
K
Pia
11 Yl6
2
2!12
2'%
3%
U.
Raised
Face
Ring
Joint
Outside
Diameter !Nominal
Diameter Length
of
Pipe
Bore
Size
L
4
4
4
3
3~
2V.
4
3~
4~
23A
4~
3~6
N
3X
4
2Y2
a
a
43A
31~6
5
a
5V.
5
5V2
8
60/.
7lA
40/.
5lA
6~6
7~6
a
a
7V.
5~
5!/2
4V.
M
51A
9
2Y2
3
3Y2
53A
4
5
6
a!/2
12
9lA
10 5/.
5~
ay.
10%
12
6!4
123A
15
13
16
16
15IA
7
lOlA
120/.
10
173A
7~
143A
12
16lA
laV2
20
20
21
24
20IA
22!/2
7~
8~
2H4
8X
163A
19
21
14
16
18
23
24
9
23Y.
25lA
27lA
24
24
27
29IA
93A
32
29Y2
2a
34Y2
31 !/2
28
28
37
333A
39lA
10
IOY2
IlIA
7
10~
27%
11
l1Y2
29!/2
31 !/2
121A
333A
12
8
10·14
20
22
24
26
28
30
346
400 lb. FLANGES
STANDARD ANSI B16.5
1. All dimensions are in inches.
2. Material most commonly used, forged
steel SA 105. Available also in stainless
steel, alloy steel and non-ferrous metal.
3. The 1/4 in. raised face is not included
in dimensions C, D and J.
4. The lengths of stud bolts do not include
the height of crown.
5. Bolt holes are 1/8 in. larger than bolt
diameters.
6. Flanges bored to dimensions shown unless otherwise specified.
7. Flanges for pipe sizes 22, 26, 28 and 30
are not covered by ANSI B16.5.
SEE FACING PAGE FOR DIMENSION K
AND DATA ON BOLTING.
A
~
~
1
1¥.4
1~
2
2~
3
3~
4
5
6
8
10
B
.88
1.09
1.36
1.70
1.95
2.44
2.94
3.57
4.07
4.57
5.66
6.72
14
16
18
8.72
10.88
12.88
14.14
16.1.6
18.18
20
22
24
20.20
22.22
24.25
26
26.25
28.25
30.25
12
28
30
J
a
a
BLIND
Diameter
of
Hub
at
Base
D
E
G
2~
%
2Y-.
1
1!t1,
.84
1.05
1.32
1%
C
2~,
2%
2~
lVa
v..
3Y,
1
1 ~,
1 y,
3
11~,
2%
v..
3¥,
p~
3Y2
2
4
2Vi
4!t1,
4%
4%
5%
5 "V,
6
6~
6%
6~
2Y-.
2 1!t1,
2 "V,
3Y,
3~6
3 1!tl6
3%
4
4 v..
6%
4Y2
7Y,
8Y,
7%
8%
8Y,
8%
l
a.~H II
I I~
~
I I ~
Diameter
of Hub
at Point
of
Welding
Length
Through
Hub
Diameter
of
"'Bore
Nominal
Pipe
Size
SLIp· ON
1.66
1.90
2.38
2.88
3.50
4.00
4.50
5.56
6.63
8.63
10.75
12.75
14.00
16.00
18.00
20.00
22.00
24.00
26~
28~,
30;1,
1 Y2
2Y,
2Y2
2~
3;1,
3 1;1,
4%
5Y-.
Outside
Diameter Thickness
of
of
Flange
Flange
H
J
3~
0/16
%
4%
4%
5Y-.
6Y,
6Y2
7Y2
8Y-.
9
5~
10
7
11
12Y2
8Va
1!t1,
1~6
%
1
1 y,
1 v..
1%
1%
1 Y2
1%
1%
12%
15
17Y2
14~
20Y2
2Y-.
16~
23
25Y2
28
2%
lOY-.
19
21
23Y,
2Y,
2Y2
2Y,
30Y2
2~
25Y-.
33
27%
2%
36
3
28%
301~,
32 1;1,
3~
3~
4
347
400 lb.
LONG WELDING NECK
"I ·Il~
H
I" I
K
~
-
I. All dimensions are in inches.
2. Material most commonly used, forged
steel SA 105. Available also in stainless
steel, alloy steel and non-ferrous metal.
3. The 1/4 in. raised face is not included in
thickness J but is included in length M.
4. The length of bolts do not include the
height of crown.
5. Bolt holes are 1/8 in. larger than bolt
diameters.
6. Dimensions, M (length of welding necks)
are based on data of major manufacturers. Long welding necks with necks
longer than listed are available on special
order.
~~
~~
I"-
~
~
~~
l"-
~r-N-
I
I'
~
~
~
~
LL-
SEE FACING PAGE FOR DIMENSION J.
Outside
Diameter
of
Raised
Face
Length of Bolts
No.
of
Holes
Diam.
of
Bolts
Bolt
Circle
K
1%
11~6
2
2~
2¥.
3Y.
4Y.
5
5Y2
6~6
70/16
8Y2
lOY.
12lA
15
16~
18Y2
21
23
25~
27~
29Y2
31 Y2
33lA
4
4
4
4
4
8
8
8
8
8
8
12
12
16
16
20
20
24
24
24
24
1%
1%
1 Y2
1%
llA
28
28
28
Y2
Y.
%
Y.
lA
%
lA
lA
~
%
¥.
%
1
1Y.
%,"
Raised
Face
Ring
Joint
Diameter Nominal
Outside
of
Diameter Lenath
Pipe
Bore
Size
L
3 v..
3
3Y2
3%
3lA
4
_3
4
4Y2
4Y.
4~
5
5¥.
6%
4~
4~
4lA
5
5
5~
7~
2 3.4
30/16
310/16
4%
5Y2
5lA
5~
7¥.
5~
5~
5~
2%
3~
9~
10%
13
15~
1~
17lA
1~
20Y..
22Y2
24~
27
3Y2
~
~
6~
8Y.
9
9
9Y4
10
8Y.
8Y2
29~
10
32
10~
11 Y.
1~
34Y2
11 Y2
1¥.
2
37
12~
39~
13
12
12 3.4
IOY2
13Y2
1
1
2Y2
7
7lA
¥.4
2Y.
6
7
9~
N
3~
5lA
6
6%
7)12
8
8Y.
8~
M
10~
12%
14lA
16lA
19
21
23Ye
27Y.
v..
1~
2
9
2~
3
cu
3~
rJl
4
,:::
0
Q..
12
'0.
-;
s::
's
0
s::
rJl
~
0
S
10-14
~
5
6
8
10
12
14
16
18
t/.l
20
22
24
26
28
30
348
600 lb. FLANGES
STANDARD ANSI B16.5
I. All dimensions are in inches.
2. Material most commonly used, forged
steel SA 105. Available also in stainless
steel, alloy steel and non-ferrous metal.
3. The 1/4 in. raised face is not included
in dimensions C, D and J.
4. The lengths of stud bolts do not include
the height of crown.
S. Bolt holes are 1/8 in. larger than bolt
diameters.
6. Flanges bored to dimensions shown unless otherwise specified.
7. Flanges for pipe sizes 22, 26, 28 and 30
are not covered by ANSI BI6.5.
WELDING NECK
SEE FACING PAGE FOR DIMENSION K
AND DATA ON BOLTING.
Nominal
Pipe
Size
A
~
B
1~
.88
1.09
1.36
1.70
1.95
2
2.44
o/.t
1
1Y<l
2~
14
16
18
2.94
3.57
4.07
4.57
5.66
6.72
8.72
10.88
12.88
14.14
16.16
18.18
20
22
24
20.20
22.22
24.25
26
28
30
26.25
28.25
30.25
3
3~
4
5
6
8
10
12
Diameter Diameter
of Hub
of
at Point
Hub
of
at
Welding
Base
Length
Through
Hub
Diameter
of
Bore
C
D
2~6
2Y<l
%
2~6
1
1 !li6
2%
1 Y.
2~
2%
3Ye
3Y-.
3¥a
4
4Y2
lY-.
1~6
10/.
1'¥!6
1'0/16
2Y.
2¥a
Outside
Diameter Thickness
of
of
Flange
Flange
E
G
H
.84
1.05
1.32
1.66
1.90
2.38
2.88
3.50
4.00
4.50
5.56
6.63
1 Y2
1%
2Y.
4%
4%
6
10~
7~6
8~
1 Y2
13
14
1 ¥.
8.63
10~
16Y2
10.75
12.75
13Y2
20
22
3~
30/16
51A
6Y.
6Y2
3'0/16
7Y2
2Y2
2~
4%
5Y-.
J
8Y-.
9
~6
%
'!li6
'¥!6
¥.
1
1 Y.
1Y-.
1¥a
1~
4%
2%
5Y-.
3
6
3¥a
6Y.
3%
6Y2
7
3'!li6
4¥!6
17
23~
2~
7Y-.
4%
14.00
16.00
18.00
19Y2
21 Y2
27
3
29Y-.
3Y-.
7Y2
5
7~
5Y-.
3Y2
34y-'
3~
5Y2
24
26Y-.
28Y-.
32
8
20.00
22.00
24.00
37
4
29~6
40
31%
33'0/16
421A
44Y2
15~
2¥!6
2Y2
2%
349
600 lb.
LONG WELDING NECK
,- I~
H
K
I
~
Il~
1. All dimensions are in inches.
2. Material most commonly used, forged
steel SA 105. Available also in stainless
steel, alloy steel and non-ferrous metal.
3. The 1/4 in. raised face is not included in
thickness J but is included in length M.
4. The length of bolts do not include the
height of crown.
5. Bolt holes are 1/8 in. larger than bolt
diameters.
6. Dimensions, M (length of welding necks)
are based on data of major manufacturers. Long welding necks with necks
longer than listed are available on special
order.
~~~
~
I'-
~-N~
~
'__-i
J
~
~
~
M
~~
LL~
SEE FACING PAGE FOR DIMENSION J.
Outside
Diameter
of
Raised
Face
Length of Bolts
No.
of
Holes
Diam.
of
Bolts
Bolt
Circle
K
1 :V.
l' Y16
2
14Raised
Face
Ring
Joint
4
4
4
4
4
8
Y2
8Y2
8
8
8
8
8
12
*
*
¥a
¥.
1
1
10%
12*
15
12
16
20
1 Y.
l'A
1 v..
16 'A
20
20
20
24
24
24
l¥a
1 Y2
1%
13*
17
19'A
20t.
23*
25*
1%
1*
l¥a
30%
33
11 Ya
12
13
12Y2
28
28
28
l¥a
2
2
36
38
40 'A
13 'A
13 3,4
14
14 'A
2Y2
2¥.
3%
4Y.
5
5Y2
6~6
7~6
18 Y2
21
23
25'A
27 v..
29Y2
31 Y2
33*
0/.
%
%
~
%
Diameter Nominal
Outside
of
Diameter Length
Pipe
Bore
Size
L
M
3 v..
3
3Y2
3Y2
3Y2
3~
-3~
"2Y.
3¥a
4
4 v..
4/{
4
4X
2Y2
4Y2
5
3~6
31~6
5
5Y2
5M
6Y2
6M
S'A
40/.
7M
7*
20/.
3 v..
4Y2
5
5¥.
60/.
7'A
8Y2
10Y2
11 Y2
28Y2
4~
Y2
:y..
2*
I
Iv..
l~
9
2
Q)
5~
S'A
.~
6
6*
7
6
0..
8~
13Y2
8%
9!4
9
9YJ
10 v..
11
15*
17
19Y2
21 Y2
11~
24
13'A
13~
14Y2
til
Q)
·a
7Y2
8*
10*
8Y2
10
10M
N
28 v..
12
~
·s=
0
=
til
('is
Q)
S
('is
CI:l
12-20
2Y2
3
3Y2
4
5
6
8
10
12
14
16
18
20
22
24
26
28
30
350
900 lb. FLANGES
STANDARD ANSI B 16. S
1. All dimensions are in inches.
2. Material most commonly used, forged
steel SA 105. Available also in stainless
steel, aHoy steel and non-ferrous metal.
3. The 1/4 in. raised face is not included
in dimensions C, D and J.
4. The lengths of stud bolts do not include
the height of crown.
S. BoIt holes are 1/8 in. larger than bolt
diameters.
6. Flanges bored to dimensions shown unless otherwise specified.
7. Flanges for pipe sizes 26, 28 and 30 are
not covered by ANSI B16.5.
SEE FACING PAGE FOR DIMENSION K
AND DATA ON BOLTING.
Nominal
Pipe
Size
A
~
%
1
1Y-.
1~
Length
Through
Hub
Diameter
of
Bore
B
C
D
.88
1.09
1.36
2%
1~
2~
2~
1%
1.70
1.95
2.44
2¥.
3~
1%
1%
4
1~
2~
2.94
3.57
4.57
4Va
2Y2
4~
2~
6
8
5.66
6.72
8.72
5
5Y2
6%
3%
4
10
12
14
10.88
12.88
14.14
7~
7~
4%
16
18
20
24
16.16
18.18
20.20
24.25
26
28
30
26.25
28.25
30.25
2
2~
3
4
5
4
8%
8Y2
9
2V.
3Y.
4~
5V.
Diameter
of
Hub
at
Base
E
G
H
.84
1.05
1.32
1~
1~
5V.
2~,
5%
lV.
2~
2~
6~
1 Y.
1.66
1.90
2.38
4V.
Outside
Diameter Thickness
of
of
Flange
Flange
J
4~
%
1
7
1~
8~
1 Y2
1%
2.88
3.50
4.50
4~
6~
11 Y2
1~
1~
5.56
6.63
8.63
7~
9~
13~
2
15
2~
2~
10.75
12.75
14.00
5
11 ~
9%
9~
18Y2
14~
21~
2~
16Y2
24
17~
25~
3Y.
3%
16.00
18.00
20.00
24.00
20
27~
3~
22~
24~
31
4
33~
29Y2
41
4~
5~
11 ~
11 ~
26%
30~
32~
42~
281~
46
5Y2
5%
12~
30~
35
48~
5~
9~
11 Y2
5~
Diameter
of Hub
at Point
of
Welding
6
6~
8
351
900 lb.
LONG WELDING NECK
I ·Il~
H
,- /-
K
~'\
1. All dimensions are in inches.
2. Material most commonly used, forged
steel SA 105. Available also in stainless
steel, alloy steel and non-ferrous metal.
3. The 1/4 in. raised face is not included in
thickness J but is included in length M.
4. The length of bolts do not include the
height of crown.
5. Bolt holes are 1/8 in. larger than bolt
diameters.
6. Dimensions, M (length of welding necks)
are based on data of major manufacturers. Long welding necks with necks
longer than listed are available on special
order.
~-j
~
~
~
~
~
~r-N-
J
tJ
~~
~
LL~
SEE FACING PAGE FOR DIMENSION J.
Outside
Diameter
of
Raised
Face
Length of Bolts
No.
of
Holes
Diam.
of
Bolts
Bolt
Circle
K
1%
1'!ti6
2
2Y2
2%
3%
4Y.
5
6~
7~
8Y2
10%
12~
15
161A
18Y2
21
23
27lA
29Y2
31 Y2
33~
4
4
4
4
4
8
8
8
8
8
12
12
16
20
20
20
20
20
20
20
20
20
~
~
¥.
1
%
%
1
¥.
3lA
3Y2
4
4%
4%
~.
Raised
Face
4lA
41Y,
5
5
Ring
Joint
Diameter Nominal
Outside
of
Diameter Length
Pipe
Bore
Size
L
5Y2
41A
-4 )12
5
5
5)12
6Y2
7Y2
7Y2
5~
5~
4Y.
6~
6lA
6
9lA
6~
7
4%
5
6lA
11
12Y2
15Y2
7Y2
7 3,4
7~
7Y2
8~
9
11~
9){
10
9)12
lOY.
14Y2
16Y2
10~
11 ){
17~
11 ){
11~
12~
13 )12
141A
20
221A
5JA
1 Y.
l1A
1 Y.
1%
1%
1%
1Y2
1%
1¥.
2
2Y2
29Y2
35Y2
13Y2
17 Y.
2~
37Y2
40lA
17Y2
3
3
18~
18lA
19Y2
20
18Y2
21
22
24lA
27
42~
18~
7~
17~
M
N
Y2
%
2!t\6
2YI
2~
9
0)
,~
rJJ
0)
12
'0..
C;
'8=
0
=
91A
24Y2
29Y2
0..
til
CIl
0)
a
12·20
JJ
1
1Y-t
l,Y2
2
2Y2
3
4
5
6
8
10
12
14
16
18
20
24
26
28
30
352
eEl
1500 lb. FLANGES
STANDARD ANSI B16.S
1. All dimensions are in inches.
2. Material most commonly used, forged
steel SA 105. Available also in stainless
steel, aHoy steel and non-ferrous metal.
3. The 1/4 in. raised face is not included
in dimensions C, D and J.
4. The lengths of stud bolts do not include
the height of crown.
5. Bolt holes are 1/8 in. larger than bolt
diameters.
6. Flanges bored to dimensions shown unless otherwise specified.
SEE FACING PAGE FOR DIMENSION K
AND DATA ON BOLTING.
Nominal
Pipe
Size
A
~
y..
1
1~
1~
2
...II
0
B
C
.88
1.09
1.36
2%
2%
2¥.
1.70
1.95
2.44
2~
~
I.
I
F:
~:
.~ e!~
a
1.lt~
SLIP· ON
JJ
a~.4~ II
I I~
~
I I ~
BLIND
Diameter
of
Hub
at
Base
D
E
G
H
1~
.84
1.05
1.32
lYl
1%
4%
5Ya
2~6
5~
1
1 Y.
2Y2
6~
lYa
2%
4Ya
7
8Yl
1 Y2
4¥.
1%
·1%
3~
1%
1%
4
2~
2.94
3.57
4.57
4Ya
4%
2~
4~
3~6
5.66
6.72
8.72
6Y.
4Y.
6%
8%
41~6
10.88
12.88
10
11 Y.
11 %
1.66
1.90
2.38
Outside
Diameter Thickness
of
of
Flange
Flange
~
2Yl
3
4
~
WELDING NECK
Diameter
of Hub
at Point
of
Welding
Length
Through
Hub
Diameter
of
Bore
£:~~
I.
J
~
1~
~
~
Q,
>...a
."
II
2Yl
2.88
3.50
4.50
9%
10Yl
1%
5~
6%
12~
2Ya
5.56
6.63
8.63
7%
9
llYl
14%
2¥.
15Y2
3~
19
3%
10.75
12.75
14.00
14Yl
17%
19Y1
23
26Yl
4~
29Y2
5~
21%
32Yl
36
38%
46
5%
6%
7
8
1~
~
5
6
8
10
12
14
16
18
20
24
'u
II
...
Q,
II
...a
~
-----
--
12~
12~
14
16
5%
6~
7Ya
------
16.00
18.00
20.00
24.00
23Y2
25~
30
4¥.
353
1500 lb.
LONG WELDING NECK
1. All dimensions are in inches.
2. Material most commonly used, forged
steel SA 105. Available also in stainless
steel, alloy steel and non-ferrous metal.
3. The 1/4 in. raised face is not included in
thickness J but is included in length M.
4. The length of bolts do not include the
height of crown.
S. Bolt holes are 1/8 in. larger than bolt
diameters.
6. Dimensions, M (length of welding necks)
are based on data of major manufacturers. Long welding necks with necks
longer than listed are available on special
order.
SEE FACING PAGE FOR DIMENSION J.
Outside
Diameter
of
Raised
Face
Length of Bolts
No.
of
Holes
Diam.
of
Bolts
Bolt
Circle
K
%Raised
Face
Ring
Joint
Outside
Diameter Nominal
Diameter Length
of
Pipe
Bore
Size
L
M
N
4
4
4
4Yi
5
6~
8
8
8
1
1Y.
1~
7V2
6!4
6~
4¥.
2~
8
7
7
5~
9Y2
7~
7~
6~
3
4
8
1Y2
1~
1%
11Y2
12Y2
15Y2
9~
9~
lOY.
10 Y2
.]2
1 ¥a
2
19
22Y2
25
12~
12
15
16
16
18Y2
21
23
27~
v..
1
12
12
16~
¥.
4
4
8
16
16
16
16
5
9
5Y2
¥.
2~
5~
27~
30Y2
32~
39
11
J1
1~
2
12
5
6
8
14~
13 ~
15 Yi
16
17
17Y2
19 Y2
21 Y,
24 J1
18Y2
20)1
22 )1
23Y2
25~
30
13~
1
10
12
14
21~
25~
12-20
16
18
20
24
354
2500 lb. FLANGES
STANDARD ANSI B 16. S
1. All dimensions are in inches.
2. Material most commonly used, forged
steel SA 105. Available also in stainless
steel, alloy steel and non-ferrous metal.
3. The 1/4 in. raised face is not included
in dimensions C, D and J.
4. The lengths of stud bolts do not include
the height of crown.
5. Bolt holes are 1/8 in. larger than bolt
diameters.
6. Flanges bored to dimensions shown unless otherwise specified.
WELDING NECK
~~~'l~
~I.~~I:====~==:::~--~
SLIP· ON
SEE FACING PAGE FOR DIMENSION K
AND DATA ON BOLTING.
Nominal
Pipe
Size
A
~
y..
1
ly..
1~
2
Length
Through
Hub
Diameter
of
Bore
...
tJ
;;
-£...
~
Q.
B
C
.88
1.09
1.36
2%
3Y.
3Y2
1.70
1.95
2.44
3%
4%
5
2~6
2.94
3.57
4.57
5%
6%
7Y2
3Y.
3%
5.66
6.72
8.72
9
10%
12Y2
10.88
12.88
16V2
D
.
BLIND
Diameter
of Hub
at Point
of
Welding
Diameter
of
Hub
at
Base
E
G
.84
1.05
1.32
Outside
Diameter Thickness
of
of
Flange
Flange
H
J
11~6
5~
1~6
2
5Y2
l~
2~
6~
1%
1.66
1.90
2.38
2%
7~
3~
8
3%
9~
1V2
1%
2
4V2
5~
10Y2
12
4~
2.88
3.50
4.50
6Y2
14
5Y.
6·
7
5.56
6.63
8.63
8
12
16V2
19
21%
5
14%
17%
26Y2
30
7~
1~6
11~6
1%
2%
2%
>.
2~
3
4
5
6
8
10
12
.a
'tJ
tJ
cc
'utJ
...
Q.
tJ
.a
~
18~
9
10
10.75
12.75
9~
2~
2%
3
3%
4~
6V2
355
2500 lb.
LONG WELDING NECK
I_lt~
H
I"
K
'"
~"
~~
1. All dimensions are in inches.
2. Material most commonly used, forged
steel SA 105. Available also in stainless
steel, alloy steel and non-ferrous metal.
3. The 1/4 in. raised face is not included in
thickness J but is included in length M.
4. The length of bolts do not include the
height of crown.
5. Bolt holes are 1/8 in. larger than bolt
diameters.
6. Dimensions, M (length of welding necks)
are based on data of major manufacturers. Long welding necks with necks
longer than listed are available on special
order.
~,,~~
~
~t-N-
~
~
~
J
"
~~
~
~
~
LL~
SEE FACING PAGE FOR DIMENSION J.
Outside
Diameter
of
Raised
Face
Length of Bolts
No.
of
Holes
Diam.
of
Bolts
Bolt
Circle
K
H'.
14,"
Raised
Face
Ring
Joint
Diameter Nominal
Outside
of
Diameter Length
Pipe
Bore
Size
L
M
N
3Y2
3*
5~
5~
~
5~
5~
~
4~
%
5*
5~
2~
4
4
8
1
1 Y.
1
5Y.
5*
6*
6~
6Y2
7
7~
2~
3~
7~
7Y2
3*
4Y.
5
8
7*
8
8~
9
9
9~
6~6
8
1 Y.
1 v..
1 Y2
7~6
lOY.
8
8
12
'*
2
2
12*
14Y2
17v..
12
13'14
15 v..
12*
14 ~
16
12*
lS
12
12
2Y2
2*
21 v..
24¥e
19 Y2
21 ~
22 ~
l'Yi6
2
2~
2¥.
3%
4
4
4
*
*
8
10*
1ov..
10~
9
1
CI)
.~
V>
CI)
4Y2
5 v..
6Y2
0..
'S,.
~
12
's'"
0
'"
1¥.t
1~
2
2~
3
4
V>
CIS
8Y2
20~
8
9
CI)
E
CIS
v..
CIl
12
14*
17¥e
12-20
5
6
8
10
12
356
RING JOINT FLANGES
r~=t
APPROXIMA TE DISTANCE BETWEEN FLANGES
t.~
Nominal
Pipe
Size
X
150
Pressure Rating lb.
300
400
Va
Va
Va
Va
-
U2
U2
U2
%2
5/
/32
5/
/ ~2
~{2
~{~
1
/32
1~
~{2
~{2
5/
/32
/32
~'32
J{6
"!{2
U6
?{2
J{6
?{2
1X
2
2/-2
3
1500
900
2500
Distance, inches
5/
/32
5/
-32
5/
/32
5/
.I 32
%
600
5/
/32
5/
~{2
~{2
1/
S/
/32
~{6
~{6
~32
~2
K6
5/ 732
5/
/32
~32
~2
6
8
10
12
14
16
18
20
22
24
5/
/32
/32
K2
5/
/32
K2
?{2
~2
J{6
~2
5/
/32
?{z
?{z
!{2
K6
732
Va
7/
/31
~/
/)2
I/.
/a
Va
Va
Va
~2
~2
~2
~{2
!{2
~2
~
~2
~
~
X
~{6
K6
K6
~2
~2
-
-
!{2
}\6
J{6
%2
K~
~
s/
716
~2
~6
~6
~2
~2
3{6
~l2
~l2
K6
$/
J{6
-
Va
Va
Va
Va
5/
732
/32
7/
Va
U2
3{6
J/
/16
3/
;16
~{2
K2
732
Va
Va
Va
Va
Va
Va
Va
Va
K2
~~2
$/
~32
~32
5/
/32
$/
732
5/
732
~~2
~32
U2
4
5
7/
-
-
-
%
RING NUMBERS
Nominal Pipe Size
..QJ .c•
/a /a
QJ «I
=.-
Q.,U
150
300,400,600
900
1500
2500
Nominal Pipe Size
QJ
.. .c•
/aQJ /a«I
=-
~u
150
300,400,600
900
1500
2500
3.4
11A 1Y2 2 2Y2 3 3Y2
.. ... R15 R17 R19 R22 R25 R29 R33
Rll R13 R16 R1B R20 R23 R2& R3l R34
.. . ,. ... .. .. . ... . .. R3l ..
R12 R14 R16
- .- R1B r-R20 R24 R27 R35 ...
R13 R16 RIB R21 R23 R26 R2B R32 ...
Vi
1
.
.
.
.
4
R3&
R37
R37
R39
R3B
5
6
8
10
12
14
16
18
20
24
R40
R41
R41
R44
R42
R43
R45
R45
R46
R47
R4B
R49
R49
R50
R51
R52
R53
R53
R54
R55
R5&
R57
R57
R58
R60
R59
R&l
R62
R63
R64
R65
R66
R67
R&8
R69
R70
R71
R72
R73
R74
R75
R76
R77
R78
R79
... ..
,
. .. ... ...
357
A
~
~ '"
a:
r
~
t-
w
r
C
~t-
R
,,'
STUDDING OUTLETS
All dimensions are in inches.
Material most commonly used,
forged steel SA-105.
150lb
SIZE lliICK
(BORE)
B
T
1/2
3/4
1
11/4
11/2
2
21/2
3
31/2
4
5
6
8
10
12
14
16
18
20
24
1.50
1.50
1.50
1.50
1.50
1.75
1.75
1.75
1.75
1.75
2.00
2.00
2.00
2.25
2.25
2.56
2.56
2.75
2.75
3.00
aD
A
3.50
3.88
4.25
4.62
5.00
6.00
7.00
7.50
8.50
9.00
10.00
11.00
13.50
16.00
19.00
21.00
23.50
25.00
27.50
32.00
RF
STUD
STUDS
aD CIRCLE NO. SIZE TPI
R
C
J
M
I
1.38
1.69
2.00
2.50
2.88
3.62
4.12
5.00
5.50
6.19
7.31
8.50
10.62
12.75
15.00
16.25
18.50
21.00
23.00
27.25
2.38
2.75
3.12
3.50
3.88
4.75
5.50
6.00
7.00
7.50
8.50
9.50
11.75
14.25
17.00
18.75
21.25
22.75
25.00
29.50
4
4
4
4
4
4
4
4
8
8
8
8
8
12
12
12
16
16
20
20
1/2
1/2
1/2
1/2
1/2
5/8
5/8
5/8
5/8
5/8
3/4
3/4
3/4
7/8
7/8
1
1
11/8
11/8
11/4
13
13
13
13
13
11
11
11
11
11
10
10
10
9
9
8
8
8
8
8
TAP
HOLE
DEPlli DEPlli
E
F
0.75
0.75
0.75
0.75
0.75
0.94
0.94
0.94
0.94
0.94
1.12
1.12
1.12
1.31
1.31
1.50
1.50
1.69
1.69
1.88
1.25
1.25
1.25
1.25
1.25
1.50
1.50
1.50
1.50
1.50
1.75
1.75
1.75
2.00
2.00
2.31
2.31
2.50
2.50
2.75
300lb
SIZE lliICK
(BORE)
B
T
1/2
3/4
1
11/4
11/2
2
21/2
3
31/2
4
5
6
8
10
12
14
16
18
20
24
1.50
1.75
1.75
1.75
2.00
1.75
2.00
2.00
2.00
2.00
2.00
2.00
2.25
2.56
2.75
2.75
3.00
3.00
3.00
3.44
aD
A
3.75
4.62
4.88
5.25
6.12
6.50
7.50
8.25
9.00
10.00
11.00
12.50
15.00
17.50
20.50
23.00
25.50
28.00
30.50
36.00
RF
STUD
STUDS
aD CIRCLE NO. SIZE TPI
R
C
J
M
I
1.38
1.69
2.00
2.50
2.88
3.62
4.12
5.00
5.50
6.19
7.31
8.50
10.62
12.75
15.00
16.25
18.50
21.00
23.00
27.25
2.62
3.25
3.50
3.88
4.50
5.00
5.88
6.62
7.25
7.88
9.25
10.62
13.00
15.25
17.75
20.25
22.50
24.75
27.00
32.00
4
4
4
4
4
8
8
8
8
8
8
12
12
16
16
20
20
24
24
24
1/2
5/8
5/8
5/8
3/4
5/8
3/4
3/4
3/4
3/4
3/4
3/4
7/8
1
11/8
11/8
11/4
11/4
11/4
11/2
13
11
11
11
10
11
10
10
10
10
10
10
9
8
8
8
8
8
8
8
TAP
HOLE
DEPlli DEPlli
E
F
0.75
0.94
0.94
0.94
1.12
0.94
1.12
1.12
1.12
1.12
1.12
1.12
1.31
1.50
1.69
1.69
1.88
1.88
1.88
2.25
1.25
1.50
1.50
1.50
1.75
1.50
1.75
1.75
1.75
1.75
1.75
1.75
2.00
2.31
2.50
2.50
2.75
2.75
2.75
3.19
359
~
1:
a:
it....
A
~w
C
r
<Il
STUDDING OUTLETS
A
"
It
I-
All dimensions are in inches.
Material most commonly used,
forged steel SA-lOS.
1500lb
SIZE rnICK
(BORE)
T
B
1(2
3/4
1
11/4
11/2
2
21(2
3
4
5
6
8
10
12
14
16
18
20
24
2.19
2.19
2.44
2.44
2.75
2.44
2.75
2.94
3.19
3.62
3.44
3.88
4.31
4.56
5.00
5.50
5.94
6.38
7.31
OD
A
4.75
5.12
5.88
6.25
7.00
8.50
9.62
10.50
12.25
14.75
15.50
19.00
23.00
26.50
29.50
32.50
36.00
38.75
46.00
RF
STUD
STUDS
OD CIRCLE NO. SIZE TPI
J
I
C
M
R
1.38
1.69
2.00
2.50
2.88
3.62
4.12
5.00
6.19
7.31
8.50
10.62
12.75
15.00
16.25
18.50
21.00
23.00
27.25
3.25
3.50
4.00
4.38
4.88
6.50
7.50
8.00
9.50
11.50
12.50
15.50
19.00
22.50
25.00
27.75
30.50
32.75
39.00
4
4
4
4
4
8
8
8
8
8
12
12
12
16
16
16
16
16
16
3/4
3/4
7/8
7/8
1
7/8
1
11/8
11/4
11(2
13/8
15/8
17/8
2
21/4
21(2
23/4
3
31(2
10
10
9
9
8
9
8
8
8
8
8
8
8
8
8
8
8
8
8
HOLE
TAP
DEP1H DEP1H
E
F
1.12
1.12
1.31
1.31
1.50
1.31
1.50
1.69
1.88
2.25
2.06
2.44
2.81
3.00
3.38
3.75
4.12
4.50
5.25
1.75
1.75
2.00
2.00
2.31
2.00
2.31
2.50
2.75
3.19
3.00
3.44
3.88
4.12
4.56
5.06
5.50
5.94
6.88
2500lb
SIZE rnICK
(BORE)
B
T
1(2
3/4
1
11/4
11(2
2
21(2
3
4
5
6
8
10
12
2.19
2.19
2.44
2.75
2.94
2.75
2.94
3.19
3.62
4.12
4.56
4.56
5.50
5.94
OD
A
5.25
5.50
6.25
7.25
8.00
9.25
10.50
12.00
14.00
16.50
19.00
21.75
26.50
30.00
. STUDS
RF
STUD
OD CIRCLE NO. SIZE TPI
R
C
J
M
I
1.38
1.69
2.00
2.50
2.88
3.62
4.12
5.00
6.19
7.31
8.50
10.62
12.75
15.00
3.50
3.75
4.25
5.12
5.75
6.75
7.75
9.00
10.75
12.75
14.50
17.25
21.25
24.38
The studding outlets tabulated
comply with the requirements of
ASME Code Sect. VIII. Div. 1.
The tabulated dimensions of
thickness, T are the minimums
4
4
4
4
4
8
8
8
8
8
8
12
12
12
3/4
3/4
7/8
1
11/8
1
11/8
11/4
11(2
13/4
2
2
21(2
23/4
10
10
9
8
8
8
8
8
8
8
8
8
8
8
TAP
HOLE
DEP1H DEP1H
F
E
1.12
1.12
1.31
1.50
1.69
1.50
1.69
1.88
2.25
2.62
3.00
3.00
3.75
4.12
1.75
1.75
2.00
2.31
2.50
2.31
2.50
2.75
3.19
3.69
4.12
4.12
5.06
5.50
required.
The outlets are available also in
stainless and other alloy steels.
Air test holes are optional.
360
NOTES
361
ua
.-
A ---I
90° Long Radius Elbow
~:""""::...:...,...,I;Z-..;.;';;';';';~~~
WELDING FITTINGS
1.
ANSI B 16.9
All dimensions are in inches.
2.
Welding fitting material conforms to SA 234 grade WPB.
3.
4.
Sizes 22, 26 and 30 in. are not covered by ANSI B 16.9 .
5.
90° Long Radius
Reducing Elbow _
For wall thicknesses see page 322.
Dimension F} applies to standard and X-STG. caps. Dimension F2 applies to heavier weight caps.
Nominal
Pipe
Size
Dimensions
Outside
Diameter
0.840
1.050
1fA,,,
~UJ~
c
D
F/s
....
B
A
7h6
Pl1I6
E
1 ....
1Y2 ....
1315
lY2
7/s
23!t6
1
1%
1~
lY2
1.660
Fls
1
2%
lY4
2 11I6
l~
lY2
1.900
2V4
Ills
3V4
1~
27116
1~
1~
2.375
3
Pis
4 1I6
2
3
3 1I6
lY2
1~
2~
2.875
3~
1~
3
5 !t6
2Y2
15
3 !t6
lYz
2
3
3.500
4Y2
2
6Y4
3
4%
2
2Y2
4.000
5V4
2Y4
7Y4
3~
5Y2
2~
3
4
4.500
6
21;2
8Y4
4
6V4
2Yz
3
5
5.563
7~
31/8
10 5!t6
5
7%
3
3Yz
6
6.625
9
3%
12 15/16
6
95h6
3~
4
8
8.625
12
5
I 65!t6
8
12 5/16
4
5
15
1
614
20 k
10
I 5 /s
5
6
12
18 3/8
6
7
IV4
.--,,~
45° Long Radius Elbow
2
~.7
. ~.
lffTYili
~AJ-A-'
1800 Long
Radius Elbow
10
90° Short Radius Elbow
180° Short Radius Return
Cap
10.750
3
3
3
12
12.750
18
1h
24 3/8
14
14.000
21
8%
28
14
21
6~
1h
16
16.000
24
10
32
16
24
7
8
18
18.000
27
llY4
36
18
27
8
9
20
20.000
30
12~
40
20
30
9
10
22
22.000
33
13Y2
44
10
10
24
24.000
36
15
48
1O~
12
26
26.000
39
16
52
1O~
... .
30
30.000
45
18~
ffi
24
30
36
45
lOY2 ... .
362
WELDING FITTINGS
1.
2.
3.
4.
~
r-t--
ANSI B 16.9
All dimensions are in inches
Welding fitting material conforms to SA 234 grade WPB.
Sizes 22,26 and 30 in. are not covered by ANSI B 16.9.
For wall thicknesses see page 322.
Nominal
Pipe
Size
Yz
Yz
3/S
%
%
Yz
1
1
%
Yz
114
}li4
1
%
Yz
lYz
IY2
114
1
%
Y2
2
2
lYz
114
1
%
2Yz
2Yz
2
lYz
Pi4
3
1
3
2Yz
2
lYz
114
3Y2
3Yz
3
2Yz
2
lYz
4
4
3Yz
3
2Yz
2
lYz
Outside
Diameter
.840
.675
l.050
.840
1.315
l.050
.840
l.660
1.315
1.050
.840
l.900
1.660
1.315
1.050
.840
2.375
l.900
l.660
1.315
1.050
2.875
2.375
l.900
l.660
1.315
3.500
2.875
2.375
l.900
l.660
4.000
3.500
2.875
2.375
1.900
4.500
4.000
3.500
2.875
2.375
l.900
+
[G.~J
Dimensions
Outlet
f
G
I
Tee
G
H
J
1
1
Jl/s
11/S
1
1
11/s
11/s
· ...
· ...
, ...
lYz
lYz
lYz
lYz
lYz
lYz
· ...
2
2
P/s
P/s
P/s
P/s
214
214
214
214
214
P/s
P/s
P/s
P/s
214
214
214
214
214
....
2Yz
....
2Yz
2Yz
2Yz
2Yz
2Yz
3
3
3
3
3
3%
3%
3%
33/8
]3/8
3%
3%
3%
3%
3%
41/8
41/8
4 1/s
4 1/s
4 1/s
4 1/s
23/8
21/8
2
1%
3
2%
25/s
2Yz
214
V/8
314
3
27/8
2%
3%
35/8
3Yz
31;4
31/8
4 1/s
4
37/s
3%
3Yz
33/s
,
lYz
2
2
2
· ...
2Yz
2Yz
2Y2
2Y2
3
3
3
3
· , ..
3Yz
3Yz
3Yz
3Yz
....
3Yz
3Yz
3Yz
3Yz
....
4
4
4
4
....
4
4
4
4
4
I
~
f---t-
lG-~GJ
Reducing Tee
[J]
S
Concentric Reducer
LJl
'---
----
Eccentric Reducer
363
F'---t_.l ,
WELDING FITTINGS
f
G
[c.-J
ANSI B 16.9
All dimensions are in inches
Welding fitting material confonns to SA 234 grade WPB.
Sizes 22, 26 and 30 in. are not covered by ANSI B 16.9.
For wall thicknesses see page 322.
1.
2
3.
4.
Nominal
Pipe
Size
I
Tee
5
,
!
?
~.--t-
6
lc-~cJ
Reducing Tee
8
I
I
I
[Jl
10
-'-'--
12
-
-
.--..I
Concentric Reducer
eJl
'-'-
14
16
-.-.
18
Eccentric Reducer
Outlet
5
4
312
3
212
2
6
5
4
312
3
212
8
6
5
4
312
10
8
6
5
4
12
10
8
6
5
14
12
10
8
6
16
14
12
10
8
6
18
16
14
Dimensions
Outside
G
Diameter
47/8
5.563
47/8
4.500
47/8
4.000
47/s
3.500
47/8
2.875
47/8
2.375
55/8
6.625
55/8
5.563
55/8
4.500
55/8
4.000
55/8
3.500
55/8
2.875
7
8.625
7
6.625
7
5.563
7
4.500
7
4.000
10.750
8.625
6.625
5.563
4.500
12.750
10.750
8.62.5
6.625
5.563
14.000
12.750
10.750
8.625
6.625
16.000
14.000
12.750
10.750
8.625
6.625
18.000
16.000
14.000
8Yz
8Yz
8Yz
812
812
10
10
10
10
10
11
11
11
11
11
12
12
12
12
12
12
13Y2
1312
1312
H
J
47/8
45/8
4'h
43/8
4Y4
4 1/8
55/8
53/8
51/8
5
47/8
....
4~
5
5
5
5
5
....
5Y2
512
5Y2
512
512
7
65/8
63/8
6 1/8
6
....
812
8
75/8
712
7Y4
10
9Y2
9
8 5/8
8Y2
11
....
10 5/8
10 1/8
13
13
13
13
9~
93/8
12
12
11 5/8
111/8
10~
10 1/8
1312
13
13
6
6
6
6
7
7
7
7
....
8
8
8
8
...
....
14
14
14
14
14
....
15
15
364
WELDING FITTINGS
1.
2
3.
4.
rL,
ANSI B 16.9
All dimensions are in inches
Welding fitting material conforms to SA 234 grade WPB.
Sizes 22, 26 and 30 in. are not covered by ANSIB 16.9.
For wall thicknesses see page 322.
Nominal
Pipe
Size
r'---L.--
Outside
Diameter
I
Tee
G
H
J
15
15
15
18
12
10
8
12.750
10.750
8.625
13'lS
13'lS
13'lS
12 5/8
12'/8
11%
20
20
18
16
14
12
10
8
20.000
18.000
16.000
14.000
12.750
10.750
8.625
15
15
15
15
15
15
15
15
14Y:z
14
14
13 5/8
13'/8
12%
.'
22
20
18
16
14
12
10
22.000
20.000
18.000
16.000
14.000
12.750
10.750
16'lS
.,
16'lS
16'lS
16Y:z
16Y:z
16Y:z
16'lS
16
15Y:z
15
15
14 5/8
14'/8
24
22
20
18
16
14
12
10
24.000
22.000
20.000
18.000
16.000
14.000
12.750
10.750
17
17
17
17
17
17
17
17
17
17
17
16Y:z
16
16
15 5/8
15'/8
30
24
22
20
18
16
30.000
24.000
22.000
20.000
18.000
16.000
22
22
22
22
22
22
22
21
22
24
30
+
[G+-J
Dimensions
Outlet
t
G
16Y2
2OY2
20
19'1S
19
..
20
20
20
20
20
20
I
--+-
,•
,
H
I
lG--GJ
Reducing Tee
..
20
20
20
20
....
.. ,.
....
20
20
20
20
20
20
20
E3
Concentric Reducer
..
24
24
24
.,
...
[I]
ell
'---'-'
,
....
Eccentric Reducer
365
at
FACE-TO-FACE DIMENSIONS OF FLANGED STEEL
GATE VALVES
(WEDGE AND DOUBLE DISC)
Pr.ssur., lit. per Sq. In.
Nominal
Sill,
Inch.s
150
1
-
1~
1~
2
.,
2~
300
-
-
9~
1~
2
2)12
.-
11~
11~
13
14
14
llY.
-,:t
4
5
6
8
10
12
1400
1600
1800
2000
2400
9
10
10)12
11~
13
14
15
16
17
18
20
16
18
19)12
I
23~
18
26~
19~
30
30
33
36
39
45
32~
35~
38~
41 )12
48)12
PrlSsur., Lb. per Sq. In.
Nominal
150
Inches
-
9~
13
llYa
12
15
15Ya
16)12
-
1~
9~
8
Siz',
1
8~
8~
~
8)12
9
7
7)12
3~
.,...
·S
8~
7)12
._~~_l 400
-
--
Dim.nsion A, Inches
1
5~
1~
1)12
6
7
2
7~
8
.,
1500
I
2500
Dimlmion A, Inches
I
10
11
12
14)12
10
11
12
14~
17~
16~
16~
20
15
18
22
24
29
33
38
40)12
44)12
12Y.
13~
15Ya
18~
22~
21 )12
26)12
31~
27~
36
26)12
32~
40~
39
44)12
49)12
54)12
50
56
60~
48
52
61
65~
76~
-
-
-
I
HOminal
Size,
Inches
8~
8~
1
9
9
1~
9~
9~
1)12
~~.~~~.
900- ...
_-1~_~=r2s00-
Dimension A, Inches
10
11
12
10
12Ve
11
13Ya
12
15~
14Y.
17Ya
-16Ys
20~
~---- 1 - - - ' _ 18Ys
23. 21 Y.
26Ya
26Y.
31%
36)12
28
2
14Y.
9Y.
llY.
11Y.
lOY.
2~
16Y.
13Y.
13Ve
._-1--'
3
11~
15Y.
14Y.
14Y.
4
12Y.
18Ve
16Y.
17Ve
22Y.
15Y.
5
18Y.
20Ya
16)12
19Y.
22Y. --~-- - -24Y.
--"40j~
29Y. - 33Y.
17Y.
8
23Y.
26Y.
.-'--33Y. -- 39Ye
50Ya
18Y.
26Y.
31---"-Ya _ 1 0 _ ------- - - - - -_ .... _45Y.
38Y.
56Ya
20Ye
30Y. I 33Y.
1~_ ---_
.. _- - 14
40Ya
50~
30Y.
32Y.
35Y.
f---- - - -.-..... 16
44Ya
5SYe
33Y.
3SY.
39Y.
----"- t-48)12
18
61Ye
36Y.
38Y. I--43Y.
-- - - - ----------- - . - - -=--
2~
8
3
8~
4
9~
Q,
>010)12
S
to11
6
CI'
c:
8
12
&i2
10
13~
14)12
12
14
IS~
16)12
16
18- - - 1----....
17~-t--39~1-41 ~ -- 47~
20
"8~
-20)12
24
4Sv.-T48Ya
55Y.
c:
'0
I
900
3
4
5
6
8
10
12
14
16
18
20
24
17
20
22
26
31
33
35
39
43
47
'55
600
Pr.ssur., Lb. per Sq. In.
Nominal
Sil.,
InchIS
9
-
3
CI
600
DimlllSion A, Inches
.....
w
400
--~.
_.
-
-~---
20
24
52)12
66Ye
61~
nY.
-
-
366
~m
I
FACE·TO·F ACE DIMENSIONS OF FLANGED STEEL
GLOBE AND ANGLE VALVES
J,-
~2XA...j
~
\
-t
.~
-A-
Raised Face
Class,lb
Nominal
SiZI,
InchlS
V,
~
1
lY.
,V,
2
2V,
3
3V,
4
5
6
8
300
150
400
600
Dimension 2 x A, Inchls
-
-
-
-
10V,
11 V,
12V,
13Y.
14
8
8V,
9V,
10V,
11 V,
14
16
19V,
-
-
v,
7V,
8V,
~
9V,
11 V,
13
14
7V,
8V,
9
9V,
11 V,
13
14
-
-
9
-
17
20
22
26
16
18
19V,
23V,
15~
17V,
22
Nominal
Sin,
InchlS
Lb.
Sq. In.
- -900 PrlsSun,15~
2500_
JIll'
Dimlnslon 2 x A, Inchls
1
lY.
,V,
2
2V,
3
4
5
6
8
10
12
14
9
10
11
12
14V,
16V,
15
18
22
24
29
33
38
40V,
9
10
11
12
14V,
16V,
18V,
21 V,
26V,
27~
32~
39
44V,
49V,
lOY.
10~
12Y.
13~
15Y.
17~
20
22~
26V,
31Y.
36
40Y.
50
56
-
Ring- Type Joint
Nominal
Siz.,
Inch.s
V,
PrISS,":'! Lb. per Sq. In.
f---
300
150
I
400
I
600
Dimension 2 x A, Inches
-
I
6K,
6K,c _ 6K,
7V,
7V,
7V,
8V,
8V,
1
8V,
-lY.
9
9
_._- - .9
,V,
9V,
9V,
9V,
7
2
8Yi
11Y.
11Y.
1lY.
- - - - - ->-2V,
9
12Y.
13Y.
13Y.
3
13Y.
14Y.
14Ya
4
12
104Y.
16Y.
17Y.
----5
14Yi"--- -16Y.
20Y.
- - - -c------ -1lBY.
16V,
6
lBY.
19Y.
22Y.
8
20
22Ya
23Y.
26Y.
10
25
25Y.
26Y.
31 Y.
12
2B
2BY.
30Y.
33Y.
14
31 Yi16
36V,
-
-~
-
~--
-
-
Nominal
Size,
Inches
Pr.ssure, lb. per Sq. In.
f---
900 __ 1.~_~-=-r=.2500
WL
Dimension 2 x A, Inches
-
V,
- - -~
- - - f - -9- . -
1
lY.
,V,
10
11
12
104Y.
16Y.
15Y.
lBY.
22Y.
204Y.
29Y.
33Y.
3ay.
40Ye
2
2V,
3
4
5
6
8
10
12
14
I
9
10
11
12
14Y.
16Y.
lBY.
21 Y.
26Ya
2B
33Y.
39Y.
o4SY.
SOY.
10%
__'2Y.
13Ye
15Y.
17Ye
20Y.
- -23
--26Ye--_ .. 31~
36V,
40Ye
50Ye
56Ye
-
367
m
I
-~-~-
FACE..TO-FACE DIMENSIONS OF FLANGED STEEL
SWING CHECK VALVES
00
•
~A~
Raised Face
Pressure, lit. per III- In.
Nominal
Siz.,
150
400
600
Dimltlsion A. Inches
Inches
2
2)4
300
Nominal
Sin,
Inches
8
8)4
10)4
11)4
11)4
)4
11)4
13
13
~
14
14
Pressure, lit. per Sq. In.
2500
1500
900
Dimension A, Inches
-
-
lOY.
9
9
10~
1
10
10
12Y.
1~
11
11
13~
1)4
12
14)4
12
14)4
lSY.
16)4
16)1
20
9)4
12)4
3Yt
10)4
13~
4
11)4
14
S
13
lS~
6
14
17)4
19}1
22
21
23Yt
26
lSVz
22~
26Vz
31
3
4
15
24Yt
lS
26)4
28
30
33
S
22
21Vz
26)1
6
24
27~
36
8
29
32~
40~
10
33
50
12
38
40)4
39
44)1
3
8
10
12
-
-
-
16
17
-
-
2
2)4
14
17~
31~
56
-
49Vz
Ring Type Joint
Pressure, Lb. per Sq. In.
Nominal
SiZt,
150
Inches
300
I
400
I
600
Dimension A, Inches
-
6U.
6U.
Vz
7Vz
7Y2
~
)4
4 13l.
~
1
SY.
5)4
1~
6
1Vz
9)1
7._- r--10-- f - - - -1--. - llY.
llY.
sVz
r-llY.
--
2 --2Vz
3
9
10
4
12
5
13Vz
6
9
9)4
NomiMI
Size,
Inches
1----
2500
-
-
lOY.
9
9
10~
8Vz
1
10
10
12Y.
9
--9)1
9
1~
11
11
13Va
1)1
12
12
lS~
14Y.
14Y.
17Va
16Y.
16Y.
20~
lSY.
lSY.
23
13Y.
13Y.
13Y.
- .- - - t -14Y.
14Y.
16Y.
14Y.
3
17Y.
--lay.
16Y.
20Y.
----- t--- '-- r - - - 19%
lSY.
22Y.
f-- --
14Vz
---=--S
20
23%
26Y.
- - - - - - 1 -21- Y.
- - -1---10
26Y.
25
25Y.
31 Y.
-- ._- I-- - - - 1------- t - - . - - 12
30Y.
33Y.
2S . - 28Y.
..--14
31)1
-~
-
1500
Dimension A, Inches
8Vz
2
2)1
12Y.
Press...e, lb. per Sq. In.
900
-
-
4
lSY.
21%
26Va
5
22Y.
26Y.
31~
6
24Y.
8
36Vz
- - - e-------=-- f - 28
40Va
29Y.
33Y.
f------
10
33Y.
39Y.
50Va
12
3SY.
4SY.
S6Va
14
40Va
SO~
-
Reference: Face-to-Face and End-to-End Dimensions of Ferrous Valves
American National Standard ANSI 816.10-1973
368
g
SCREWED COUPLINGS
Full Coupling
1. All dimensions are in inches.
2. Material forged carbon steel conforms to
the requirements of Specification SA-lOS.
3. Threads comply with ANSI Standard B2.11968.
111
I-A-J
Half Coupling
Half Coupling
Full Coupling
Nominal
Pipe
Size
6000lb
3000lb
6000lb
3000lb
Length Diameter Length DiameteI Length
B
A
A
A
B
Diameter Length
B
A
DiameteJ
B
1/8
1 1/4
3/4
1 1/4
7/8
5/8
3/4
5/8
7/8
1/4
1 3/8
3/4
1 3/8
1
11/16
3/4
11/16
I
3/8
1 1/2
7/8
1 1/2
1 1/4
3/4
7/8
3/4
I 1/4
1/2
1 7/8
I 1/8
1 7/8
1 1/2
15/16
1 1/8
15/16
I 1/2
3/4
2
I 3/8
2
1 3/4
1
1 3/8
1
1 3/4
1
2 3/8
1 3/4
2 3/8
2 1/4
13/16
1 3/4
13/16
2 1/4
1 1/4
2 5/8
2 1/4
2 5/8
2 1/2
1 5/16
2 1/4
1 5/16
2 1/2
1 1/2
3 1/8
2 1/2
3 1/8
3
1 9/16
2 1/2
19/16
3
2
33/8
3
33/8
3 5/8
1 11/H
3
I 11/16 3 5/8
2 1/2
3 5/8
3 5/8
3 5/8
4 1/4
1 13/16
3 5/8
1 13/16 4 1/4
3
4 1/4
4 1/4
4 1/4
5
2 1/8
4 1/4
2 1/8
5
3 1/2
4 1/2
43/4
4 1/2
53/4
2 1/4
43/4
2 1 /4
53/4
4
43/4
5 1/2
43&4
6 1/4
23/8
5 1/2
23/8
6 1/4
369
SYMBOLS FOR PII~E FITTINGS
American Standard: ANSI Z32.2.3
Flanged
Bushing
Screwed
Bell and
Spigot
-D-.
'E----i-
--3
Cap
Cross
Reducing
Straight Size
Crossover
Elbow
45- Degree
.~
~
Welded
..-
Soldered
$
~
~ ~ 'T.
I
.~
+ +*+ +
t
fJ\i
Y'E
(
t
(
t
90 - Degree
~
r rC r
Turned Down
G-t
G--+
G-E
~
G-&
Turned Up
&t
@--+-
~
&*
e-e-
C*
~
Base
Double Branch
L. ~ '4
+-r T
Long Radius
F'
~
Reducing
~
~
Side Outlet
(Outlet Down)
Side Outlet
(Outlet Up)
~
r
r
~
~ ~
1
370
SYMBOLS FOR PIPE FITTINGS
Flanged
Screwed
Bell and
Spigot
Welded
le
Street
Soldered
Joint
Connecting
Pipe
Expansion
-+-
~
-€-
"*-
-e-
t::::::=I-
-E:3-
-:£:::f
-a::::JE7
Lateral
r y r
~
Orifice Plate
-1:1-
Reducing Flange
-iD--
Plugs
Bull Plug
-to
Pipe Plug
t
C>
----t<:J
(
-IC>t- -
--t:>+-
~
~
~
-i~
~
~
~
€t::::.e-
-+-+-
-++-
-3---E-
*--*-
-e----&
Tee
Straight Size
~
~
~
't'
xL
~
(Outlet Up)
t-0-iI-
+-0-+
7--0--t-
*07(
-e0-e-
(Outlet Down)
+-e-t
+-e-t
~
~
-e-e-e-
Double Sweep
~
~
Reducer
Concentric
Eccentric
Sleeve
Reducing
rL L
~ ~ ~
371
SYMBOLS FOR PIPE FITTINGS
Flanged
Screwed
Single Sweep
*T t
Side Outlet
(Outlet Down)
....L
Side Outlet
(Outlet Up)
Union
Valves
Angle Valve
Check, also
Angle Check
Bell and
Spigot
~
~
~ ~
~
-+t--
Welded
~
--4-
? ? ?
Soldered
-eje-
? ?
Gate, also
Angle Gate
(Elevation)
Ball Valve
Gate, also
Angle Gate
(Plan)
~
r-
iC«Jr
-te::J-
G::l-
(3:::J-
Globe, also
Angle Globe
(Elevation)
l?- lr-
F
~
Globe
(Plan)
@:]-
~
(3:::J3-
Automatic Valve
By-Pass
GovernorOperated
Reducing
(*
~
(3::::)(-
00-
~
-t-11
Check Valve
(Straight Way)
-I'J-
~
~
~
~
Cock
-II{11-
~Q~
--3QE-
~Q~
-BQe-
372
-
SYMBOLS FOR PIPE FITTINGS
Diaphragm Valve
Flanged
Screwed
~
-Jr
,.-,
Float Valve
Gate Valve
Motor-Operated
Globe Valve
Motor-Operated
Hose Valve,
also Hose Globe
Angle, also
Hose Angle
Gate
Globe
Lockshield Valve
I Cl
Bell and
Spigot
:-21
-t*J-
-ckl-
-[><J-
-(><J-
-*-
~
--IXr
-{XJ-
~
~
~
~
-[>¢J
--t>¢J
-I>¢J
--(>::l::l
Welded
Soldered
r-ll~
~
r-~
~
~
~
-E{><Je-
-J!~
~
-€t,)r"'...&
~
k
--tt.- -Jr-
Plu, Valve
~
-c-:J-
.~~
Quick Opening
or Butterfly Valve
~
~
~
~
~
~
~
-€1*9-
Safety Valve
~
374
WEIGHTS
1.
The tables on the following pages show the weights of
different vessel components made of steel.
2.
All weights are calculated with the theoretical weight of
steel: 1 cubic inch = 0.28333 pounds.
3.
To obtain the actual weight of a vessel, add 6% to the total
weight. This will cover the overweights of material which
comes from the manufacturing tolerances and the weight of
the weldings.
4.
The weights of shells shown in the tables refer to one lineal
foot of shell-length. The weights tabulated in columns
headed by "I.S." and "O.S." are the weights of shell when
the given diameter signifies inside or outside diameter.
5.
The weights of the heads include:
A. For ellipsodial heads: 2 inch straight flange or the wall
thickness, whichever is greater.
B. For ASME flanged and dished heads: lY2 inch straight
flange.
C. For hemispherical heads: 0 inch straight flange.
6.
The weights of pipe fittings made by different manufacturers
show in many cases considerable deviations, which reflect
manufacturing differences. The weights of pipe fittings
shown in these tables refer to the products of Ladish
Company.
7.
All dimensions in inches.
All weights in pounds.
375
WEIGHT OF SHELLS & HEADS
WALL THICKNESS
1/4"
DIAM.
VESSEL
5/16"
HEAD
SHELL
SHELL
ELLIP F.&D. HEMIS
I.S.
O.S.
20
28
36
46
56
41
48
54
61
68
39
46
52
59
66
28
35
41
51
58
19
24
29
35
43
26
35
46
58
71
41
47
55
62
70
68
81
95
110
126
74
81
88
94
101
72
79
86
92
99
69
78
87
100
114
51
58
69
85
101
119
138
158
100
113
128
139
156
80
89
98
110
120
143
161
180
201
222
108
114
121
128
134
106
112
119
126
133
129
144
160
177
195
123
138
150
179
202
226
256
279
11 1
127
143
159
175
165
215
270
330
398
131
168
210
257
309
245
320
404
498
602
141
161
182
202
222
139
159
179
199
219
214
285
351
434
520
163
210
263
322
386
307
400
506
624
755
96
193
209
225
241
257
191
207
223
239
255
453
543
624
723
820
365
421
492
556
637
717
840
974
1118
1272
243
263
283
303
324
239
259
279
299
319
598
695
806
925
1050
456
532
614
702
796
897
1052
1220
1399
1592
102
108
114
120
126
273
289
305
321
337
271
287
303
319
335
922
1031
1150
1255
1445
710
801
883
984
1075
1435
1608
1792
1985
2188
344
364
385
405
425
339
359
379
399
419
1180
1320
1468
1622
1820
896
1001
1104
1230
1344
1796
2013
2242
2484
2738
132
138
144
353
369
385
351
367
383
1590
1730
1880
1186
1286
1406
2401
2624
2856
446
466
486
439
459
480
1990
2160
2350
1482
1607
1758
3004
3282
3573
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
84
90
ELLIP F.&D. HEMIS
HEAD
I.S.
O.S.
33
38
44
49
54
31
36
42
49
52
22
28
33
41
47
14
19
23
28
35
60
65
70
76
81
58
63
68
74
79
55
62
70
78
89
86
92
97
102
108
84
90
95
100
106
113
129
145
161
177
78
87
100
III
376
WEIGHT OF SHELLS & HEADS
WALL THICKNESS
3/8"
DIAM.
VESSEL
SHELL
I.S.
12
O.S.
50
58
66
74
82
47
55
63
71
79
90
98
106
114
122
87
95
103
7/16"
HEAD
SHELL
ELUP F.&D. HEMIS
HEAD
ELUP F.&D. HEMIS
I.S.
O.S.
58
67
77
86
95
54
63
73
82
91
41
49
61
71
85
26
33
41
52
61
37
50
65
82
100
33
22
42
50
61
70
28
35
42
52
32
43
55
70
85
119
82
94
105
121
137
61
70
82
94
105
103
122
143
166
190
105
114
123
133
142
101
110
119
129
138
97
109
122
141
160
71
82
97
109
122
121
143
168
194
223
130
138
146
154
162
127
135
143
151
159
154
173
192
213
234
121
134
147
165
180
216
243
272
303
336
151
161
170
179
189
148
157
166
176
185
180
191
224
248
273
141
156
172
192
210
253
285
319
355
393
170
194
218
242
266
167
191
215
239
263
257
331
415
508
610
196
252
316
386
463
370
482
609
751
907
198
226
254
282
310
194
222
250
278
306
300
386
484
592
711
229
295
368
450
540
433
564
712
877
1060
96
290
314
338
362
386
287
311
335
359
383
718
836
965
1110
1260
547
638
737
842
955
1079
1265
1466
1682
1912
338
366
394
422
450
334
362
391
419
447
842
983
1136
1298
1473
639
745
860
983
1115
1260
1478
1713
1965
2234
102
108
114
120
126
410
434
458
482
506
407
431
455
479
503
1419
1582
1760
1950
2170
1075
1202
1335
1476
1624
2158
2418
2694
2984
3288
478
506
534
562
591
475
503
531
559
587
1658
1854
2061
2249
2530
1254
1402
1558
1722
1894
2521
2825
3146
3484
3840
132
138
144
530
554
579
527
551
576
2490
2595
2820
1779
1928
2110
3608
3942
4292
619
647
675
615
643
671
2790
3025
3300
2075
2264
2461
4213
4604
5011
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
84
90
III
377
WEIGHT OF SHELLS & HEADS
WALL THICKNESS
VESSEL
9/16"
1/2"
DIAM.
HEAD
SHELL
HEAD
SHELL
ELLIP F.&D. HEMIS
ELLIP F.&D. HEMIS
I.S.
O.S.
47
56
70
81
97
30
38
47
59
70
43
58
75
94
115
76
88
100
112
124
69
81
93
105
117
52
63
78
91
109
35
44
54
67
78
49
65
85
106
131
114
125
136
146
157
110
125
140
161
182
81
94
110
125
140
139
165
193
223
255
136
148
160
172
184
129
141
153
165
177
124
143
162
181
205
91
107
124
140
157
157
186
218
252
288
174
184
195
206
217
168
178
189
200
211
206
230
256
283
313
161
178
196
220
240
290
327
366
407
450
196
208
220
232
244
189
201
213
225
237
231
259
288
319
352
181
200
220
247
270
327
369
413
459
508
227
259
291
323
355
221
253
285
317
349
343
442
553
677
813
261
337
421
514
617
496
646
815
1005
1214
256
292
328
364
400
249
285
321
357
393
386
497
622
762
915
294
379
473
578
694
560
728
919
1133
1368
96
387
419
451
483
515
381
413
445
477
509
962
1124
1298
1484
1683
730
852
983
1124
1274
1443
1692
1960
2248
2557
436
472
508
544
580
429
465
501
537
573
821
1083
1264 958
1460 1106
1669 1264
1894 1433
1626
1906
2209
2533
2880
102
108
114
120
126
547
579
611
647
676
541
573
605
638
670
1894
2119
2355
2571
2890
1433 2884
1602 3232
1780 3599
1968 3986
2165 4393
617
653
689
725
761
610
646
682
718
754
2131 1612
2384 1802
2650 2002
2892 2214
3234 2435
3249
3640
4054
4489
4947
132
138
144
708
740
777
702
734
766
3340
3460
3760
2372
2588
2813
797
833
869
790
826
862
3660 2668
3897 2911
4240 3165
5427
5930
6454
12
14
I.S.
O.S.
67
88
99
110
61
72
82
93
104
120
131
142
152
163
78
16
18
20
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
84
90
4820
5266
5732
378
WEIGHT OF SHELLS & HEADS
WALL THICKNESS
5/8"
DIAM.
VESSEL
SHELL
1.5.
12
O.S.
11/16"
HEAD
SHELL
ELUP F.&D. HEMIS
I.S.
0.5.
HEAD
ELUP F.&D. HEMIS
16
III
20
124
137
76
89
103
116
129
151
164
177
191
204
143
156
169
183
196
138
161
180
201
228
101
121
138
156
175
176
208
243
281
322
166
181
196
211
225
156
171
186
201
215
154
177
198
221
251
113
133
151
171
195
194
230
269
311
355
218
231
244
258
271
210
223
236
250
263
257
288
326
355
391
201
223
245
275
300
365
411
460
512
566
240
255
269
284
299
230
245
259
274
289
283
317
353
390
430
221
245
270
302
330
403
454
508
565
625
284
324
364
404
444
276
316
356
396
436
428
552
691
846
1017
327
421
526
643
772
623
811
1024
1261
1523
313
357
401
445
489
303
347
391
435
479
471
607
760
931
1118
360
458
579
707
849
688
895
1129
1390
1677
96
484
524
564
604
644
476
516
556
596
636
1203
1405
1622
1855
2104
912
1065
1229
1405
1592
1810
2121
2458
2818
3204
533
577
621
665
710
523
567
611
655
700
1323
1545
1784
2D41
2315
1003
1171
1352
1545
1751
1994
2337
2707
3104
3529
102
108
114
120
126
685
725
765
805
848
677
717
757
797
837
2368 1791
2648 2003
2944 2225
3213 2460
3578 2706
3614
4049
4509
4993
5502
754
798
842
886
930
744
788
832
876
920
2605
2913
3239
3535
3910
1970
2203
2448
2706
2977
3980
4459
4965
5498
6058
132
138
144
885
925
965
877
917
957
3980 2965
4325 3234
4720 3516
6036
6595
7178
974
1018
1062
964
1008
1052
4317
4703
5185
3261
3557
3868
6646
7261
7902
14
18
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
84
90
84
97
58
70
87
101
121
40
50
61
74
86
55
73
95
119
146
93
108
122
137
152
83
98
112
127
142
64
79
95
113
133
44
55
67
83
97
61
81
105
132
162
379
WEIGHT OF SHELLS & HEADS
WALL THICKNESS
VESSEL
13/16"
3/4"
DIAM.
HEAD
SHELL
I.S.
O.S.
SHELL
ELLIP F.&D. HEMIS
I.S.
O.S.
HEAD
ELLIP F.&D. HEMIS
102
118
134
150
166
90
106
122
138
154
70
88
104
126
145
48
60
74
92
108
67
90
116
145
177
1 11
128
146
163
180
97
114
132
149
166
76
95
113
136
157
53
67
82
100
117
73
98
126
158
193
182
198
214
230
246
170
186
202
218
234
171
193
216
241
274
126
145
165
187
216
213
252
295
340
389
198
215
233
250
267
184
201
219
236
253
185
209
234
261
304
137
160
182
412
234
232
275
321
370
423
262
278
294
310
326
250
266
282
298
314
309
345
393
425
469
241
267
294
330
361
442
497
556
618
684
285
302
319
337
354
271
288
305
323
340
335
378
425
470
508
261
289
323
357
391
480
541
605
672
743
342
390
438
486
534
330
378
426
474
522
514
662
829
1015
1220
393
505
631
772
926
753.
979
1234
1520
1835
371
423
475
527
579
357
409
461
513
565
567
729
911
1107
1337
425
547
683
836
1003
818
1063
1340
1650
1991
96
582
630
678
726
775
570
618
666
714
763
1443
1685
1947
2226
2525
1095
1277
1475
1685
1911
2179
2554
2958
3391
3855
631
683
735
788
840
617
669
721
774
826
1564
1835
2120
2433
2757
1186
1384
1597
1825
2070
2365
2771
3209
3679
4181
102
108
114
120
126
823
871
919
967
1015
811
859
907
955
1003
2842
3178
3533
3856
4243
2150
2403
2671
2952
3248
4348
4870
5422
6004
6616
892
944
996
1048
1100
878
930
982
1034
1086
3103
3457
3854
4204
4614
2329
2603
2893
3198
3518
4716
5282
5881
6511
7174
132
138
144
1063
1111
1159
1051
1099
1147
4655
5082
5650
3558
3881
4219
7257
7928
8628
1152
1204
1256
1138
1190
1242
5059
5522
6067
3854
4205
4571
7869
8596
9356
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
84
90
380
WEIGHT OF SHELLS & HEADS
WALL THICKNESS
VESSEL
12
16
18
20
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
84
90
96
HEAD
SHELL
I.S.
14
1 5/16"
7/8"
DIAM.
O.S.
HEAD
SHELL
ELLIP F.&D. HEMIS
I.S.
O.S.
ELLIP F.&D. HEMIS
120
139
157
176
195
104
123
141
160
179
82
103
122
147
170
59
74
90
107
127
80
106
137
171
209
130
150
170
190
210
III
131
151
171
191
90
110
135
157
185
67
83
101
123
144
86
115
148
1-85
226
213
232
251
270
288
197
216
235
254
272
199
225
252
288
327
147
175
199
225
252
251
297
347
401
458
230
250
270
290
310
211
231
251
271
291
213
241
271
310
351
167
194
220
249
282
271
320
374
431
493
307
326
344
363
382
291
310
328
347
366
366
412
458
506
558
281
312
352
385
421
519
584
653
726
803
330
350
370
390
410
311
331
351
371
391
393
442
491
543
597
314
347
387
422
462
558
628
702
780
863
400
456
512
568
624
384
440
496
552
608
611
789
982
1200
1440
458
589
736
900
1080
883
1148
1447
1780
2149
430
491
551
611
671
411
471
531
591
651
654
836
1051
1285
1543
507
643
802
979
1174
949
1233
1554
1911
2306
680
736
792
849
905
664
720
776
833
889
1702
1986
2293
2620
2970
1278
1491
1720
1966
2229
2551
2989
3461
3968
4509
731
791
851
911
971
711
771
832
892
952
1823
2128
2456
2807
3182
1387
1616
1864
2129
2412
2738
3207
3714
4257
4837
5085
5695
6340
7019
7734
1031
1091
1151
1212
1272
1012
1072
1132
1192
1252
3580
4002
4447
4852
5341
2712
3036
3366
3720
4091
5454
6109
6800
7529
8294
4150 8482
4528 9266
4923 10084
1332
1392
1452
1312
1372
1432
5853
6389
6948
4480 9097
4886 9937
5310 10813
102
108
114
120
126
945
961
1017 1001
1073 1057
1129 1113
1185 1169
3341 2508
3735 2804
4150 3115
4528 3444
4985 3789
132
138
144
1241
1297
1353
5463
5963
6485
1225
1281
1337
381
WEIGHT OF SHELLS & HEADS
WALL THICKNESS
1"
DIAM.
VESSEL
12
HEAD
SHELL
I.S.
O.S.
1-1/16"
HEAD
SHELL
ELLIP F.&D. HEMIS
I.S.
O.S.
ELLIP F.&D. HEMIS
139
160
182
203
224
117
138
160
181
202
98
118
144
168
200
76
93
113
139
162
93
124
159
198
242
148
171
193
216
239
124
147
169
192
215
104
125
153
178
212
83
102
122
150
175
100
132
170
212
259
246
267
289
310
331
223
245
266
287
308
228
257
288
330
374
187
214
242
273
313
290
343
400
462
528
262
284
307
330
352
238
260
283
306
328
242
277
31 1
350
397
202
231
261
294
338
310
366
427
493
563
353
374
396
417
438
330
351
372
393
415
421
471
523
579
637
347
383
421
460
502
598
673
752
835
923
375
398
420
443
466
351
374
396
419
442
448
500
562
614
677
373
412
452
495
539
638
801
890
984
459
523
587
651
715
436
500
564
628
692
698
897
1121
1371
1646
556
698
869
1059
1268
1015
1318
1661
2043
2465
489
557
625
693
761
465
533
601
669
737
741
953
1191
1457
1749
597
749
931
1134
1357
1082
1404
1769
2175
2624
96
779
844
908
972
1036
756
821
885
949
1013
1945
2270
2620
2994
3394
1496
1741
2008
2292
2596
2926
3427
3967
4547
5166
829
805
897
874
965
942
1033 1010
110 1 1078
2067
2412
2783
3181
3606
1590
1851
2134
2435
2758
3114
3647
4221
4838
5496
102
108
114
120
126
1100
1164
1228
1292
1356
1077
1141
1205
1269
1333
3819
4268
4743
5175
5697
2917
3258
3617
3996
4393
5825
6523
7261
8039
8856
1169
1237
1306
1374
1442
1146
1214
1282
1350
1418
4057 3099
4535 "3462
5038 3843
5498 4246
6053 4667
6197
6939
7724
8550
9419
132
138
144
1420
1484
1549
1397
1461
1526
6243
6815
7411
4809 9712
5243 10609
5697 11544
1510
1578
1646
1486
1554
1623
6633
7241
7874
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
84
90
7~7
5108 10329
5571 11282
6053 12276
382
WEIGHT OF SHELLS & HEADS
WALL THICKNESS
1-1/8"
DIAM.
VESSEL
12
HEAD
SHELL
I.S.
O.S.
1-3/16"
SHELL
ELLIP F.&D. HEMIS
LS.
O.S.
HEAD
ELLIP F.&D. HEMIS
158
182
206
230
254
131
155
179
203
227
110
133
163
189
225
90
110
132
162
189
106
141
181
226
276
167
192
218
243
268
137
162
188
213
238
116
143
172
203
237
97
120
143
171
200
113
150
193
240
293
278
302
326
350
374
251
275
299
323
347
256
298
333
371
421
217
248
281
315
362
330
390
454
524
598
294
319
345
370
395
264
289
315
340
365
279
318
352
391
444
230
266
301
337
382
351
414
482
555
634
398
422
446
470
494
371
395
419
443
467
474
530
601
651
717
400
442
484
530
576
678
762
851
946
1045
421
466
471
497
522
391
416
441
467
492
500
560
634
687
756
423
466
517
565
615
718
807
902
1001
1106
518
591
663
735
807
491
563
635
707
779
785
1009
1261
1543
1852
639
800
994
1209
1446
1149
1491
1877
2308
2783
548
624
700
776
852
518
594
670
746
822
828
1065
1331
1628
1954
674
852
1049
1276
1526
1216
1577
1986
2441
2943
96
879
951
1023
1095
1167
852
924
996
1068
1140
2189
2554
2947
3368
3818
1684
1960
2260
2579
2920
3303
3867
4476
5129
5827
929
1005
1081
1157
1233
899
975
1051
1127
1203
2310
2695
3108
3555
4030
1788
2082
2398
2736
3097
3492
4089
4732
5422
6159
102
108
114
120
126
1239
1312
1384
1456
1528
1212
1284
1356
1428
1500
4296
4802
5336
5822
6409
3282
3666
4070
4496
4942
6569
7356
8187
9062
9982
1309
1385
1461
1537
1613
1279
1355
1431
1507
1583
4535
5069
5632
6145
6765
3480 6942
7772 7773
4314 8651
4764 9576
5236 10547
132
138
144
1600
1672
1744
1573
1645
1717
7024
7667
8338
5410 10947
5899 11956
6408 13010
1690
1766
1842
1660
1736
1812
7414
8093
8801
5731 11566
6248 12632
6786 13744
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
-S4
90
383
WEIGHT OF SHELLS & HEADS
WALL THICKNESS
VESSEL
1-5/16"
1-1/4"
DIAM.
LS.
O.S.
SHELL
HEAD
SHELL
ELUP F.&D. HEMIS
LS.
O.S.
HEAD
ELUP F.&D. HEMIS
177
204
230
257
284
144
171
197
224
251
122
154
181
217
250
105
129
154
181
210
120
160
204
254
310
187
215
243
271
299
150
178
206
234
262
129
161
193
228
267
112
138
165
193
225
127
169
216
269
327
311
337
364
391
417
278
304
331
358
384
292
331
371
412
467
242
284
322
360
402
371
438
510
587
670
327
355
383
411
439
290
318
346
374
402
307
347
390
439
497
258
303
343
384
428
392
462
538
619
707
444
471
497
524
551
411
438
464
491
518
526
589
667
724
796
446
490
551
601
654
759
853
952
1057
1168
467
495
523
552
580
430
486
515
543
559
625
700
768
844
474
521
585
638
694
800
899
1003
1113
1230
578
658
738
818
898
545
625
705
785
865
872
1121
1401
1714
2057
710
904
1104
1343
1606
1284
1665
2095
2575
3104
608
692
776
860
944
571
655
739
823
907
924
1187
1482
1812
2173
753
958
1169
1421
3374
1352
1752
2205
2709
3265
96
979
1059
1139
1219
1299
945
1025
1105
1185
1265
2432 1893
2837 2204
3275 2537
3742 2894
4242 3274
3683
4311
4988
5715
6491
1029
1113
1197
1281
1365
991
1075
1159
1243
1328
2567
2994
3455
3947
4473
1988
2314
2664
3039
3438
3873
4533
5245
6009
6824
102
108
114
120
126
1379
1459
1539
1619
1700
1346
1426
1506
1586
1666
4774 3678
5336 4106
5929 4558
6469 5032
7121 5530
7317
8192
9116
10090
11113
1449
1533
1617
1701
1786
1418
1496
1580
1664
1748
5032
5623
6248
6815
7501
3862 7692
4311
8611
4786 9582
5283 10606
5807 11681
132
138
144
1780
1860
1940
1746
1826
1906
7804 6051
8519 6596
9264 7165
12186
13308
14480
1870
1954
2038
1832
1916
2000
8220
8971
9755
6354 12808
6926 13986
7524 15217
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
84
90
45~
384
WEIGHT OF SHELLS & HEADS
WALL THICKNESS
1-3/8"
DIAM.
VESSEL
SHELL
I.S.
O.S.
1-7/16"
HEAD
SHELL
ELUP F.&D. HEMIS
I.S.
O.S.
HEAD
ELLIP F.&D. HEMIS
196
225
255
284
313
156
185
215
244
273
142
169
206
239
285
119
148
176
206
239
135
178
228
283
345
206
237
267
298
329
162
193
223
254
285
151
180
220
255
303
126
155
184
220
253
143
188
240
298
363
343
372
402
431
460
303
332
362
391
421
322
364
408
466
527
275
323
364
408
454
412
486
566
651
743
360
390
421
452
482
316
346
377
408
438
342
386
432
493
558
292
337
380
426
481
434
511
594
684
780
490
519
548
578
607
450
479
508
538
567
593
662
734
812
892
502
553
620
676
734
841
945
1054
1170
1293
513
544
575
605
636
469
500
531
561
592
627
699
775
857
941
532
585
648
707
768
882
991
1106
1228
1355
637
725
813
901
989
597
685
773
861
949
977
1253
1563
1910
2289
796
1012
1234
1500
1768
1420
1841
2315
2844
3427
667
759
851
943
1035
623
715
807
899
991
1030
1320
1646
2061
2407
840
1057
1301
1568
1861
1489
1929
2426
2979
3590
96
1078
1166
1254
1342
1430
1038
1126
1214
1302
1390
2703
3152
3635
4152
4704
2083
2424
2791
3184
3602
4065
4757
5503
6303
7159
1128
1220
1312
1404
1496
1083
1175
1267
1360
1452
2841
3312
3819
4360
4938
2177
2534
2917
3328
3766
4257
4981
5761
6599
7493
102
108
114
120
126
1518
1606
1694
1783
1871
1478
1566
1654
1743
1831
5291
5911
6567
7162
7882
4046 8068
4517 9032
5014 10050
5535 11122
6084 12249
1588
1680
1772
1865
1957
1544
1636
1728
1820
1912
5553
6203
6890
7513
8267
4230 8445
4722 9453
5241 10518
5786 11640
6360 12818
132
138
144
1959 1919 8636 6656 13430
2047 2007 9424 7256 14666
2135 2095 10246 7882 15955
2049
2141
2233
2004 9113
2097 9881
2189 10742
6959 14054
7586 15346
8240 16695
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
84
90
385
WEIGHT OF SHELLS & HEADS
WALL THICKNESS
1-1/2"
DIAM.
VESSEL
12
HEAD
SHELL
I.S.
O.S.
1-9/16"
SHELL
ELLIP F.&D. HEMIS
I.S.
O.S.
HEAD
ELLIP F.&D. HEMIS
216
248
280
312
344
168
200
232
264
296
162
192
234
271
321
134
162
192
234
271
150
198
252
313
381
227
260
294
327
361
174
207
241
274
308
173
204
248
287
340
144
174
206
249
287
158
208
265
328
399
376
408
440
472
504
328
360
392
424
456
363
409
457
521
589
310
352
397
444
508
455
536
623
717
817
394
427
461
494
527
341
374
408
441
474
384
432
483
550
621
329
745
415
470
536
476
561
652
750
855
536
568
600
633
665
488
520
552
585
617
661
738
817
903
991
562
618
676
738
802
924
1038
1158
1285
1418
561
594
628
661
694
508
541
575
608
641
696
777
860
950
1042
592
652
712
777
844
966
1085
1210
1343
1482
697
793
889
985
1082
649
745
841
937
1034
1084
1388
1729
2111
2526
885
1103
1368
1636
1954
1558
2018
2537
3115
3753
728
828
928
1028
1129
675
775
875
975
1075
1140
1457
1815
2212
2647
931
1110
1436
1716
2049
1628
2107
2649
3251
3916
96
1178
1274
1370
1466
1562
1130
1226
1322
1418
1514
2980
3472
4003
4569
5173
2272
2644
3044
3472
3930
4449
5205
6021
6895
7829
1229
1329
1420
1529
1629
1175
1275
1376
1476
1576
3122
3635
4189
4781
5411
2382
2770
3171
3617
4093
4643
5431
6281
7192
8166
102
108
114
120
126
1658
1754
1851
1947
2043
1610
1706
1803
1899
1995
5815
6496
7213
7864
8652
4414 8823
4928 9875
5468 10987
6038 12158
6636 13389
1729
1829
1930
2030
2130
1676
1776
1876
1976
2076
6081
6792
7540
8219
9041
4598
5133
5696
6290
6913
9201
10298
11457
12678
13960
132
138
144
2139
2235
2331
2091 9590
2187 10339
2283 11239
7262 14678
7916 16027
8599 17436
2230
2330
2430
2176 10020
2276 10738
2376 11741
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
84
90
7564 15304
8246 16710
8957 18188
386
WEIGHT OF SHELLS & HEADS
WALL THICKNESS
VESSEL
12
16
18
20
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
84
90
96
HEAD
SHELL
I.S.
14
1-11/16"
1-5/8"
DIAM.
O.S.
HEAD
SHELL
ELLIP F.&D. HEMIS
I.S.
O.S.
ELLIP F.&D. HEMIS
236
271
305
340
375
180
215
249
284
319
184
217
263
304
359
153
186
220
265
304
166
218
277
344
417
247
283
319
355
391
186
222
258
294
330
195
230
277
321
379
163
198
235
280
315
174
228
290
359
436
410
444
479
514
548
354
388
423
458
492
405
455
509
578
653
348
393
443
495
564
498
586
681
783
892
427
463
499
535
571
366
402
438
474
570
427
480
535
608
686
361
415
466
521
585
520
611
710
817
930
583
618
653
687
722
527
562
597
631
666
732
815
903
997
1094
623
685
748
817
886
1009
1132
1263
1401
1546
608
644
680
716
752
547
583
619
655
691
770
856
948
1045
1147
647
711
785
857
930
1051
1180
1316
1459
1610
757
861
965
1069
1174
701
805
909
1013
1117
1195
1527
1900
2314
2768
978
1216
1505
1797
2144
1698
2197
2761
3388
4080
788
896
1004
1112
1221
727
835
943
1051
1159
1253 1015
1598 1275
1987 1562
2418 1880
2891 2226
1768
2288
2873
3526
4245
1278
1382
1486
1590
1694
1221
1325
1430
1534
1638
3264 2492
3799 2897
4375 3298
4994 3762
5650 4257
4836
5657
6542
7490
8504
1329
1437
1545
1653
1761
1267
1376
1484
1592
1700
3408 2603
3965 3008
4565 3443
5207 3926
5892 4441
5031
5884
6803
7789
8842
6348 4782 9581
7088 5338 10723
7867 5924 11928
8575 6541 13198
9431 7190 14533
1869
1978
2086
2194
2302
1808
1916
2024
2133
2241
6618
7388
8198
8935
9825
4966
5567
6177
6819
7493
9961
11148
12401
13720
15107
2263 10450 7867 15931
2367 11138 8576 17394
2471 12243 9316 18921
2410
2518
2626
2349 10851 8198 16560
2457 11669 8936 18079
2565 12749 9705 19666
102
108
114
120
126
1798 1742
1903 1846
2007 1950
2111 2054
2215 2159
132
138
144
2319
2423
2527
387
WEIGHT OF SHELLS & HEADS
WALL THICKNESS
1-3/4"
DIAM.
VESSEL
SHELL
I.S.
O.S.
1-13/16"
HEAD
SHELL
ELLIP F.&D. HEMIS
I.S.
O.S.
HEAD
ELLIP F.&D. HEMIS
257
294
332
369
407
192
229
267
304
342
206
243
294
338
399
172
211
249
296
327
182
238
303
375
455
267
306
344
383
422
197
236
274
313
352
218
257
314
356
420
182
223
264
311
345
190
249
316
391
473
444
481
519
556
593
379
416
454
491
528
450
504
562
639
719
374
437
490
547
607
542
637
740
850
969
461
499
538
577
615
391
429
468
507
545
473
530
590
670
754
394
460
515
575
638
564
663
770
885
1007
631
668
706
743
780
566
603
641
678
715
807
898
993
1094
1200
671
737
823
897
973
1094
1228
1369
1518
1675
654
693
732
770
809
584
623
662
700
739
845
940
1040
1144
1254
704
772
862
939
1018
1138
1276
1423
1577
1740
818
930
1042
1154
1267
753
865
977
1089
1201
1311
1670
2074
2523
3015
1053
1332
1620
1963
2308
1839
2378'
2986
3664
4410
848
964
1080
1196
1313
778
894
1010
1126
1243
1370
1743
2163
2630
3141
1101
1392
1691
2047
2407
1910
2469
3100
3802
4576
1379
1491
1603
1715
1827
1313
1426
1538
1650
1762
3552 2715
4132 3119
4756 3588
5421 4091
6134 4626
5226
6111
7065
8089
9181
1429
1545
1661
1777
1893
1359
1475
1591
1707
1823
3700
4301
4948
5639
6379
2829
3299
3737
4237
4792
5422
6339
7328
8389
9521
102
108
114
120
126
1940 1874 6888 5150 10343
2052 1986 7688 5796 11574
2164 2099 8529 6430 12874
2276 2211 9295 7098 14243
2388 2323 10220 7797 15681
2010
2126
2242
2358
2474
1940 7162
2056 7991
2172 8865
2288 9659
2404 10618
5334
6003
6660
7351
8076
10725
12001
13348
14767
16257
132
138
144
2500 2435 11252 8530 17189
2612 2547 12201 9296 18766
2725 2659 13256 10094 20412
2590
2707
2823
2520 11650 8535 17820
2637 12673 96~8 19453
2753 13768 10455 21159
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
84
90
96
388
WEIGHT OF SHELLS & HEADS
WALL THICKNESS
1-7/8"
DIAM.
VESSEL
HEAD
SHELL
I.S.
O.S.
1-15/16"
SHELL
ELLIP F.&D. HEMIS
208
249
291
332
374
243
285
343
394
462
201
247
293
342
382
206
270
342
423
512
414
482
540
602
668
587
689
800
929
1046
495
536
578
619
661
415
456
498
539
581
521
583
648
737
825
435
498
558
622
699
610
716
830
953
1085
883
981
1086
1194
1309
736
808
902
981
1063
1181
1325
1477
1637
1805
702
743
785
826
867
622
663
705
746
787
923
1025
1134
1246
1365
770
845
932
1014
1099
1225
1374
1531
1697
1871
804
924
1044
1164
1284
1429
1817
2253
2737
3268
1150 1981
1452 - 2561
1762 3214
2132 3941
2506 4743
909
1033
1157
1282
1406
829
953
1077
1202
1326
1489
1892
2344
2846
3397
1200
1501
1835
2203
2607
2054
2653
3329
4081
4910
96
1480
1600
1720
1840
1960
1405
1525
1645
1765
1885
3846
4470
5141
5858
6624
2944
3380
3886
4383
4958
5618
6568
7592
8690
9862
1530
1654
1778
1902
2027
1450
1574
1698
1822
1947
3995
4642
5357
6080
6873
3040 5816
3512 6798
4015 7857
4552 8992
5123 10204
102
108
114
120
126
2081
2201
2321
2441
2561
2005 7436
2126 8295
2246 9201
2366 10024
2486 11017
5518
6210
6890
7604
8355
11108
12429
13823
15292
16834
2151
2275
2399
2523
2647
2071 7714
2195 8603
2319 9540
2443 10358
2567 11420
132
138
144
2681
2802
2922
2606 12058 9140 18451
2726 13146 9960 20142
2846 14280 10816 21907
2772
2896
3020
2692 12460 9444 19084
2816 13623 10291 20832
2940 14756 11176 22657
16
20
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
84
90
231
271
326
375
441
191
235
278
327
363
478
518
558
598
638
403
443
483
523
563
497
556
619
701
789
679
719
759
799
839
604
644
684
724
764
879
999
1119
1239
1360
ELLIP F.&D. HEMIS
288
329
371
412
454
18
203
243
283
323
363
O.S.
198
259
329
407
493
12
14
278
318
358
398
438
I.S.
HEAD
--
5722
6417
7120
7858
8633
11492
12858
14299
15818
17413
389
WEIGHT OF SHELLS & HEADS
WALL THICKNESS
VESSEL
2 1/4"
2"
• DIAM.
SHELL
I.S.
O.S.
HEAD
SHELL
ELLIP F.&D. HEMIS
I.S.
O.S.
HEAD
ELLIP F.&D. HEMIS
299
342
384
427
470
214
257
299
342
385
256
300
361
414
484
210
259
307
358
400
215
281
356
439
531
342
391
439
487
535
216
282
330
379
427
307
358
362
425
495
248
296
349
406
467
251
326
411
506
612
513
555
598
641
683
428
470
513
556
598
546
610
678
767
862
456
514
576
642
730
633
742
861
988
1124
583
631
679
727
775
475
523
571
619
667
578
648
723
801
904
533
603
678
757
840
726
851
986
1130
1285
726
769
812
854
897
641
684
727
769
812
963
1068
1181
1298
1421
804
882
962
1047
1134
1269 823
1423 871
1586 919
1757 967
1937 1015
715
763
811
859
907
1014
1130
1277
1380
1515
927
1019
1115
1216
1321
1449
1623
1834
2001
2205
940
1068
1196
1325
1453
855
983
1239
1367
1550
1968
2436
2956
3526
1250
1550
1909
2274
2708
2126
2745·
3444
4221
5078
1063
1208
1352
1496
1640
955
1100
1244
1388
1532
1655
2115
2632
3204
3833
1438
1802
2181
2632
3085
2419
3125
3922
4808
5787
96
1581
1709
1837
1965
2094
1496
1624
1752
1880
2008
4145
4814
5573
6302
7122
3140 6013
3645 7028
4145 8122
4722 9295
5288 10546
1784
1929
2073
2217
2361
1676
1821
1965
2109
2253
4519 . 3618 6854
5260 4146 8012
6058 4760 9194
6913 5364 10528
7823 6058 11952
102
108
114
120
126
2222
2350
2478
2606
2734
2137 7992
2265 8911
2393 9880
2521 10692
2649 11824
11877
13287
14776
16345
17992
2505
2650
2794
2938
3082
2397 8790 6737
2542 9814 7513
2686 10893 8332
2830 11874 9193
2974 13059 10096
132
138
144
2863
2991
3119
2777 12862 9748 19718
2906 14100 10623 21523
3034 15232 11536 23408
3226
3371
3514
3118 14301 11041 22291
3263 15597 12029 24343
3407 16952 13059 26424
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
84
90
IIII
5937
6624
7349
8112
8911
13466
15073
16767
18554
20328
390
WEIGHT OF PIPES AND FITTINGS
NOM.
NOM.
PIPE
WALL
PIPE DESIGNATION
1 ft.
THK.
SIZE
~
ELBOW
,,
90°
L.R.
90°
S.R.
RETURN
45°
L.R.
6
180°
L.R.
"
180°
S.R.
ft
..
TEE
0.4
0.5
0.4
Y2
STD
XSTG
SCH.160
XXSTG
.109
.147
.187
.294
0.9
1.1
1.3
1.7
0.2
0.3
0.1
0.2
%
STD
XSTG
SCH.160
XXSTG
.113
.154
.218
.308
1.1
1.5
1.9
2.4
0.2
0.3
0.1
0.2
0.4
0.7
1
STD
XSTG
SCH.160
XXSTG
.133
.179
.250
.358
1.7
2.2
2.8
3.7
0.4
0.5
0.6
0.8
0.3
0.3
0.3
0.4
0.8
1.0
1.2
1.5
.140
.191
.250
.382
2.3
3.0
3.8
5.2
0.6
0.9
1.0
1.4
0.4
0.7
0.9
0.4
0.5
0.5
0.8
1.3
1.8
2.0
2.7
0.8
l~
STD
XSTG
SCH.160
XXSTG
1.4
1.8
1.3
1.6
2.0
2.5
lY2
STD
XSTG
SCH.160
XXSTG
.145
.200
.281
.400
2.7
3.6
4.9
6.4
0.9
1.2
1.4
1.9
0.6
0.8
1.2
1.0
0.4
0.7
1.0
1.1
1.9
2.4
3.3
4.0
1.1
1.5
2.4
2.7
2.0
2.3
3.0
3.4
2
STD
XSTG
SCH.160
XXSTG
.154
.218
.343
.436
3.7
5.0
7.5
9.0
1.6
2.2
3.3
3.5
1.0
1.5
2.2
2.3
0.8
1.2
1.6
2.0
3.2
4.4
6.0
7.5
2.0
3.0
4.0
5.0
3.5
4.0
5.0
6.3
2Y2
STD
XSTG
SCH.160
XXSTG
.203
.276
.375
.552
5.8
7.7
10.0
13.7
3.3
4.0
5.1
7.0
2.1
2.8
3.4
5.0
1.8
2.1
3.0
3.8
6.5
8.0
12.0
14.0
4.3
5.6
6.0
9.7
6.0
7.0
8.0
10.5
3
STD
XSTG
SCH.160
XXSTG
.216
.300
.438
.600
7.6
10.3
14.3
18.6
5.0
6.5
8.5
11.0
3.0
4.3
6.0
7.3
2.6
3.5
4.4
5.8
10.2
13.0
18.0
22.0
6.0
8.5
12.0
14.6
7.0
8.5
10.0
13.5
0.3
0.4
0.5
0.4
0.5
0.5
0.6
0.6
0.5
0.8
1.0
0.8
0.9
1.0
1.3
391
WEIGHT OF PIPES AND FITTINGS
ELBOW
NOM. PIPE
NOM.
PIPE DESIGNATION WALL 1 Ft.
SIZE
THK.
<.-
,,
90°
L.R.
90°
S.R.
RETURN
0
45
L.R.
6
1800
L.R.
1800
S.R.
",. f t
..
TEE
3'12
STD
XSTG
XXSTG
.226
.318
.636
9.1
12.5
22.9
6.8
8.4
16.0
4.5
6.0
1l.0
3.5
4.5
8.5
1.3.0
16.8
32.00
9.0
12.0
22.0
9.0
12.0
18.0
4
STD
XSTG
SCH.120
SCH. 160
XXSTG
.237
.337
.438
.531
.674
10.8
15.0
19.0
22.5
27.5
9.0
13.5
15.6
18.0
20.0
6.3
8.5
10.4
12.0
13.0
4.5
6.1
7.8
8.8
10.S
18.5
25.0
31.3
40.0
40.0
12.5
17.0
20.8
24.0
27.0
12.0
15.8
23.5
25.0
25.0
5
STD
XSTG
SCH.120
SCH.160
XXSTG
.258
.375
.500
.625
.750
14.6
20.S
27.0
33.0
3S.6
15.5
22.0
27.8
32.0
36.0
9.6
14.0
lS.6
22.0
24.0
7.5
10.S
13.9
16.0
19.0
30.0
44.0
55.6
65.0
72.0
19.0
2S.0
37.2
44.0
48.0
21.0
26.0
44.5·
55.0
40.0
6
STD
XSTG
SCH. 120
SCH.160
XX STG.
.280
.432
.562
.71S
.864
19.0
28.6
36.4
45.3
53.2
24.5
35.0
45.2
57.065.0
lS.0
23.0
30.0
3S.0
44.0
12.0
17.5
22.6
30.0
32.0
50.0
70.0
90.3
120.0
130.0
35.0
46.0
60.0
76.0
87.0
34.0
40.0
64.0
62.0
68.0
8
SCH. 20
SCH.30
STD
SCH.60
X. STG.
SCH. 100
SCH.120
SCH.140
SCH. 160
XX STG.
.250
.277
.322
.406
.500
.593
.718
.812
.906
.875
22.4
24.7
2S.6
35.6
43.4
50.9
60.6
67.8
74.7
72.4
36.5
40.9
50.0
58.0
71.0
84.0
100.8
111.0
120.0
118.0
24.4
27.0
34.0
39.1
47.5
56.0
66.0
74.0
80.0
79
18.2
20.4
23.0
29.4
35.0
42.0
50.4
55.0
62.0
60.0
73.0
81.9
95.0
117.0
142.0
168.0
202.0
222.0
230.0
236.0
4S.8
54.0
68.0
78.0
100.0
112.0
133.0
149.0
160.0
158.0
54.0
57.0
55.0
76.0
75.0
97.0
115.0
133.0
152.0
148.0
10
SCH.20
SCH.30
STD.
XSTG.
.250
.307
.365
.500
28.0
34.2
40.5
54.7
56.8
71.4
8S.0
107.0
38.2
46.8
58.0
70.0
28.4
35.7
43.0
53.0
114.0
143.0
177.0
215.0
76.4 73.0
94.0 81.0
115.0 85.0
140.0 105.0
(cont.)
392
WEIGHT OF PIPES AND FITTINGS
RETURN
ELBOW
NOM.
NOM.
WALL
PIPE DESIGNATION
THK.
SIZE
PIPE
I ft.
~
(cont.)
180°
L.R.
180°
S.R.
TEE
A
~
67
79
92
107
130
267
318
370
428
530
177
212
246
286
348
161
180
215
241
260
.250
33.4
.330 43.8
.375
49.6
.406
53.6
.500
65.4
.562
73.2
.687
88.6
.843 108.0
1.000 125.5
1.125 140.0
1.312 161.0
82
108
125
132
160
182
219
268
311
347
450
55
72
80
88
104
121
146
177
207
231
300
41
54
62
66
84
91
109
134
155
174
225
164
216
230
264
320
364
439
535
622
694
910
109
145
155
176
218
242
292
354
414
462
600
120
136
120
147
160
226
245
304
353
404
480
.250
312
.375
.438
.500
.593
.750
.937
1.093
1.250
1.406
37.0
46.0
55.0
63.0
72.0
85.0
107.0
131.0
151.0
171.0
190.0
106
132
160
183
205
245
310
70
87
105
122
140
163
205
53
66
80
91
100
123
154
212
264
325
366
400
490
619
140
175
210
244
275
326
410
193
210
165
252
230
311
369
213
850
.250
.312
.375
.500
.656
42.0
52.0
63.0
83.0
108.0
10
12
SCH.20
SCH.30
STD.
SCH.40
X STG
SCH.60
SCH. 80
SCH.100
SCH. 120
SCH.140
SCH.160
14
SCH.I0
SCH.20
STD.
SCH.40
XSTG
SCH.60
SCH. 80
SCH. 100
SCH. 120
SCH.140
SCH.160
(cont.)
45°
L.R.
88
106
123
143
174
.592
.718
.843
1.000
1.125
16
90°
S.R.
133
159
185
214
260
SCH.80
SCH.100
SCH. 120
SCH.140
SCH.160
SCH.10
SCH.20
SCH. 30 STD
SCHAOXSTG
SCH.60
..
.
" "
90°
L.R.
64.4
77.0
89.2
104.2
116.0
425
572
382
286
1092
764
139
172
206
276
355
92
115
132
174
236
69
86
100
135
178
277
344
412
550
710
184
230
260
340
472
201
222
195
280
458
393
WEIGHT OF PIPES AND FITTINGS
NOM.
NOM.
WALL
PIPE DESIGNATION
THK.
SIZE
(cont.)
~
45°
L.R.
6
A
1618
1080
118
146
167
205
219
259
340
422
88
110
126
154
167
195
247
317
352
438
510
616
690
780
989
1268
226
292
330
410
430
518
680
844
281
307
249
399
332
525
612
710
217
320
420
506
690
861
144
210
275
338
457
573
109
160
206
253
345
431
434
640
830
1012
1380
1722
288
410
.. 550
676
914
1146
439
342
480
706
834
1021
262
174
131
524
348
477
394
197
787
414
520
260
1040
550
540
.250
.312
.375
.438
.500
.562
.750
.937
1.156
1.375
1.562
1. 781
47
59
71
82
93
105
138
171
208
244
275
309
176
219
260
308
340
390
494
634
.250
.375
.500
.593
.812
1.031
1.281
1.50C
1. 750
1.968
53
79
105
123
167
209
256
297
342
379
.250
.312
.375
.437
.500
58
72
87
103
115
20
TEE
405
809
SCH.10
SCH. 20 STD
SCH.30XSTG
SCH.40
SCH.60
SCH.80
SCH.100
SCH.120
SCH.140
SCH. 160
180°
S.R.
600
225
18
...
"
180°
L.R.
900
300
SCH.10
SCH.20
STD
SCH.30
XSTG
SCH.40
SCH.60
SCH.80
SCH.100
SCH.120
SCH.140
SCH.160
(cont.)
90°
S.R.
450
.843
1.031
1.218
1.438
1.593
22
RETURN
ELBOW
137
165
193
224
245
SCH.80
SCH.100
SCH.120
SCH.140
SCH.160
16
,
PIPE
1 ft.
90°
L.R ..
548
394
WEIGHT OF PIPES AND FITTINGS
NOM.
PIPE
SIZE
NOM.
WALL
DESIGNAI1ON
THK.
ELBOW
PIPE
1 FT
<JIll
(cant.)
.562
.625
.688
.750
129
143
157
170
.250
.375
.500
.562
.687
.968
1.218
1.531
1.812
2.062
2.343
63
95
125
141
171
238
297
367
429
484
542
26
.250
.312
.375
.437
.500
.562
.625
.688
.750
67
84
103
119
136
153
169
186
202
30
.312
.375
.500
99
119
158
22
24
SCH.10
SCH. 20 STD
XSTG
SCH.30
SCH.40
SCH.60
SCH.80
SCH.100
SCH.120
SCH.140
SCH. 160
RETURN
, , ,..
90 0
L.R.
90 0
S.R.
45°
L.R.
1800
L.R.
6
314
460
600
702
846
1188
1470
208
298
392
470
564
783
977
180 0
S.R.
ft
416
590
780
940
1128
1566
1954
..
TEE
677
528
610
977
1257
1446
1673
157
238
300
351
423
594
735
627
890
1200
1404
1692
2377
2940
550
275
1100
770
729
365
1458
875
306
367
488
1223
1465
1950
612
734
975
464
618
930
1235
1058
1060
1200
395
WEIGHT
NOM.
PIPE
SIZE
'12
SA
1
114
Ph
2
2'12
3
3'12
4
5
6
8
10
12
14
16
20
24
30
OF
FLANGES
300 Ibs.
1SO Ibs.
SLIP
ON
LONG.
WELD WELD
NECK NECK BLIND STUDS
SLIP
ON
WELD
NECK
LONG.
WELD BLIND STUDS
NECK
1.0
2.0
2.0
1.0
1.5
2.0
2.0
1.0
1.5
2.0
2.0
1.0
2.5
3.0
3.0
2.0
2.0
2.5
8.0
2.0
1.0
3.0
4.0
10.0
4.0
2.0
2.5
2.5
10.0
3.0
1.0
4.5
5.0
14.0
6.0
2.0
3.0
4.0
12.0
3.0
1.0
6.5
7.0
17.0
7.0
3.5
5.0
6.0
16.0
4.0
1.5
7.0
8.0
19.0
8.0
4.0
8.0
10.0
21.0
7.0
1.5
10.0
12.0
28.0
12.0
7.0
9.0
1l.5
24.0
9.0
1.5
13.0
16.0
36.0
16.0
7.5
11.0
12.0
31.0
13.0
3.5
16.0
20.0
45.0
21.0
7.5
12.0
16.0
47.0
17.0
4.0
21.0
25.0
54.0
27.0
7.5
13.0
20.0
57.0
20.0
6.0
26.0
34.0
86.0
35.0
8.0
18.0
24.0
77.0
26.0
6.0
35.0
45.0 108.0
50.0
11.5
28.0
42.0 103
45.0
6.5-
54.0
70.0
150
81.0
18.0
37.0
55.0 150
70.0
15.0
77.0
99.0
218
127
38.0
60.0
85.0 215
110
15.0 110
142
289
184
49.0
77.0 114
221
131
22.0 164
186
342
236
62.0
93.0 142
254
170
31.0 220
246
426
307
83.0
18 120
155
278
209
41.0 280
305
493
390
101
155
170
324
272
52.0 325
378
575
492
105
22 159
224
333
69.0 433
429
594
157
210
260
439
411
71.0 490
545
823
754
174
26 248
270
470
498
93.6 552
615
870
950
239
319
375
600
681
112.0 779
858
1130
1403
307
396
WEIGHT
NOM.
PIPE
SIZE
%
%
1
IlJt
1%
2
2Y2
3
3%
4
5
6
8
10
I
, 12
14
16
18
20
22
24
26
30
FLANGES
OF
400 Ibs.
SLIP
ON
600 Ibs.
LONG.
WELD WELD
NECK NECK BLIND STUDS
SLIP
ON
WELD
NECK
LONG.
WELD BLIND STUDS
NECK
2.0
3.0
2.0
1.0
2.0
3.0
2.0
1.0
3.0
3.5
3.0
2.0
3.0
3.5
3.0
2.0
3.5
4.0
11.0
4.0
2.0
3.5
4.0
11.0
4.0
2.0
4.5
5.5
14.0
6.0
2.0
4.5
5.5
14.0
6.0
2.0
6.5
8.0
17.0
8.0
3.5
6.5
8.0
17.0
8.0
3.5
8.0
10.0
21.0
10.0
4.5
8.0
10.0
21.0
10.0
4.5
12.0
14.0
29.0
15.0
7.5
12.0
14.0
29.0
15.0
8.0
15.0
18.0
38.0
20.0
7.7
15.0
18.0
38.0
20.0
8.0
21.0
26.0
48.0
29.0
11.6
21.0
26.0
48.0
29.0
11.6
24.0
30.0
67.0
33.0
12.0
33.0
37.0
80.0
41.0
12.5
31.0
39.0
90.0
44.0
12.5
63.0
68.0 128
68.0
19.5
39.0
49.0 115.0
61.0
19.0
80.0
73.0 158
86.0
30.0
63.0
78.0 140
100
30.0
97.0 112.0 215
139
40.0
91.0 110.0 230
155
52.0
177
189
324
231
72.0
91.0
129
160
301
226
69.0
215
226
500
295
191
233
336
310
88.0
259
347
417
378
118
253
294
416
398
114
366
481
564
527
152
310
360
481
502
139
476
555
654
665
193
378
445
563
621
180
612
690
840
855
242
464
465
685
205
643
710
962
267
539
640
799
936
274
876
977
1100
1175
.365
616
680
970
1111
307
898
960
1250
1490
398
859
940
1230
1596
453
1158
1230 1520
1972
574
397
WEIGHT
Y2
FLANGES
900 lbs.
NOM.
prp~
SIZE
OF
SLIP
ON
1500 lbs.
LONG.
WELD WELD
NECK NECK BLIND STUDS
SLIP
ON
LONG.
WELD WELD
NECK NECK BLIND STUDS
6.0
7.0
4.0
3.2
6.0
7.0
4.0
3.2
6.0
7.0
6.0
3.3
6.0
7.0
6.0
3.3
7.5
8.5
15.0
9.0
7.5
8.5
15.0
9.0
6.0
10.0
10.0
18.0
10.0
10.0
10.0
18.0
10.0
6.0
14.0
14.0
23.0
14.0
14.0
14.0
23.0
14.0
9.0
25.0
24.0
44.0
25.0
25.0
24.0
44.0
25.0
12.5
36.0
36.0
65.0
35.0
19.0
36.0
36.0
72.0
35.0
19.0
3
31.0
29.0
72.0
32.0
12.5
48.0
48.0
84.0
48.0
25.0
4
53.0
51.0
98.0
54.0
25.0
73.0
69.0 118
73.0
3·1.0
83.0
86.0 143
87.0
33.0
132.0 132.0 195
142
60.0
76.0
3,4
1
PA
lY2
2
2Y2
3Y2
5
6
8
10
12
14
16
18
20
108.0 110.0 199
113
40.0
164
164
235
159
172
187
310
197
69.0
258
273
366
302
121
245
268
385
290
95.0 436
454
610
507
184
326
372
667
413
124
690
1028
775
306
380
562
558
494
159
940
1030
975
425
459
685
670
619
199
1250
1335
1300
570
647
924
949
880
299
09
r/}E-<
E-«
1625
1750
1750
770
792
1164
1040
1107
361
::r: u
C!)~
2050
2130
2225
1010
3325
3180
3625
1560
667
ZZ
-p..
~p..
22
24
30
~<
2099
687
26 1450 1650 1650 2200
765
1525
1575
2200
3025
1074
2075
2150
3025
1480 2107
1990 2290
1775
2200
398
WEIGHT
NOM.
PIPE
SIZE
'12
%
1
11,4
1'12
2
2'12
3
2500 Ibs.
SLIP
ON
LONG.
WELD WELD
NECK NECK BLIND STUDS
7.0
8.0
7.0
3.4
9.0
9.0
10.0
3.6
12.0
13.0
20.0
12.0
6.0
18.0
20.0
30.0
18.0
9.0
25.0
28.0
38.0
25.0
12.0
38.0
42.0
55.0
39.0
21.0
55.0
52.0
85.0
56.0
27.0
83.0
94.0 125.0
86.0
37.0
3'12
4
5
6
8
10
12
14
16
18
20
22
24
26
30
FLANGES
OF
127
146
185
133
.61
210
244
300
223
98
323
378
450
345
145
485
576
600
533
232
925
1068
1150
1025
445
1300
1608
1560
1464
622
SLIP
ON
LONG.
WELD WELD
NECK NECK BLIND STUDS
399
Manufacturers' Standard Gauge for
SHEET STEEL
This gage system replaces U.S. Standard Gage for Steel Sheets. It is based on
weight 41. 82 pounds per square foot per inch of thickness. In ordering steel
sheets, it is advisable to specify the inch equivalent of gage.
Mfgrs'
Standard
Gage
Number
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Inch
Equivalent
Lbs.
Per
Square
Inch
Lbs.
Per
Square
Foot
Mfgrs'
Standard
Gage
Number
Inch
Equivalent
Lbs.
Per
Square
Inch
Lbs.
Per
Square
Foot
.2391
.2242
.2092
.1943
.1793
.1644
.1495
.1345
.1196
.1046
.0897
.0747
.0673
.0598
.0538
.0478
.0418
.0359
.069444
.065104
.060764
.056424
.052083
.047743
.043403
.039062
.034722
.030382
.026042
.021701
.019531
.017631
.015625
.013889
.012153
.010417
10.0000
9.3750
8.7500
8.1250
7.5000
6.8750
6.2500
5.6250
5.0000
4.3750
3.7500
3.1250
2.8125
2.5000
2.2500
2.0000
1.7500
1.5000
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
.0329
.0299
.0269
.0239
.0209
.0179
.0164
.0149
.0135
.0120
.0105
.0097
.0090
.0082
.0075
.0067
.0064
.0060
.0095486
.0086806
.0078125
.0069444
.0060764
.0052083
.0047743
.0043403
.0039062
.0034722
.0030382
.0028212
.0026042
.0023872
.0021701
.0019531
.0018446
.0017361
1.3750
1.2500
1.1250
1.0000
.87500
.75000
.68750
.62500
.56250
.50000
.43750
.40625
.37500
.34375
.31250
.28125
.26562
.25000
GALVANIZED SHEET
Galv.
Sheet
Gage
Number
Ounces
Per
Square
Foot
Pounds
Per
Square
Foot
Pound
Per
Square
Inch
Thickness
Equivalent
for Galv.
Sheet
Gage. No.
8
9
10
11
12
13
14
15
16
17
18
19
20
112.5
102.5
92.5
82.5
72.5
62.5
52.5
47.5
42.5
38.5
34.5
30.5
26.5
7.03125
6.40625
5.78125
5.15625
4.53125
3.90625
3.28125
2.96875
2.65625
2.40625
2.15625
1.90625
1.65625
.048828
.044488
.040148
.035807
.031467
.027127
.022786
.020616
.018446
.016710
.014974
.013238
.011502
.1681
.1532
.1382
.1233
.1084
.0934
.0785
.0710
.0635
.0575
.0516
.0456
.0396
Galv.
Sheet
Gage
Number
Ounces
Per
Square
Foot
Pounds
Per
Square
Foot
Pound
Per
Square
linch
Thickness
Equivalent
for Galv.
Sheet
Gage No.
21
22
23
24
25
26
27
28
29
30
31
32
24.5
22.5
20.5
18.5
16.5
14.5
13.5
12.5
11.5
10.5
9.5
9.0
1.53125
1.40625
1.28125
1.15625
1.03125
.90625
.84375
.78125
.71875
.65625
.59375
.56250
.0106340
.0097656
.0088976
.0080295
.0071615
.0062934
.0058594
.0054253
.0049913
.0045573
.0041233
.0039062
.0366
.0336
.0306
.0276
.0247
.0217
.0202
.0187
.0172
.0157
.0142
.0134
400
WEIGHT OF PLATES
Pounds Per Linear Foot
Thickness, Inches
Width
In.
~
U
~6
.16
.32
.48
.64
.21
.43
.64
.85
.80
.96
1.12
1.28
~
~
1~6
%;
Y2
?16
.27 .32
.53 .64
.80 .96
1.06 1.28
.37
.74
1.12
1.49
.43
.85
1.28
1.70
.48 .53
.58
.96 1.06 Ll7
1.43 1.59 1.75
1.91 2.13 2.34
.64
1.28
1.91
2.55
.69 .74 .80 .85
1.38 1.49 1.59 1.70
2.07 2.23 2.39 2.55
2.76 2.98 3.19 3.40
1.06
1.28
1.49
1.70
1.33
1.59
1.86
2.13
1.59
1.91
2.23
2.55
1.86 2.13
2.23 2.55
2.60 2.98
2.98 3.40
2.39
2.87
3.35
3.83
2.66
3.19
3.72
4.25
3.19
3.83
4.46
5.10
3.45
4.14
4.83
5.53
1.43
1.59
1.75
1.91
1.91
2.13
2.34
2.55
2.39
2.66
2.92
3.19
2.87 3.35 3.83
3.19 3.72 4.25
3.51 4.09 4.68
3.83 4.46 5.10
4.30
4.78
5.26
5.74
4.78 5.26 5.74 6.22 6.69 7.17 7.65
5.31 5.84 6.38 6.91 7.44 7.97 8.50
5.84 6.43 7.01 7.60 8.18 8.77 9.35
6.38 7.01 7.65 8.29 8.93 9.56 10.2
3~ 2.07
3Y2 2.23
3% 2.39
2.55
4
2.76
2.98
3.19
3.40
3;45
3.72
3.98
4.25
4.14 4.83 5.53 6.22 6.91 7.60 8.29
4.46 5.21 5.95 6.69 7.44 8.18 8.93
4.78 5.58 6.38 7.17 7.97 8.77 9.56
5.10 5.95 6.80 7.65 8.50 9.35 10.2
8.98
9.67
10.4
11.1
9.67
10.4
11.2
11.9
10.4
11.2
12.0
12.8
11.1
11.9
12.8
13.6
4~ 2.71
4V2 2.87
4% 3.03
3.19
5
3.61
3.83
4.04
4.25
4.52
4.78
5.05
5.31
5.42
5.74
6.06
6.38
6.32 7.23 8.13 9.03 9.93
6.69 7.65 8.61 9.56 10.5
7.07 8.08 9.08 10.1 11.1
7.44 8.50 9.56 10.6 11.7
10.8
11.5
12.1
12.8
11.7
12.4
13.1
13.8
12.6
13.4
14.1
14.9
13.6
14.3
15.1
15.9
14.5
15.3
16.2
17.0
5~ 3.35
5V2 3.51
5% 3.67
3.83
6
4.46
4.68
4.89
5.10
5.58
5.84
6.11
6.38
6.69
7.01
7.33
7.65
7.81 8.93 10.0
8.18 9.35 10.5
8.55 9.78 11.0
8.93 10.2 11.5
15.6 16.7 17.9
16.4 17.5 18.7
17.1 18.3 19.6
17.9 19.1 20.4
61,4
6V2
6%
7
3.98
4.14
4.30
4.46
5.31
5.53
5.74
5.95
6.64
6.91
7.17
7.44
7.97 9.30 10.6
8.29 9.67 ILl
8.61 10.0 11.5
8.93 10.4 11.9
71,4
7Y2
7%
8
4.62
4.78
4.94
5.10
6.16
6.38
6.59
6.80
7.70
7.97
8.23
8.50
9.24
9.56
9.98
10.2
10.8
11.2
ll.5
11.9
12.3
12.8
13.2
13.6
8 1,4
8V2
8%
9
5.26
5.42
5.58
5.74
7.01
7.23
7.44
7.65
8.77
9.03
9.30
9.56
7.86 9.83
8.08 10.1
8.29 10.4
8.50 10.6
1,4
V2
%
1
1~
1V2
1%
2
2~
2V2
2%
3
9 1,4 5.90
9Y2 6.06
9% 6.22
10
6.38
%
1!{6
2.92
3.51
4.09
4.68
1~
Va
1
3.72 3.98 4.25
4.46 4.78 5.10
5.21 5.58 5.95
5.95 6.38 6.80
11.2
11.7
12.2
12.8
12.3
12.9
13.4
14.0
13.4
14.0
l4.7
15.3
14.5
15.2
15.9
16.6
12.0
12.4
12.9
13.4
13.3
13.8
14.3
14.9
14.6
15.2
15.8
16.4
15.9
16.6
17.2
17.9
17.3 18.6 19.9 21.3
18.0 19.3 20.7 22.1
18.7 20.1 21.5 23.0
19.3 20.8 22.3 23.8
13.9
14.3
14.8
15.3
15.4
15.9
16.5
17.0
17.0
17.5
18.1
18.7
18.5
19.1
19.8
20.4
20.0
20.7
21.4
22.1
21.6 23.1 24.7
22.3 23.9 25.5
23.1 24.7 26.4
23.8 25.5 27.2
10.5
10.8
11.2
ll.5
12.3 14.0 15.8 17.5 19.3
12.6 14.5 16.3 18.1 19.9
13.0 14.9 16.7 18.6 20.5
13.4 15.3 17.2 19.1 21.0
21.0
21.7
22.3
23.0
22.8
23.5
24.2
24.9
24.5
25.3
26.0
26.8
11.8
12.1
12.4
12.8
13.8
14.1
14.5
14.9
15.7 17.7 19.7
16.2 18.2 20.2
16.6 18.7 20.7
17.0 19.1 21.3
21.6
22.2
22.8
23.4
23.6 5.6
24.2 26.2
24.9 26.9
25.5 27.6
26.3
27.1
27.9
28.7
28.1
28.9
29.8
30.6
27.5 29.5 31.5
28.3 30.3 32.3
29.0 31.1 33.2
29.8 31.9 34.0
401
WEIGHT OF PLATES
Pounds Per Linear Foot
Width
In.
Thickness, Inches
;,s
7.(
~6
I%;
1
26.1 28.3 30.5
26.8 29.0 31.2
27.4- 29.7 32.0
28.1. 30.4 32.7
32.7
33.5
34.3
35.1
34.9
35.7
36.6
37.4
28.7
29.3
30.0
30.6
33.5
34.2
35.0
35.7
35.9
36.7
37.5
38.3
38.3
39.1
40.0
40.8
23.9 26.6 29.2 31.9 34.5
24.9 27.6 3Q.4 33.2 35.9
25.8 28.7 32.6 34.4 37.3
26.8 29.8 32.7 35.7 38.7
37.2
3S.7
40.2
41.7
39.8
41.4
43.0
44.6
42.5
44.2
45.9
47.6
43.1
44.6
46.1
47.6
46.2
47.8
49.4
51.0
49.3
51.0
52.7
54.4
VB
?16
Y2
%;
%
1!{6
13.1
13.4
13.7
14.0
15.3
15.6
16.0
16.4
17.4
17.9
18.3
18.7
19.6
20.1
20.6
21.0
21.8
22.3
22.8
23.4
24.0
24.5
25.1
25.7
12.0
12.2
12.5
12.8
14.3 16.7 19.1
14.7 17.1 19.6
15.0 17.5 20.0
15.3 17.9 20.4
21.5
22.0
22.5
23.0
23.9
24.4
25.0
25.5
26.3
26.9
27.5
28.1
31.1
31.8
32.5
33.2
15.9 18.6 21.3
16.6 19.3 22.1
17.2 20.1 23.0
17.9 20.8 23.8
1014 6.53 8.71 10.9
10Y2 6.69 8.93 11.2
1034 6.85 9.14 11.4
11
7.01 9.35 11.7
%
1;{6
Va
1114
11Y2
11%
12
7.17 9.56
7.33 9.78
7.49 9.99
7.65 10.2
12%
13
13Y2
14
7.97
8.29
8.61
8.93
10.6
11.1
11.5
11.9
13.3
13.8
14.3
14.9
14Y2
15
15Y2
16
9.24
9.56
9.88
10.2
12.3
12.8
13.2
13.6
15.4 18.5
15.9 19.1
16.5 19.8
17.0 20.4
21.6
22.3
23.1
23.8
24.7 27.7 30.8 33.9 37.0 40.1
25.5 28.7 31.9 35.1 38.3 41.4
26.4 29.6 32.9 36.2 39.5 42.8
27.2 30.6 34.0 37.4 40.8 44.2
16Y2
17
17%
18
10.5
10.8
11.2
11.5
14.0
14.5
14.9
15.3
17.5
18.1
18.6
19.1
21.0
21.7
22.3
23.0
24.5
25.3
26.0
26.8
2S.1
2S.9
29.8
30.6
42.1
43.4
44.6
45.9
45.6
47.0
48.3
49.7
49.1
50.6
52.1
53.6
52.6
54.2
55.8
57.4
56.1
57.8
59.5
61.2
18Y2
19
19Y2
20
11.8
12.1
12.4
12.8
15.7
16.2
16.6
17.0
19.7
20.2
20.7
21.3
23.6
24.2
24.9
25.5
27.5
28.3
29.0
29.8
31.5 35.4 39.3 43.2 47.2
32.3 36.3 40.4 44.4 48.5
33.2 37.3 41.4 45.6 49.7
34.0 38.3 42.5 46.8 51.0
51.1
52.5
53.9
55.3
55.0
56.5
58.0
59.5
59.0
60.6
62.2
63.8
62.9
64.6
66.3
68.0
20Y2
21
21Y2
22
13.1
13.4
13.7
14.0
17.4
17.9
18.3
18.7
21.8
22.3
22.8
23.4
26.1
26.8
27.4
28.1
30.5
31.2
32.0
32.7
34.9
35.7
36.6
37.4
52.3
53.6
54.8
56.1
56.6
58.0
59.4
60.8
61.0
62.5
64.0
65.5
65.3 69.7
66.9 71.4
68.5 73.1
70.1 74.8
22%
23
23%
24
14.3
14.7
15.0
15.3
19.1
19.6
20.0
20.4
23.9
24.4
25.0
25.5
28.7
29.3
30.0
30.6
33.5
34.2
35.0
35.7
38.3 43.0 47.8 52.6 57.4
39.1 44.0 48.9 53.8 58.7
40.0 44.9 49.9 54.9 59.9
40.8 45.9 51.0 56.1 61.2
62.2
63.5
64.9
66.3
66.9
68.4
69.9
71.4
71.7 76.5
73.3 78.2
74.9 79.9
76.5 81.6
25
26
27
28
15.9 21.3
16.6 22.1
17.2 23.0
17.9 23.8
26.6
27.6
28.7
29.8
31.9
33.2
34.4
35.7
37.2
38.7
40.2
41.7
42.5
44.2
45.9
47.6
47.8
49.7
51.6
53.6
53.1
55.3
57.4
59.5
58.4
60.8
63.1
65.5
63.8 69.1 74.4
66.3 71.8 77.4
68.9 74.6 SO.3
71.4 77.4 83.3
79.7 85.0
82.9 88.4
86.1 91.8
89.3 95.2
29
30
31
32
18.5
19.1
19.8
20.4
24.7
25.5
26.4
27.2
30.8
31.9
32.9
34.0
37.0
38.3
39.5
40.8
43.1
44.6
46.1
47.6
49.3
51.0
52.7
54.4
55.5
57.4
59.3
61.2
61.6
63.8
65.9
68.0
67.S
70.1
72.5
74.8
74.0
76.5
79.1
81.6
31.6
32.5
33.5
34.4
39.2
40.2
41.1
42.1
35.1
36.1
37.2
38.3
43.6
44.6
45.7
46.8
38.6
39.7
40.9
42.1
47.9
49.1
50.3
51.4
80.1
82.9
85.6
88.4
86.3 92.4 9S.6
89.3 95.6 102
92.2 98.8 105
95.2 102 109
402
WEIGHT OF PLATES
Pounds Per Linear Foot
Thickness, Inches
Width
In.
~6
%
lYt6
~
63.1
65.0
66.9
68.9
70.1
72.3
74.4
76.5
77.1
79.5
81.8
84.2
84.2
86.7
89.3
91.8
31.5
32.3
33.2
34.0
39.3 47.2 55.0 62.9 70.8 78.6 86.5
40.4 48.5 56.5 64.6 72.7 80.8 88.8
41.4 49.7 58.0 66.3 74.6 82.9 91.2
42.5 51.0 59.5 68.0 76.5 85.0 93.5
94.4
96.9
99.5
102
102
105
108
111
26.1
26.8
27.4
28.1
34.9
35.7
36.6
37.4
43.6
44.6
45.7'
46.8
52.3
53.6
54.8
56.1
61.0
62.5
64.0
65.5
69.7
71.4
73.1
74.8
78.4
80.3
82.2
84.2
87.1
89.3
91.4
93.5
105
107
45
46
47
48
28.7
29.3
30.0
30.6
38.3
39.1
40.0
40.8
47.8
48.9
49.9
51.0
57.4
58.7
59.9
61.2
66.9
68.4
69.9
71.4
76.5
78.2
79.9
81.6
86.1
88.0
89.9
91.8
95.6
97.8
99.9
102
49
50
51
52
31.2
21.9
32.5
33.2
41.7
42.5
43.4
44.2
52.1
53.1
54.2
55.3
62.5
63.8
65.0
66.3
72.9 83.3 93.7 104
74.4 85.0 95.6 106
75.9 86.7 97.5 108
77.4 88.4 99.5 111
53
54
55
56
33.8
34.4
35.1
35.7
45.1
45.9
46.8
47.6
56.3
57.4
58.4
59.5
67.6 78.8
68.9 80.3
70.1 81.8
71.4 83.3
57
58
59
60
36.3
37.0
37.6
38.3
48.5
49.3
50.2
51.0
60.6
61.6
62.7
63.8
61
62
63
64
38.9
39.5
40.2
20.8
51.9
52.7
53.6
54.4
65
66
67
68
41.4
42.1
42.7
43.4
55.3
56.1
57.0
57.8
69
70
71
72
44.0
44.6
45.3
45.9
~6
VB
~
U
33
34
35
36
21.0
21.7
22.3
23.0
28.1
28.9
29.8
30.6
35.1 42.1 49.1
36.1 43.4 50.6
37.2 44.6 52.1
38.3 45.9 53.6
37
38
39
40
23.6
24.2
24.9
25.5
41
42
43
44
?16
Y2
56.1
57.8
59.5
61.2
IlH'6
l~
1
105
108
112
115
112
116
119
122
110
113
116
119
118
121
124
128
126
129
133
136
122
125
128
131
131
134
137
140
139
143
146
150
VB
91.2 98.2
93.9 101
96.1 104
99.5 107
95.8
98.2
101
103
112
113
116
119
122
105
108
110
112
115
117
120
122
124
127
130
133
134
137
140
143
143
147
150
153
153
156
160
163
115
117
119
122
125
128
130
133
135
138
141
144
146
149
152
155
156
159
163
166
167
170
173
177
llO
90.1
91.8
93.5
95.2
101
103
105
107
113
115
117
119
124
126
129
131
135
138
140
143
146
149
152
155
158
161
164
167
169
172
175
179
180
184
187
190
72.7
74.0
75.2
76.5
84.8 96.9
86.3 98.6
87.8 100
89.3 102
109
111
113
115
121
123
125
128
133
136
138
140
145
148
151
153
158
160
163
166
170
173
176
179
182
185
188
191
194
197
201
204
64.8
65.9
66.9
68.0
77.8
79.1
80.3
81.6
90.7 1()t.
92.2 105
93.7 107
95.2 109
117
119
121
122
130
132
134
136
143
145
147
150
156
158
161
163
169
171
174
177
182
185
187
190
194
198
201
204
207
211
214
218
69.1
70.1
71.2
72.3
82.9
84.2
85.4
86.7
96.7
98.2
99.7
101
111
112
114
116
124
126
128
130
138
140
142
145
152
154
157
159
166
168
171
173
180
182
185
188
193
196
199
202
207
210
214
217
221
224
228
231
58.7 73.3
59.5 74.4
60.4 75.4
61.2 76.5
88.0
89.3
90.5
91.8
103
104
106
107
117
119
121
122
132
134
136
138
147
149
151
153
161
164
166
168
176
179
181
184
191
193
196
199
205
208
211
214
220
223
226
230
235
238
241
245
403
WEIGHTS OF PLATES
Pounds Per Linear Foot
Thickness, Inches
Width
In. I
~
~
~6
%
?{6
Y2
%
%
l!{S
~
IHs
VB
1~6
1
46.5
47.2
47.8
48.5
62.1
62.9
63.8
64.6
77.6
78.6
79.7
80.8
93.1
94.4
95.6
96.9
109
110
112
113
124
126
128
129
140
142
143
145
155
157
159
162
171
173
175
178
186
189
191
194
202
204
207
210
217
220
223
226
233
236
239
242
248
252
255
258
49.1
78 49.7
79 50.4
80 51.0
65.5
66.3
67.2
68.0
81.8
82.9
83.9
85.0
98.2
99.5
101
102
115
116
118
119
131
133
134
136
147
149
151
153
164
166
168
170
180
182
185
187
196
199
202
204
213
216
218
221
229
232
235
238
245
249
252
255
262
265
269
272
81
82
83
84
51.6
52.3
52.9
53.6
68.9
69.7
70.6
71.4
86.1
87.1
88.2
89.3
103
105
106
107
121
122
124
125
138
139
141
143
155
157
159
161
172
174
176
179
189
192
194
196
207
209
212
214
224
227
229
232
241
244
247
250
258
261
265
268
275
279
282
286
85
86
87
88
54.2
54.8
55.5
56.1
72.3
73.1
74.0
74.8
90.3
91.4
92.4
93.5
lOS
110
111
112
126
128
129
131
145 163
146 165
148 166
150 168
181
183
185
187
199
201
203
206
217
219
222
224
235
238
240
243
253
256
259
262
271
274
277
281
289
292
296
299
89 56.7
90 57.4
91
92
75.7
76.5
77.4
78.2
94.6
95.6
96.7
97.8
114
115
116
117
132
134
135
137
151
153
155
156
170
172
174
176
189
191
193
196
20S
210
213
215
227
230
232
235
246
249
251
254
265
268
271
274
284
287
290
293
303
306
309
313
93
94
95
96
79.1
79.9
80.8
81.6
98.8
99.9
101
102
119
120
121
122
138
140
141
143
158
160
162
163
178
180
182
184
198
200
202
204
217
220
222
224
237
240
242
245
257
260
262
265
277
280
283
286
296
300
303
306
316
320
323
326
98
100
102
104
83,3
85.0
86.7
88.4
104
106
lOS
111
125
128
130
133
146
149
152
155
167
170
173
177
187
191
195
199
20S
213
217
221
229
234
238
243
250
255
260
265
271
276
282
287
292
298
304
309
312
319
325
332
333
340
347
354
106
108
110
112
90.1
91.8
93.5
95.2
113
115
117
119
135
138
140
143
158
161
164
167
180
184
187
190
203
207
210
214
225
230
234
238
248
253
257
262
270
275
281
286
293
298
304
309
315
321
327
333
338
344
351
357
360
367
374
381
114
116
118
120
96.9
98.6
100
102
121
123
125
128
145
148
151
153
170
173
176
179
194
197
201
204
218
222
226
230
242
247
251
255
267
271
276
281
291
296
301
306
315
321
326
332
339
345
351
357
363
370
376
383
388
394
401
40S
122
124
126
128
104
105
107
109
130
132
134
136
156
158
161
163
182
185
187
190
207
211
214
218
233
237
241
245
259
264
268
272
285
290
295
299
311
316
321
326
337
343
348
354
363
369
375
381
389 415
395 422
402 428
40S 435
73
74
75
76
77
I
404
WEIGHT OF CIRCULAR PLATES
ALL DIMENSIONS IN INCHES
WEIGHTS IN POUNDS
3/16
~
5116
y.
1/16
1.00
1.25
1.50
1.75
.042
.065
.094
.128
.056
.087
.125
.170
.070
.109
.156
.213
.083
.130
.188
.256
2.00
2.25
2.50
2.75
.167
.211
.261
.315
.223
.282
.348
.421
.278
.352
.435
.526
.334
.422
.521
.631
3.00
3.25
3.50
3.75
.375
.441
.511
.587
.501
.588
.681
.782
.626
.734
.852
.978
4.00
4.25
4.50
4.75
.668
.754
.845
.941
.890
).005
1.126
1.255
1.113
1.256
1.408
1.569
5.00
5.25
5.50
5.75
1.043
1.150
1.262
1.379
1.391
1.533
1.683
1.839
6.00
6.50
7.00
7.50
1.502
1.763
2.044
2.347
2.003
2.350
2.726
3.129
8.00
8.50
9.00
9.50
2.670 3.560 4.450
3.014 4.019 5.024
3.379 4.S06 5.632
3.765 5.020 6.275
DIA
13116
Y2
'11&
o/a
11116
%
.097
.152
.219
.298
.111
.174
.250
.341
.125
.196
.282
.383
.139
.217
.313
.426
.153
.239
.344
.468
.167
.261
.375
.511
.181
.282
.407
.554
.389
.493
.608
.736
.445
.563
.695
.841
.SOl
.634
.782
.946
.556
.704
.869
1.052
.612
.774
.956
1.157
.668
.845
1.043
1.262
.723
.915
1.130
1.367
.876
.751
.881 1.028
1.022 1.192
1.173 1.369
1.001
1.175
1.363
1.564
1.126
1.322
1.533
1.76.0
Ya
1
.209
.326
.469
.639
.223
.348
.501
.681
.779 .834
.986 1.056
1.217 1.304
1.472 1.577
.890
1.126
1.391
1.683
1.252 1.377 1.502
1.469 1.616 1.763
1.704 1.874 2.044
1.956 2.151 2.347
1.627 1.752 1.877
1.910 2.056 2.203
2.215 2.385 2.555
2.542 2.738 2.933
2.003
2.350
2.726
3.129
1.335 1.558 1.780 2.003
1.S07 1.758 2.009 2.261
1.690 1.971 2.253 2.534
1.883 2.196 2.510 2.824
2.225
2.512
2.816
3.138
2.893
3.265
3.661
4.079
1.738
1.916
2.103
2.299
2.086 2.434 2.781
2.300 2.683 3.066
2.524 2.945 3.365
2.759 3.218 3.678
3.477 3.824 4.172
3.833 4.216 4.600
4.207 4.627 5.048
4.598 5.058 5.517
2.503
2.938
3.407
3.911
3.004
3.525
4.088
4.693
3.129
3.450
3.786
4.138
3.504 4.005 4.506
4.113 4.700 5.288
4.770 5.451 6.133
5.476 6.258 7.040
5.006
5.875
6.814
7.822
5.340 6.230 7.120_ 8.010 8.900
6.028 7.033 8.038 9.043 10.04
6.758 7.885 9.011 10.13 11.26
7.530 8.785 10.04 11.29 12.55
2.448 2.670
2.763 3.014
3.098 3.379
3.451 3.765
.195
.304
.438
.596
lo/i6
3.115
3.517
3.942
4.393
3.338 3.560
3.768 4.019
4.224 4.S06
4.706 5.020
4.520 4.867 5.215
4.983 5.366 5.749
5.469 5.889 6.310
5.977 6.437 6.897
5.563
6.133
6.731
7.356
5.507 6.008 6.508 7.009 7.509 8.010
6.463 7.051 7.638 8.226 8.813 9.401
7.496 8.177 8.858 9.540 10.22 10.90
8.605 9.387 10.16 10.95 11.73 12.51
9.790
11.05
12.39
13.80
10.68
12.05
13.51
15.06
11.57 12.46 13.35
13.06 14.06 15.07
14.64 15.77 16.89
16.31 17.57 18.82
14.24
16.07
18.02
20.08
10.00
10.50
11.00
11.50
4.172 5.563 6.953 8.344 9.734
4.600 6.133 7.666 9.199 10.73
5.048 6.731 ··8.413 10.09 11.77
5.517 7.356 9.196 11.03 12.87
11.12 12.51
12.26 13.79
13.46 15.14
14.71 16.55
13.90
15.33
16.82
18.39
15.29 16.68
16.86 18.39
18.SO 20.19
20.23 22.06
18.07 19.46 20.85
19.93 21.46 22.99
21.87 23.55 25.24
23.90 25.74 27.58
22.25
24.53
26.92
29.42
12.00
12.50
13.00
13.50
6.008 8.010 10.01
6.519 8.691 10.86
7.051 9.401 11.75
7.603 10.13 12.67
14.00
14.50
15.00
15.50
8.177
8.771
9.387
10.02
16.00
16.50
17.00
17.50
12.01
13.03
14.10
15.20
14.01
15.21
16.45
17.74
16.02
17.38
18.80
20.27
18.02
19.55
21.15
22.81
20.02
21.72
23.50
25.34
22.02
23.90
25.85
27.87
24.03
26.07
28.20
30.41
26.03
28.24
30.55
32.94
28.03
3D.42
32.90
35.48
30.03
32.59
35.25
38.01
32.04
34.76
37.60
40.55
10.90
11.69
12.51
13.36
13.62 16.35
14.61 17.54
15.64 18.77
16.70 20.04
19.07
20.46
21.90
23.38
21.80
23.39
25.03
26.72
24.53
26.31
28.16
30.06
27.25
29.23
31.28
33.41
29.98 32.70
32.16 35.08
34.41 37.54
36.75 40.09
35.43
38.00
40.67
43.43
38.15
40.93
43.80
46.77
40.88
43.85
46.93
SO. 11
43.61
46.78
50.06
53.45
10.68
11.35
12.05
12.77
14.24
15.14
16.07
17.03
17.80
18.93
20.09
21.29
21.36
22.71
24.11
25.55
24.92
26.50
28.13
29.81
28.48
30.28
32.15
34.07
32.04
34.07
36.17
38.32
35.60
37.86
40.18
42.58
39.16 42.72
41.64 45.43
44.20 48.22
46.84 51.10
46.28
49.21
52.24
55.36
49.84
53.00
56.26
59.62
53.40
56.79
60.28
63.88
56.96
60.57
64.30
68.14
18.00
18.50
19.00
19.50
13.51
14.27
15.06
15.86
18.02 22.52 27.03
19.03 23.79 28.55
20.08 25.1;) 30.12
21.15 26.43 31.72
31.54
33.31
35.14
37.01
36.04
38.07
40.16
42.30
40.55
42.83
45.18
47.59
45.05
47.59
50.20
52.87
49.56
52.35
55.22
58.16
54.06
57.11
60.24
63.45
58.57
61.87
65.26
68.74
63.07
66.63
70.28
74.03
67.58
71.39
75.30
79.31
72.09
76.15
80.32
84.60
20.00
20.SO
21.00
21.50
16.68
17.53
18.39
19.28
22.25 27.81 33.37
23.37 29.22 35.06
24.53 30.66 36.79
25.71 32.14 38.56
38.93
40.90
42.92
44.99
44.SO
46.75
49.06
51.42
SO.06
52.59
55.19
57.85
55.62
58.44
61.32
64.28
61.18 66.75
64.28 70.13
67.46 73.59
70.71 77.13
72.31
75.97
79.72
83.56
77.87
81.81
85.85
89.99
83.43 89.00
87.66 93.50
91.99 98.12
96.42 102.85
405
WEIGHT OF CIRCULAR PLATES
ALL DIMENSIONS IN INCHES
WEIGHTS IN POUNDS
DIA
31!6
\t4
51!6
Ya
11!6
22
22Y2
23
23Y2
24
24Yl
25
25Y2
26
26Y2
27
27Yl
28
28Y2
29
29Y2
30
30Yl
31
31Y2
32
32Yl
33
33Yl
34
34Y2
35
35Yl
36
36Y2
37
37Yl
20
21
22
23
24
25
26
27
28
29
30
32
33
34
35
36
38
39
40
41
43
44
45
47
48
50
51
53
54
56
57
59
27
28
29
31
32
33
35
36
38
39
41
42
34
35
37
38
45
47
48
50
52
53
55
57
59
61
62
64
66
68
70
72
74
76
78
40
42
44
46
48
50
52
54
56
59
61
63
65
68
70
73
75
78
80
83
85
88
91
38
38Yz
39
39Yz
40
40Yz
41
41Yz
42
42Yz
43
43I!z
44
44Yz
45
45Yz
46
46Yz
47
47\7
48
48Yz
49
49Y7
60
62
63
65
67
68
70
72
74
75
77
79
81
83
84
86
88
90
92
94
96
98
100
102
80
82
85
87
89
91
94
96
98
100
103
105
108
110
113
115
118
120
123
126
128
131
134
136
44
40
42
43
45
47
49
51
53
55
56
58
61
63
65
67
69
71
73
76
78
Ya
61
63
66
69
72
75
78
81
85
88
91
95
98
90 102
94 105
97
109
100 113
103 116
107 120
110 124
114 128
118 132
121
136
125 140
129 145
132 149
136 153
140 158
144 162
148 167
152 171
156_ ,-176
67
70
74
77
80
83
87
102
105
108
111
114
117
47
49
51
54
56
58
61
63
66
68
71
74
76
79
82
85
88
91
94
97
100
103
106
109
113
116
119
123
126
130
133
137
120
124
127
130
134
137
140
144
147
151
154
158
162
165
169
173
J77
180
184
188
192
196
200
204
141
144
148
152
156
160
164
168
172
176
180
184
188
193
197
202
206
210
215
220
224
229
234
239
161
165
169
i74
178
182
187
192
196
201
206
211
215
220
225
230
235
241
246
251
256
262
267
273
94
80
96
99
83
85
88
90
93
95
98
il!6
~-
100
103
106
108
III
114
117
120
123
126
129
132
135
138
141
144
147
150
154
157
160
164
167
170
~
Y2
54
56
59
61
64'
67
70
72
75
78
81
84
87
181
186
190
195
200
205
210
216
221
226
231
237
242
248
253
259
265
271
276
282
288
294
301
307
90
94
98
101
105
109
113
117
121
125
129
134
138
142
147
151
156
161
166
170
175
180
185
190
196
201
206
212
217
223
228
234
240
245
251
257
263
269
275
282
288
294
301
307
314
320
327
334
341
1J1!6
%
1l1!6
74
81
87
77
84
92
81
88
96
84
92
100
88
96 104
92 100 109
96 104 113
99 109 118
103 113 122
107 117 127
112 122 132
116 126 137
120 131
142
124 136 147
129 140 152
157
133 145
138 150 163
142 155 168
147 160 174
152 166 179
157 171
185
162 176 191
167 182 197
172 187 203
177
193 209
182 199 215
187 204 221
193 210 228
198 216 234
204 222 W
209 228 247
215 ~5 254
221
241
261
227
247
268
233 254· 275
239 260 282
245 267 289
274
251
297
257
281
304
263
287 311
270
294 319
276 301
327
283 309 334
289 316 342
296 323 350
303 330 358
310 338 366
317 345 374
324 353 383
331
361
391
338 369 399
345 377 408
352 384 417
360 393 4.25
367 401
434
375 409 443
Ya
151!6
1
94
99
103
108
112
117
122
127
132
137
142
147
153
158
164
169
175
181
187
193
199
206
212
218
225
232
238
245
252
259
267
274
101
106
110
115
120
125
130
136
141
146
152
158
164
169
175
182
188
194
200
207
214
220
227
234
241
248
256
263
270
278
286
293
108
113
118
123
128
134
139
145
150
156
162
168
174
181
187
194
200
207
214
221
228
235
242
250
257
265
273
280
288
296
305
313
281
289
296
304
312
319
327
335
343
352
360
368
377
386
394
403
412
421
430
439
449
458
467
477
301
309
317
325
334
342
351
359
368
377
386
395
404
413
422
432
441
451
461
471
481
491
501
511
321
330
338
347
356
365
374
383
392
402
411
421
431
441
451
461
471
481
492
502
513
523
534
545
406
WEIGHT OF CIRCULAR PLATES
ALL DIMENSIONS IN INCHES
WEIGHTS IN POUNDS
DIA
lf16
Y4
5/16
Ys
'/16
YI
9/16
Ya
50
50'4
51
51 Yz
52
52Yi
53
53Yz
54
5417
55
55Y7
56
56Yz
57
571h
58
58Y7
59
59Yz
60
60Yz
61
61 Yz
62
62Yz
63
63Yz
64
64Yz
65
65Yl
66
66Yz
67
67Yz
68
68Yz
69
69'll
70
70'll
71
104
106
109
III
113
115
117
119
122
124
126
129
131
133
136
138
140
143
145
148
150
153
155
158
160
163
166
168
171
174
176
179
182
184
187
190
193
196
199
202
204
207
210
213
216
219
222
225
228
232
235
238
241
244
247
251
139
142
145
148
150
153
156
159
162
165
168
17l
1/4
178
181
184
187
190
194
197
200
204
207
210
214
217
221
224
228
231
235
239
242
246
250
253
257
261
265
269
273
276
280
284
288
292
296
301
305
309
313
317
321
326
330
334
174
177
181
184
188
192
195
199
203
207
210
214
218
222
226
230
234
238
242
246
250
255
259
263
267
272
276
280
285
289
294
298
303
307
312
317
322
326
331
336
341
346
351
355
360
365
371
376
381
386
391
396
402
407
412
418
209
213
217
221
226
230
234
239
243
248
252
257
262
266
271
276
281
286
290
295
300
305
310
316
321
326
331
336
342
347
353
358
363
369
375
380
386
392
397
403
409
415
421
427
433
439
445
451
457
463
469
476
482
488
495
501
243
248
253
258
263
268
273
279
284
289
294
300
305
311
316
322
327
333
339
345
350
356
362
368
374
380
386
393
399
405
411
418
424
430
437
444
450
457
463
470
477
484
491
498
505
512
519
526
533
540
548
555
562
570
577
585
278
284
289
295
301
307
313
318
324
330
337
343
349
355
361
368
374
381
387
394
401
407
414
421
428
435
442
449
456
463
470
477
485
492
499
507
514
522
530
537
545
553
561
569
577
585
593
601
609
617
626
634
643
651
660
668
313
319
326
332
338
345
352
358
365
372
379
386
392
400
407
414
421
428
436
443
451
458
466
473
481
489
497
505
513
521
529
537
545
553
562
570
579
587
596
605
613
622
631
640
649
658
667
676
685
695
704
713
723
732
742
752
348
355
362
369
376
383
391
398
406
413
421
428
436
444
452
460
468
476
484
492
501
509
517
526
535
543
552
561
570
579
588
597
606
615
624
634
643
653
662
672
681
691
701
7ll
721
731
741
751
762
772
782
793
803
814
825
835
7l'll
72
72'll
73
73'll
74
74'll
75
75'll
76
76Yz
77
77'll
11/16
%
382 417
390 426
398 434
406 443
414
451
422 460
430
469
438 478
446 487
454
496
463
505
471
514
480 523
488 533
497 542
506 552
515 561
524 571
532 581
542 591
551
601
560 611
569 621
579 631
588 641
598 652
607 662
617 673
627 684
636 694
646
705
656 716
666
727
676
738
687
749
697
760
707
772
718
783
728
795
739 806
750 818
760
829
841
771
782 853
793 865
804 877
815 889
826 902
838 914
849 926
860 939
872 951
884
964
895
977
907
989
919 1002
13/16
Ys
15/16
1
452
461
470
479
489
498
508
517
527
537
547
557
567
577
587
598
608
619
629
640
651
662
673
684
695
706
718
729
740
752
764
776
787
799
812
824
836
848
861
873
886
899
911
924
937
950
963
977
990
1003
1017
1031
1044
1058
1072
1086
487
497
506
516
526
537
547
557
568
578
589
600
611
622
633
644
655
666
678
689
701
713
724
736
748
761
773
785
797
810
823
835
848
861
874
887
900
914
927
940
954
968
981
995
1009
1023
1038
1052
1066
1081
1095
1110
1125
1139
1154
1169
521
532
543
553
564
575
586
597
608
620
631
643
654
666
678
690
702
714
726
738
751
764
776
789
802
815
828
841
854
868
881
895
909
922
936
950
965
979
993
1008
1022
1037
1052
1066
1081
1096
1112
1127
1142
1158
1173
1189
1205
1221
1237
1253
556
567
579
590
602
613
625
637
649
661
673
685
698
710
723
736
749
761
775
788
801
814
828
842
855
869
883
897
911
926
940
955
969
984
999
1014
1029
1044
1059
1075
1090
1106
1122
1137
1153
1170
1186
1202
1218
1235
1252
1268
1285
1302
1319
1336
407
WEIGHT OF CIRCULAR PLATES
ALL DIMENSIONS IN INCHES
WEIGHTS IN POUNDS
DIA
3/16
14
5/16
%
7/16
Yz
9/16
18
11/16
%
13iJ6
!Is
15/16
1
78
78Yz
79
79Yz
80
80Yz
81
81 Yz
82
82Yz
83
83Yz
84
84Yz
85
85Yz
86
86Yz
87
87Yz
88
88Yz
89
89Yz
90
90Yz
91
91 Yz
92
92Yz
93
93Yz
94
94Y1
95
254
257
260
264
267
270
274
277
281
284
287
291
294
298
301
305
309
312
316
319
323
327
330
334
338
342
345
349
353
357
361
365
369
373
377
380
384
389
393
397
401
405
409
413
417
421
426
430
434
438
443
447
451
456
460
464
338
343
347
352
356
360
365
369
374
379
383
388
392
397
402
407
411
416
421
426
431
436
441
446
451
456
461
466
471
476
481
486
492
497
502
507
513
518
523
529
534
540
545
551
556
562
567
573
579
584
590
596
602
607
613
619
423
428
434
439
445
451
456
462
468
473
479
485
491
496
502
508
514
520
526
532
538
545
551
557
563
569
576
582
589
595
601
608
614
621
628
634
641
648
654
661
668
675
681
688
695
702
709
716
723
731
738
745
752
759
767
774
508
514
521
527
534
541
547
554
561
568
575
582
589
596
603
610
617
624
632
639
646
654
661
668
676
683
691
699
706
714
722
729
737
745
753
761
769
777
785
793
801
810
818
826
834
843
851
860
868
877
885
894
902
911
920
929
592
600
608
615
623
631
639
647
655
663
671
679
687
695
703
712
720
728
737
745
754
762
771
780
788
797
806
815
824
833
842
851
860
869
879
888
897
907
916
925
935
944
954
964
973
983
993
1003
1013
1023
1033
1043
1053
1063
1073
1083
677
686
694
703
712
721
730
739
748
757
766
776
785
794
804
813
823
832
842
852
862
871
881
891
901
911
921
931
942
952
962
973
983
994
1004
1015
1025
1036
1047
1058
1068
1079
1090
1101
1113
1124
1135
1146
1157
1169
1180
1192
1203
1215
1227
1238
761
771
781
791
801
811
821
831
842
852
862
873
883
894
904
915
926
936
947
958
969
980
991
1003
1014
1025
1036
1048
1059
1071
1082
1094
1106
1118
1130
1141
1153
1166
1178
1190
1202
1214
1227
1239
1252
1264
1277
1289
1302
1315
1328
1341
1354
1367
1380
1393
846
857
868
879
890
901
912'
924
935
947
958
970
981
993
1005
1017
1029
1041
1053
1065
1077
1089
1102
1114
1126
1139
1152
1164
1177
1190
1203
1216
1229
1242
1255
1268
1282
1295
1308
1322
1336
1349
1363
1377
1391
1405
1419
1433
1447
1461
1475
1490
1504
1519
1533
1548
931
943
955
967
979
991
1004
1016
1029
1041
1054
1067
1079
1092
1105
1118
1131
1145
1158
1171
1185
1198
1212
1225
1239
1253
1267
1281
1295
1309
1323
1337
1352
1366
1381
1395
1410
1425
1439
1454
1469
1484
1499
1514
1530
1545
1560
1576
1592
1607
1623
1639
1655
1670
1687
1703
1015
1028
1041
1055
1068
1081
1095
1108
1122
1136
1150
1164
1177
1192
1206
1220
1234
1249
1263
1278
12:12
1307
1322
1337
1352
1367
1382
1397
1412
1428
1443
1459
1475
1490
1506
1522
1538
1554
1570
1586
1603
1619
1636
1652
1669
1686
1702
1719
1736
1753
1770
1788
1805
1822
1840
1857
1100
1114
1128
1143
1157
1172
1186
1201
1216
1230
1245
1260
1276
1291
1306
1322
1337
1353
1368
1384
1400
1416
1432
1448
1464
1481
1497
1514
1530
1547
1564
1580
1597
1614
1632
1649
1666
1684
1701
1719
1736
1754
1772
1790
1808
1826
1844
1862
1881
1899
1918
1937
1955
1974
1993
2012
1184
1200
1215
1230
1246
1262
1277
1293
1309
1325
1341
1357
1374
1390
1407
1423
1440
1457
1474
1491
1508
1525
1542
1560
1577
1595
1612
1630
1648
1666
1684
1702
1720
1739
1757
1776
1794
1813
1832
1851
1870
1889
1908
1927
1947
1966
1986
2006
2026
2045
2065
2086
2106
2126
2146
2167
1269
1285
1302
1318
1335
11352
1369
1386
1403
1420
1437
1454
1472
1489
1507
1525
1543
1561
1579
1597
1615
1634
1652
1671
1690
1708
1727
1746
1766
1785
1804
1824
1843
1863
1883
1902
1922
1943
1963
1983
2003
2024
2044
2065
2086
2107
2128
2149
2170
2192
2213
2235
2256
2278
2300
2322
1354
1371
1389
1406
1424
1442
1460
1478
1496
1514
1533
1551
1570
1589
1608
1627
1646
1665
1684
1704
1723
1743
1762
1782
1802
1822
1843
1863
1883
1904
1924
1945
1966
1987
2008
2029
2051
2072
2094
2115
2137
2159
2181
2203
2225
2247
2270
2292
2315
2338
2361
2384
2407
2430
2453
2477
951~
913
50Yz
97
97~~
98
98Yz
99
99Yz
100
100Yz
101
101Yz
102
102Yz
103
1031;,
104
104Yz
105
105Yz
408
WEIGHT OF CIRCULAR PLATES
ALL DIMENSIONS IN INCHES
DIA
106
106\1
107
107\1
108
108\1
109
109\1
110
110\1
111
111\1
112
112\1
113
113\1
114
114\1
115
115\1
116
116\1
117
117\1
118
118\1
119
119\1
120
120\1
121
121\1
122
122\1
123
123Y,
124
124\1
125
125\1
126
126\1
127
127Y1
128
128\1
129
129YI
130
1301;7
131
131 \1
132
1321;7
133
133 1h
3/16
\t4
469
473
478
482
487
491
496
500
505
509
514
519
523
528
533
537
542
547
552
557
561
566
571
576
581
586
591
596
601
606
611
616
621
626
631
636
641
647
652
657
662
668
673
678
684
689
694
700
705
710
716
721
727
732
738
744
625
631
637
643
649
655
661
667
673
679
685
692
698
704
710
717
723
729
736
742
749
755
761
768
775
781
788
794
801
808
814
821
828
835
842
848
855
862
869
876
883
890
897
904
911
919
326
933
940
947
955
962
969
977
984
991
51I6
781
789
796
804
811
819
826
834
841
849
857
864
872
880
888
896
904
912
920
928
936
944
952
960
968
976
985
993
1001
1010
1018
1026
1035
1043
1052
1061
1069
1078
1086
1095
1104
1113
1121
1130
1139
1148
1157
1166
1175
1184
1193
1202
1212
1221
1230
1239
%
938
946
955
964
973
982
991
1000
1010
1019
1028
1037
1047
1056
1065
1075
1084
1094
1103
1113
1123
1132
1142
1152
1162
1172
1182
1192
1202
1212
1222
1232
1242
1252
1262
1273
1283
1293
1304
1314
1325
1335
1346
1356
1367
1378
1389
1399
1410
1421
1432
1443
1454
1465
1476
1487
WEIGHTS IN POUNDS
7/16
1094
1104
1115
1125
1135
1146
1157
1167
1178
1189
1199
1210
1221
1232
1243
1254
1265
1276
1287
1299
1310
1321
1333
1344
1355
1367
1379
1390
1402
1413
1425
1437
1449
1461
1473
1485
1497
1509
1521
1533
1545
1558
1570
1582
1595
1607
1620
1633
1645
1658
1671
1683
1696
1709
1722
1735
\1
1250
1262
1274
1286
1298
1310
1322
1334
1346
1358
1371
1383
1396
1408
1421
1433
1446
1459
1471
1484
1497
1510
1523
1536
1549
1562
1575
1589
1602
1615
1629
1642
1656
1669
1683
1697
1711
1724
1738
1752
1766
1780
1794
1809
1823
1837
1851
1866
1880
1895
1909
1924
1338
1953
1968
1983
91I6
1406
1420
1433
1446
1460
1473
1487
1501
1514
1528
1542
1556
1570
1584
1598
1612
1627
1641
1655
1670
1684
1699
1713
1728
1743
1758
1772
1787
1802
1817
1832
1848
1863
1878
1894
1909
1924
1940
1956
1971
1987
2003
2019
2035
2051
2067
2083
2099
2115
2131
2148
2164
2181
2197
2214
2231
%
I III 6
1563 11719
1577 1735
1592 1751
1607 1768
1622 1784
1637 1801
1652 1817
1667 1834
1683 1851
1698 1868
1713 1885
1729 1902
1744 1919
1760 1936
1776 1953
1791 1971
1807 1988
1823 2005
1839 2023
1855 2041
1871 2058
1887 2076
1904 2094
1920 2112
1936 2130
1953 2148
1969 2166
1986 2184
2003 2203
2019 2221
2036 2240
2053 2258
2070 2277
2087 2296
.2104 2314
2121 2333
2138 2352
2156 2371
2173 2390
2190 2409
2208 2429
2225 2448
2243 2467
2261 2487
2278 2506
2296 2526
2314 2546
2332 2565
2350 2585
2368 2605
2386 2625
2405 2645
2423 2665
2441 2686
2460 2706
2478 2726
%
1875
1893
1911
1928
1946
1965
1983
2001
2019
2038
2056
2075
2093
2112
2131
2150
2169
2188
2207
2226
2246
2265
2284
2304
2324
2343
2363
2383
2403
2423
2443
2463
2484
2504
2525
2545
2566
2587
2607
2628
2649
2670
2692
2713
2734
2756
2777
2799
2820
2842
2864
2886
2908
2930
2952
2974
13/16
2031
2050
2070
2089
2109
2128
2148
2168
2187
2207
2227
2248
2268
2288
2308
2329
2349
2370
2391
2412
2433
2454
2475
2496
2517
2539
2560
2582
2603
2625
2647
2669
2691
2713
2735
2757
2780
2802
2825
2847
2870
2893
2916
2939
2962
2985
3008
3032
3055
3079
3102
3126
3150
3174
3198
3222
Ya
2188
2208
2229
2250
2271
2292
2313
2334
2356
2377
2399
2420
2442
2464
2486
2508
2530
2552
2575
2597
2620
2642
2665
2688
2711
2734
2757
2780
2804
2827
2850
2874
2898
2922
2945
2969
2994
3018
3042
3066
3091
3115
3140
3165
3190
3215
3240
3265
3290
3316
3341
3367
3392
3418
3444
3470
lYi6
2344
2366
2388
2411
2433
2456
2478
2501
2524
2547
2570
2593
2617
2640
2664
2687
2711
2735
2759
2783
2807
2831
2855
2880
2905
2929
2954
2979
3004
3029
3054
3079
3105
3130
3156
3182
3207
3233
3259
3285
3312
3338
3364
3391
3418
3444
3471
3498
3525
3552
3580
3607
3635
3662
3690
3718
1
2500
2524
2547
2571
2595
2619
2644
2668
2692
2717
2741
2766
2791
2816
2841
2866
2892
2917
2943
2968
2994
3020
3046
3072
3098
3124
3151
3177
3204
3231
3258
3285
3312
3339
3366
3394
3421
3449
3477
3504
3532
3561
3589
3617
3645
3674
3703
3731
3760
3789
3818
3848
3877
3906
3936
3966
409
WEIGHT OF CIRCULAR PLATES
ALL DIMENSIONS IN INCHES
WEIGHTS IN POUNDS
DIA
3/16
Y4
5/16
%
7/16
12
9116
%
11/16
Y4
13j16
Va
15116
1
134
13412
135
135»
136
13612
137
13712
138
1381;7
139
13912
140
14012
141
14112
142
1421h
143
14312
144
14412
145
14512
146
14612
147
14712
148
14812
149
14912
150
15012
151
15112
152
15212
153
15312
154
15412
155
15512
156
15612
157
15712
158
15812
159
15912
160
16012
161
16112
749
755
760
766
772
777
783
789
795
800
806
812
818
824
829
835
841
847
853
859
865
871
877
883
889
895
902
908
914
520
'926
932
939
945
951
958
964
970
977
983
989
996
1002
1009
1015
1022
1028
1035
1041
1048
1055
1061
1068
1075
1081
1088
999
1006
1014
1021
1029
1036
1044
1052
1059
1067
1075
1082
1090
1098
1106
1114
1122
1130
1137
1145
1153
1161
1170
1178
1186
1194
1202
1210
1218
1227
1235
1243
1252
1260
1268
1277
1285
1294
1302
1311
1319
1328
1336
1345
1354
1362
1371
1380
1389
1397
1406
1415
1424
1433
1442
1451
1249
1258
1267
1277
1286
1296
1305
1315
1324
1334
1343
1353
1363
1373
1382
1392
1402
1412
1422
1432
1442
1452
1462
1472
1482
1492
1503
1513
1523
1533
1544
1554
1564
1575
1585
1596
1606
1617
1628
1638
1649
1660
1671
1681
1692
1703
1714
1725
1736
1747
1758
1769
1780
1791
1802
1814
1498
1509
1521
1532
1543
1555
1566
1578
1589
1601
1612
1624
1635
1647
1659
1671
1682
1694
1706
1718
1730
1742
1754
1766
1779
1791
1803
1815
1828
1840
1852
1865
1877
1890
1902
1915
1928
1940
1953
1966
1979
1992
2005
2018
2031
2044
2057
2070
2083
2096
2109
2123
2136
2149
2163
2176
1748
1761
1774
1787
1800
1814
1827
1840
1854
1867
1881
1894
1908
1922
1935
1949
1963
1977
1991
2005
2019
2033
2047
2061
2075
2089
2104
2118
2132
2147
2161
2176
2190
2205
2220
2234
2249
2264
2279
2294
2309
2324
2339
2354
2369
2384
'2399
2415
2430
2446
2461
2476
2492
2508
2523
2539
1998
2013
2028
2043
2058
2073
2088
2103
2119
2134
2149
2165
2181
2196
2212
2228
2243
2259
2275
2291
2307
2323
2339
2355
2371
2388
2404
2420
2437
2453
2470
2487
2503
2520
2537
2553
2570
2587
2604
2621
2638
2656
2673
2690
2707
2725
2742
2760
2777
2795
2813
2830
2848
2866
2884
2902
2247
2264
2281
2298
2315
2332
2349
2366
2384
2401
2418
2436
2453
2471
2488
2506
2524
2541
2559
2577
2595
2613
2631
2650
2668
2686
2705
2723
2741
2760
2779
2797
2816
2835
2854
2873
2892
2911
2930
2949
2968
2988
3007
3026
3046
3065
3085
3105
3124
3144
3164
3184
3204
3224
3244
3264
2497
2516
2534
2553
2572
2591
2610
2629
2648
2668
2687
2706
2726
2745
2765
2784
2804
2824
2844
2864
2884
2904
2924
2944
2964
2985
3005
3026
3046
-3067
3087
3108
3129
3150
3171
3192
3213
3234
3255
3277
3298
3320
3341
3363
3384
3406
3428
3450
3472
3494
3516
3538
3560
3582
3605
3627
2747
2767
2788
2809
2829
2850
2871
2892
2913
2934
2956
2977
2998
3020
3041
3063
3085
3106
3128
3150
3172
3194
3216
3238
3261
3283
3306
3328
3351
3373
3396
3419
3442
3465
3488
3511
3534
3558
3581
3604
3628
3651
3675
3699
3723
3747
3771
3795
3819
3843
3867
3892
3916
3941
3965
3990
2996
3019
3041
3064
3087
3109
3132
3155
3178
3201
3224
3247
3271
3294
3318
3341
3365
3389
3412
3436
3460
3484
3509
3533
3557
3582
3606
3631
3655
3680
3705
3730
3755
3780
3805
3830
3246
3270
3295
3319
3344
3368
3393
3418
3443
3468
3493
3518
3543
3569
3594
3620
3645
3671
3697
3723
3749
3775
3801
3827
3854
3880
3907
3933
3960
3987
4014
4041
4068
4095
4122
4149
4177
4204
4232
4260
4287
4315
4343
4371
4400
4428
4456
4485
4513
4542
4570
4599
4628
4657
4686
4715
3496
3522
3548
3575
3601
3628
3654
3681
3708
3735
3762
3789
3816
3843
3871
3898
3926
3953
3981
4009
4037
4065
4093
4122
4150
4178
4207
4236
4264
4293
4322
4351
4381
4410
4439
4469
4498
4528
4558
4587
4617
4647
4677
4708
4738
4768
4799
4830
4860
4891
4922
4953
4984
5015
5047
5078
3746
3774
3802
3830
3858
3887
3915
3944
3973
4001
4030
4059
4088
4118
4147
4177
4206
4236
4266
4295
4325
4356
4386
4416
4446
4477
4508
4538
4569
4600
4631
4662
4693
4725
4756
4788
4819
4851
4883
4915
4947
4979
5012
5044
5076
5109
5142
5175
5207
5240
5274
5307
5340
5374
5407
5441
3995
4025
4055
4085
4115
4146
4176
4207
4237
4268
4299
4330
4361
4392
4424
4455
4487
4518
4550
4582
4614
4646
4678
4710
4743
4775
4808
4841
4874
4907
4940
4973
5006
5040
5073
5107
5141
5175
5209
5243
5277
5311
5346
5380
5415
5450
~'856
3881
3906
3932
3958
3983
4009
4035
4061
4087
4113
4140
4166
4192
421'9
4245
4272
4299
4326
4353
5~84
5519
5555
5590
5625
5661
5696
5732
5768
5803
410
WEIGHT OF CIRCULAR PLATES
WEIGHTS IN POUNDS
ALL DIMENSIONS IN INCHES
DIA
162
16212
163
16312
164
16412
16S'
16512
166
16612
167
16712
168
168Yl
169
169Yl
170
170Yl
171
171Yl
172
17212
173
173Yl
174
174Yl
175
175Yl
176
176Yl
177
177Yl
178
178 112
179
17912
180
18012
181
18112
182
18212
183
18312
184
18412
185
18512
186
18612
187
18N?
188
188Yl
189
189Yl
3lis
Y4
5/16
Ys
7/16
1095
1102
1108
1115
1122
1129
1136
1143
1150
1157
1164
1170
1177
1185
1192
1199
1206
1213
1220
1227
1234
1241
1249
1256
1263
1270
1278
1285
1292
1300
1307
1314
1322
1329
1337
1344
1352
1359
1367
1374
1382
1390
1397
1405
1412
1420
1428
1436
1443
1451
1459
1467
1475
1482
1490
1498
1460
1469
1478
1487
1496
1505
1514
1524
1533
1542
1551
1561
1570
1579
1589
1598
1608
1617
1627
1636
1646
1655
1665
1674
1684
1694
1704
1713
1723
1733
1743
1753
1762
1772
1782
1792
1802
1812
1822
1832
1843
1853
1863
1873
1883
1894
1904
1914
1924
1935
1945
1956
1966
1977
1987
1998
1825
1836
1847
1859
1870
1882
1893
1905
1916
1928
1939
1951
1962
1974
1986
1998
2009
2021
2033
2045
2057
2069
2081
2093
2105
2117
2129
2142
2154
2166
2178
2191
2203
2215
2228
2240
2253
2265
2278
2291
2303
2316
2329
2341
2354
2367
2380
2393
2406
2418
2431
2444
2458
2471
2484
2497
2190
2203
2217
2231
2244
2258
2555
2571
2586
2602
2618
2634
2650
2666
2682
2699
2715
2731
2747
2764
2780
2797
2813
2830
2846
2863
2880
2897
2913
2930
2947
2964
2981
2998
3015
3033
3050
3067
3084
3102
3119
3136
3154
3172
3189
3207
3224
3242
3260
3278
3296
3314
3332
3350
3368
3386
3404
3422
3441
3459
3477
3496
'i.?72
2285
2299
2313
2327
2341
2355
2369
2383
2397
241l
2426
2440
2454
2468
2483
2497
2512
2526
2541
2555
2570
2585
2599
2614
2629
2644
2659
2673
2688
2703
2718
2734
2749
2764
2779
2794
2810
2825
2840
2856
2871
2887
2902
2918
2933
2949
2965
2981
2996
I 12
2920
2938
2956
2974
2992
3010
3029
3047
3066
3084
3103
3121
3140
3159
3177
3196
3215
3234
3253
3272
3291
3310
3330
3349
3368
3388
3407
3427
3446
346b
3485
3505
3525
3545
3565
3585
3605
3625
3645
3665
3685
3705
3726
3746
3767
3787
3808
3828
3849
3870
3890
3911
3932
3953
3974
3995
9liS
Ys
liliS
3285
3305
3325
3346
3366
3387
3407
3428
3449
3470
3491
3511
3532
3554
3575
3596
3617
3638
3660
3681
3703
3724
3746
3768
3789
3811
3833
3855
3877
3899
3921
3943
3966
3988
4010
4033
4055
4078
4100
4123
4146
4169
4191
4214
4237
4260
4284
4307
4330
4353
4377
4400
4424
4447
4471
4494
3650
3672
3695
3718
3740
3763
3786
3809
3832
3855
3878
3902
3925
3948
3972
3995
4019
4043
4066
4090
4114
4138
4162
4186
4210
4235
4259
4283
4308
4332
4357
4381
4406
4431
4456
4481
4506
4531
4556
4581
4606
4632
4657
4683
4708
4734
4759
4785
4811
4837
4863
4889
4915
4941
4968
4994
4015
4039
4064
4089
4114
4139
4165
4190
4215
4241
4266
4292
4317
4343
4369
4395
4421
4447
4473
4499
4525
4552
4578
4605
4631
4658
4685
4712
4738
4765
4792
4820
4847
4874
4901
4929
4956
4984
5011
5039
5067
5095
5123
5151
5179
5207
5235
5264
5292
5321
5349
5378
5407
5435
5464
5493
%
4380
4407
4434
4461
4488
4516
4543
4571
4598
4626
4654
4682
4710
4738
4766
4794
4823
4851
4880
4908
4937
4966
4994
5023
5052
5081
5111
5140
5169
5199
5228
5258
5287
5317
5347
5377
5407
5437
5467
5497
5528
5558
5589
5619
5650
5681
5711
5742
5773
5804
5836
5867
5898
5930
5961
5993
13/16
Va
15lis
4744
4774
4803
4833
4862
4892
4922
4952
4982
5012
5042
5072
5102
5133
5163
5194
5225
5255
5286
5317
5348
5379
5411
5442
5473
5505
5537
5568
5600
5632
5664
5696
5728
5760
5792
5825
5857
5890
5923
5955
5988
6021
6054
6087
6121
6154
6187
6221
6254
6288
6322
6356
6390
6424
6458
6492
5109
5141
5173
5205
5236
5268
5300
5333
5365
5397
5430
5462
5495
5528
5561
5594
5627
5660
5693
5726
5760
5793
5827
5861
5894
5928
5962
5997
6031
6065
6099
6134
6169
6203
6238
6273
6308
6343
6378
6414
6449
6484
6520
6556
6591
6627
6663
6699
6736
6772
6808
6845
6881
6918
6955
6991
5474
5508
5542
5576
5610
5645
5679
5714
5748
5783
5818
5852
5887
5923
5958
5993
6028
6064
6100
6135
6171
6207
6243
6279
6315
6352
6388
6425
6461
6498
6535
6572
6609
6646
6684
6721
6759
6796
6834
6872
6910
6948
6986
7024
7062
7101
7139
7178
7217
7255
7294
7333
7373
7412
7451
7491
1
5839
5875
5912
5948
5984
6021
6058
6094
6131
6168
6205
6243
6280
6317
6355
6393
6430
6468
6506
6544
6583
6621
6659
6698
6737
6775
6814
6853
6892
6931
6971
7010
7050
7089
7129
7169
7209
7249
7289
7330
7370
7411
7451
7492
7533
7574
7515
7656
7698
7739
7781
7822
7864
7906
7948
7990
411
WEIGHT OF CIRCULAR PLATES
ALL DIMENSIONS IN INCHES
I
WEIGHTS IN POUNDS
DIA
3/16
1f4
5/16
%
7/16
lh
9/16
%
11/16
Y.
13/16
Ya
15/16
1
190
190Y1
191
191Yz
192
192Yl
193
193Y2
194
194Yl
195
195Y2
196
196Y7
197
1971h
198
198Y2
199
199Y2
200
1506
1514
1522
1530
1538
1546
1554
1562
1570
1578
1586
1595
IG03
1611
1619
1627
1636
1644
1652
1660
1669
2008
2019
2029
2040
2051
2061
2072
2083
2094
2104
2115
2126
2137
2148
2159
2170
2181
21£2
2203
2214
2225
2510
2523
2537
2550
2563
2577
2590
2603
2617
2630
2644
2658
2G71
2685
2698
2712
2726
2740
2754
2767
2781
3012
3028
3044
3060
3076
3092
3108
3124
3140
3157
3173
3189
3205
3222
3238
3255
3271
3288
3304
3321
3338
3514
3533
3551
3570
3589
3607
3626
3645
3664
3683
3702
3721
3740
3759
3778
3797
3816
3836
3855
3874
3894
4016
4037
4059
4080
4101
4123
4144
4166
4187
4209
4230
4252
4274
4296
4318
4340
4362
4384
4406
4428
4450
4518
4542
4566
4590
4614
4638
4662
4686
4710
4735
4759
4784
4808
4833
4857
4882
4907
4932
4956
4981
5006
5020
5047
5073
5100
5126
5153
5180
5207
5234
5261
5288
5315
5342
5370
5397
5424
5452
5479
5507
5535
5563
5522
5551
5581
5610
5639
5669
5698
5728
5757
5787
5817
5847
5877
5907
5937
5967
5997
6027
6058
6088
6119
6024
6056
6088
6120
6152
6184
6216
6248
6281
6313
6346
6378
6411
6444
6476
6509
6542
6575
6609
6642
6675
6526
6561
6595
6630
6664
6699
6734
6769
6804
6839
6874
6910
6945
6980
7016
7052
7087
7123
7159
7195
7231
7028
7065
7102
7140
7177
7214
7252
7290
7327
7365
7403
7441
7479
7517
7556
7594
7633
7671
7710
7749
7788
7530
7570
7610
7650
7690
7730
7770
7810
7851
7891
7932
7973
8013
8054
8095
8137
8178
8219
8261
8302
8344
8032
8075
8117
8160
8202
8245
8288
8331
8374
8417
8461
8504
8548
8591
8635
8679
8723
8767
8811
8856
8900
412
WEIGHT OF BOLTS
With square heads and hexagon nuts in pounds per 100
Length
Under
Head
Inches
Diameter of Bolt in Inches
~
VB
Y2
%
%
Ys
1
2.38
2.71
3.05
3.39
6.11
6.71
7.47
8.23
13.0
14.0
15.1
16.5
24.1
25.8
27.6
29.3
38.9
41.5
44.0
46.5
67.3
70.8
95.1
99.7
3.73
4.06
4.40
4.74
8.99
9.75
10.5
11.3
17.8
19.1
20.5
21.8
31.4
33.5
35.6
37.7
49.1
52.1
55.1
58.2
74.4
77.9
82.0
86.1
5.07
5.41
5.75
6.09
12.0
12.8
13.5
14.3
23.2
24.5
25.9
27.2
39.8
41.9
44.0
46.1
61.2
64.2
67.2
70.2
6.42
6.76
7.10
7.43
15.1
15.8
16.6
17.3
28.6
29.9
31.3
32.6
48.2
50.3
52.3
54.4
73.3
76.3
79.3
82.3
7.77
8.11
8.44
8.78
18.1
18.9
19.6
20.4
33.9
35.3
36.6
38.0
85.3
88.4
91.4
94.4
9.12
9.37
9.71
10.1
21.1
21.7
22.5
23.3
39.3
40.4
41.8
43.1
10.4
10.7
11.0
11.4
24.0
24.8
25.5
26.3
44.4
45.8
47.1
48.5
56.5
5&.6
60.7
62.8
64.9
66.7
68.7
70.8
72,9
75.0
77.1
79.2
11.7
27.0
28.6
30.1
31.6
49.8
52.5
55.2
57.9
10
10Y2
11
11 %
33.1
34.6
36.2
37.7
12
12%
13
13%
14
14%
15
15%
39.2
1
1~
IY2
1%
2
2~
2Y2
2%
3
3~
3%
3%
4
4~
412
4%
5
5~
5Y2
5%
6
6~
6%
6 3,4
7
7~
7%
7%
8
8Y2
9
9%
16
Per Inch
Additional
Notes:
1.3
3.0
1%
17.1
104
109
114
119
143
149
155
161
206
213
90.2
94.4
98.5
103
124
129
135
140
168
174
181
188
221
229
237
246
107
145
151
156
162
195
202
208
215
254
262
271
279
III
115
119
167
172
178
183
222
229
236
242
288
296
304
313
97.4
100
103
106
123
127
131
136
140
143
147
151
188
193
198
204
321
329
337
345
109
112
115
118
156
160
164
168
209
214
220
225
249
255
262
269
275
282
289
296
354
362
371
379
81.3
85.5
89.7
93.9
121
127
133
139
172
180
189
197
231
241
252
263
303
316
330
343
387
404
421
438
60.6
63.3
66.0
68.7
98.1
102
106
110
145
151
157
163
205
213
221
230
274
284
295
306
357
371
384
398
454
471
488
505
71.3
74.0
76.7
79.4
115
119
123
127
170
176
182
188
238
246
254
263
316
327
338
349
411
425
439
452
522
538
556
572
82.1
84.8
87.5
90.2
131
135
140
144
194
200
206
212
271
279
287
296
359
370
381
392
466
479
493
507
589
605
622
639
92.9
148
218
304
402
520
656
5.4
8.4
12.1
16.5
21.4
27.2
33.6
Bolt is Regular Square Bolt, ASA B18.2 and nut is finished Hexagon Nut, ASA B18.2.
This table conforms to weight standards adopted by the Industrial Fasteners Institute.
413
WEIGHTS OF OPENINGS
NOZZLES
With ANSI Welding Neck Flange and Reinforcing Pad
(Table for Quick Reference)
CLASS
SIZE
1Y2
2
3
4
6
8
10
12
14
16
18
20
24
150
300
600
900
6
9
16
25
45
65
95
135
165
215
331
428
589
11
12
25
40
70
110
145
220
285
370
610
708
1131
13
15
40
60
120
175
285
365
515
695
935
1245
1815
17
28
45
75
155
260
375
550
775
965
1379
1693
3041
1500
18
30
70
105
225
380
620
920
NOZZLES
With ASA Welding Neck Flange, Reinforcing Pad, Blind Flange
Studs and Gasket (Table for .Quick Reference)
CLASS
SIZE
3
4
6
8
10
12
14
16
18
20
24
150
300
600
900
25
42
71
110
165
245
296
440
540
700
1000
41
67
120
191
272
404
521
800
1000
1200
1885
60
101
206
314
516
660
893
1300
1600
2100
2990
129
268
457
665
963
1269
1600
2250
2800
5140
1500
118
178
384
682
1127
1695
77
3510
4460
5700
9350
SCREWED COUPLINGS
NOMINAL PIPE SIZE
%
30001b
60001b
0.25
0.50
%
0.44
1.00
1
1%
0.63
2.13
2.19
4.38
2
3.13
7.75
2%
4.00
10.75
3
6.75
13.50
414
WEIGHTS OF PACKING
Pounds Per Cubic Foot
SIZE
!i
%
Yz
RASCHIG RING
CERAMIC
CARBON
60
133
46
61
94
55
75
Yz
%
%
CARBON
STEEL
INTALOX
PLASTIC
54
50
45
27
132
56
62
50
52
%
37
7.25
44
34
94
1
42
39
27
30
5.50
44
71
1
l!i
lYz
lYz
2
3Yz
PALL RING
CARBON
STEEL
3
46
62
31
43
49
34
26
4.75
42
41
37
27
24
4.50
42
37
25
23
46
37
4.25
4
36
The data condensed from the technical literature of the U. S. Stoneware Co.
The weights of carbon steel in percentage of other metals: Stainless
Steel 105%, Copper 120%, Aluminum 37%, Monel or Nickel 115%
WEIGHTS OF INSULATION
POUNDS PER CUBIC FOOT
CALCIUM SILICATE
12.5
FOAMGLASS
9.0
MINERAL WOOL
8.0
GLASS FIBER
4-8
FOAMGLASS
8-10
For mechanical design of vessel add 80% to these weights which covers the
weight of seal, jacketing and the absorbed moisture.
415
SPECIFIC GRAVITIES
METALS 62°F.
Aluminum .............................. 2.70
Antimony ............................. 6.618
Barium .................................... 3. 78
Bismuth ................................ 9.781
Boron ................................... 2.535
Brass: 80 C., 2 OZ ............... 8.60
70 C., 3 OZ ............... 8.44
60 C., 4 OZ ............... 8.36
50 C., 5 OZ ............... 8.20
Bronze: 90 C., 10 T. ................ 8.78
Cadmium ............................... 8.648
Calcium .................................. 1.54
Chromium ............................... 6.93
Cobalt .................................... 8.71
Copper ................................... 8.89
Gold ....................................... 19.3
Iridium ................................. 22.42
Iron - cast .................... 7.03 - 7.73
Iron - wrought ............ 7.80 - 7.90
Lead ................................... 11.342
Magnesium ........................... 1.741
Manganese ............................... 7.3
Mercury(68°F.) ................. 13.546
Molybdenum .......................... 10.2
Nickel ...................................... 8.8
Platinum .............................. 21.37
Potassium ............................ 0.870
Silver ....................... 10.42 - 10.53
Sodium ............................... 0.9712
Steel ....................................... 7.85
Tantalum ................................. 16.6
Tellurium ................................ 6.25
Tin .......................................... 7.29
Titanium ................................... 4.5
Tungsten ..................... 18.6-19.1
Uranium ................................. 18.7
Vanadium ................................. 5.6
Zinc ............................. 7.04 -7.16
HYDROCARBONS 60/600 F.
Ethane ................................ 0.3564
Propane .............................. 0.5077
N-butane ............................ 0.5844
Iso-butane .......................... 0.5631
N-pentane .......................... 0.6310
Iso-pentane ........................ 0.6247
N-hexane ............................ 0.6640
2-methylpentane ................ 0.6579
3-methylpentane ................ 0.6689
2,2-dimethylbutane
(neohexane) ................. 0.6540
2, 3-dimethylbutane .......... 0.6664
N-heptane .......................... 0.6882
2-methylhexane .................. 0.6830
3-methylhexane .................. 0.6917
2, 2-dimethylpentane ......... 0.6782
2, 4-dimethylpentane ......... 0.6773
I, 1-dimethylcyclopentane 0.7592
N-octane ............................ 0.7068
Cyclopentane ..................... 0.7504
Methylcyclopentane .......... 0.7536
Cyclohexane ...................... 0.7834
Methylcyclohexane ........... 0.7740
Benzene .............................. 0.8844
Toulene ............................... 0.8718
LIQUIDS 62°F.
Acetic Acid ........................... 1.06
Alcohol, commercial .............. 0.83
Alcohol, pure ......................... 0.79
Ammonia ................................ 0.89
Benzine .................................. 0.69
Bromine .................................. 2.97
Carbolic acid .......................... 0.96
Carbon disulphide ................. 1.26
Cotton-seed oil ...................... 0.93
Ether, sulphuric .................... 0.72
Fluoric acid ........................... 1.50
Gasoline ................................ 0.70
Kerosene ................................ 0.80
Linseed oil ............................ 0.94
Mineral oil ............................. 0.92
Muriatic acid .......................... 1.20
Naphtha ................................. 0.76
Nitric Acid ............................ 1.50
Olive oil ................................ 0.92
Palm oil ................................. 0.97
Petroleum oil ......................... 0.82
Phosphoric acid .................... 1.78
Rape oil ................................. 0.92
Sulphuric acid ....................... 1.84
Tar .......................................... 1.00
Turpentine oil .................:...... 0.87
Vinegar ................................... 1.08
Water ...................................... 1.00
Water, sea ............................... 1.03
Whale oil ............................... 0.92
GASSES 32°F.
Air ................................................
Acetylene ....................................
Alcohol vapor ..............................
Ammonia.....................................
Carbon dioxide .......... ..................
Carbon monoxide ........................
Chlorine .......................................
Ether vapor ..................................
Ethylene ......................................
Hydrofluoric acid .......................
Hydrogen ....................................
Illuminating gas ...........................
Mercury vapor ............................
Marsh gas ....................................
Nitrogen .......................................
Nitric oxide ..................................
Nitrous oxide ................................
Oxygen ........................................
1.000
0.920
1.601
0.592
1.520
0.967
2.423
2.586
0.967
1.261
0.069
0.400
6.940
0.555
0.971
1.039
1.527
1.106
Sulphur dioxide ............................ 2.250
Water vapor ................................. 0.623
NITSCELLANEOUSSOLIDS
62° F.
Asbestos .................................. 2.4
Asphaltum ............................... 1.4
Borax ........................................ 1.8
Brick, common ...... .................... 1.8
Brick, fire ................................. 2.3
Brick, hard ............................... 2.0
Brick, pressed .......................... 2.2
Brickwork, in mortar ............... 1.6
Brickwork, in cement... ............ 1. 8
Cement, Portland (set) ............. 3.1
Chalk ........................................ 2.3
Charcoal ................................... 0.4
Coal, anthracite ....................... 1.5
Coal, bituminous ..................... 1.3
Concrete ................................... 2.2
Earth, dry ................................. 1.2
Earth, wet.... ............................. 1. 7
Emery ....................................... 4.0
Glass ........................................ 2.6
Granite ..................................... 2.7
Gypsum .................................... 2.4
Ice ............................................ 0.9
Iron slag ................................... 2.7
Limestone ................................ 2.6
Marble ...................................... 2.7
Masonry ................................... 2.4
Mica ......................................... 2.8
Mortar ...................................... 1.5
Phosphorus .............................. I. 8
Plaster of Paris ........................ 1.8
Quartz ...................................... 2.6
Sand, dry .................................. 1.6
Sand, wet ................................. 2.0
Sandstone ................................ 2.3
Slate ......................................... 2.8
Soapstone ................................ 2.7
Sulphur .................................... 2.0
Tar, bituminous ........................ 1.2
Tile ........................................... 1.8
Tap rock ................................... 3.0
Speci~c gravity of sO.lids and liquids is
the ratIO of theIr denSity to the density of
water at a specified temperature.
Specific gravity of gases is the ratio of
their density to the density of air at standard conditions of pressure and temperature.
To find the weight per cubic foot of a
material, multiply the specific gravity
by 62.36.
EXAMPLE: The weight of a cubic foot
of gasoline 62.36 x 0.7 =43.65Ibs.
416
VOLUME OF SHELLS AND HEADS
I.D.
of
Vessel
in.
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
84
90
96
102
108
114
120
126
132
138
144
Cylindrical SHELL/LIN. FT.
Cu.Ft.
0.8
1.1
1.4
1.8
2.2
2.6
3.1
3.7
4.3
4.9
5.6
6.3
7.1
7.9
8.7
9.6
12.6
15.9
19.6
23.8
28.3
33.2
38.5
44.2
50.3
56.7
63.6
70.9
78.5
86.6
95.0
103.9
113.1
2: 1 ELLIP. HEAD*
Gal.
Bbl.
Wt. of
Water
lb.
Cu.Ft.
Gal.
Bbl.
Wt. of
Water
lb.
5.9
8.0
10.4
13.2
16.3
19.7
23.5
27.6
32.0
36.7
41.8
47.2
52.9
58.9
65.3
72.0
94.0
119.0
146.9
177.7
211.5
248.2
287.9
330.5
376.0
424.4
475.9
530.2
587.5
647.7
710.9
777.0
846.0
0.14
0.19
0.25
0.31
0.39
0.47
0.56
0.66
0.76
0.87
0.99
1.12
1.26
1.40
1.55
1.71
2.24
2.83
3.50
4.23
5.04
5.91
6.85
7.87
8.95
10.11
11.33
12.62
13.99
15.42
16.93
18.50
20.14
49
67
87
110
136
165
196
230
267
306
349
394
441
492
545
601
784
993
1226
1483
1765
2071
2402
2758
3138
3542
3971
4425
4903
5405
5932
6484
7060
0.1
0.2
0.3
0.4
0.6
0.8
1.0
1.3
1.7
2.0
2.5
3.0
3.5
4.2
4.8
5.6
8.4
11.9
16.3
21.8
28.3
35.9
44.9
55.2
67.0
80.3
95.4
112.2
130.9
151.5
174.2
190.1
226.2
0.98
1.55
2.32
3.30
4.53
6.03
7.83
9.96
12.44
15.30
18.57
22.27
26.47
31.09
36.27
41.98
62.67
89.23
122.4
162.9
211.5
268.9
335.9
413.1
501.3
601.4
713.8
839.5
979.2
1134
1303
1489
1692
0.02
0.04
0.06
0.08
0.11
0.14
0.19
0.24
0.30
0.36
0.44
0.53
0.63
0.74
0.86
1.00
1.49
2.12
2.91
3.88
5.04
6.40
8.00
9.84
11.94
14.32
17.00
20.00
23.31
27.00
31.03
35.46
40.29
8.17
12.98
19.37
27.58
37.83
50.35
65.37
83.11
103.8
127.7
155.0
185.9
220.1
259.5
302.6
350.4
523.0
744.6
1021
1360
1765
2244
2802
3447
4184
5018
5957
7006
8171
9459
10876
12428
14120
*Volume within the straight flange is not included
417
VOLUME OF SHELLS AND HEADS
1.0.
of
Vessel
in.
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
84
90
96
102
108
114
120
126
132
138
144
ASME F & D. HEAD*
I
Cu.Ft.
Gal.
0.08
0.12
0.19
0.27
0.37
0.50
0.65
0.82
1.10
1.30
1.64
1.88
2.15
2.75
3.07
3.68
5.12
7.30
10.08
13.54
17.65
22.32
28.47
35.56
42.51
52.14
60.96
73.66
84.35
97.32
108.7
127.0
147.9
0.58
0.94
1.45
2.04
2.80
3.78
4.86
6.14
8.21
9.70
12.30
14.10
16.10
20.60
23.00
27.50
38.30
54.60
75.40
101
13~
167
213
266
318
390
456
551
631
728
813
950
1106
I
HEMIS. HEAD*
Bbl.
Wt. of
Water
lb.
Cu.Ft.
Gal.
Bbl.
Wt. of
Water
lb.
0.01
0.04
0.03
0.05
0.07
0.09
0.12
0.15
0.20
0.23
0.29
0.34
0.38
0.49
0.55
0.65
0.91
1.30
1.80
2.41
3.14
3.98
5.07
6.33
7.57
9.29
10.86
13.12
15.02
17.33
19.36
22.62
26.33
4.83
7.83
12.08
17.00
28.33
31.49
40.49
51.15
68.40
80.81
102.5
117.5
134.1
171.6
191.6
229.1
319.1
454.9
628.2
843.9
1100
1391
1775
2216
2649
3249
3799
4590
5257
6065
6773
7915
9214
0.26
0.42
0.62
0.88
1.21
1.61
2.09
2.66
3.33
4.09
4.96
5.95
7.07
8.31
9.70
11.22
16.76
- 23.86
32.73
43.56
56.55
71.90
89.80
110.4
134.0
160.8
190.9
224.5
261.8
303.1
348.5
398.2
452.4
1.96
3.11
4.64
6.61
9.07
12.07
15.67
19.92
24.88
30.60
37.14
44.54
52.88
62.19
72.53
83.97
125.3
178.5
244.8
325.8
423.0
537.8
671.7
826.2
1003
1203
1428
1679
1958
2267
2607
2978
3384
0.05
0.07
0.11
0.16
0.22
0.29
0.37
0.47
0.59
0.73
0.88
1.06
1.26
1.48
1.73
2.00
2.98
4.25
5.83
7.76
10.07
12.80
16.00
19.67
23.87
28.63
34.00
39.98
46.63
53.98
62.06
70.91
80.57
16.34
25.95
38.74
55.16
75.66
100.7
130.7
166.2
207.6
255.4
309.9
371.7
441.2
519.0
605.3
700.7
1046
1489
2043
2719
3530
4488
5606
6895
8368
10037
11914
14012
16343
18919
21752
24856
28241
*Volume within the straight flange is not included
418
PARTIAL VOLUMES IN HORIZONTAL CYLINDERS
l
I
I
~J3
Partial volumes of horizontal cylinder
equals total volume x coefficient
(found from table below)
10
EXAMPLE
HORIZONTAL CYLINDER D = 10 ft., 0 in. H = 2.75 ft. L = 60 ft., 0 in.
TOTAL VOLUME: 0.7854 x D2 xL Find the partial volume of
the cylindrical shell
Total volume: 0.7854 x 102 x 60 = 4712.4 cu. ft.
Coefficient from table:
H/D = 2.75/10 =.275
Refer to the first two figures (.27) in the column headed (H/D) in the table
below. Proceed to the right until the coefficient is found under the column
headed (5) which is the third digit. The coefficient of 0.275 is found to be
.223507
Total volume x coefficient = partial volume
4712.4 x .223507 = 1053.25 cu. ft.
cu. ft. multiplied by 7.480519 = U. S. Gallon
cu. ft. multiplied by 28.317016 = Liter
COEFFICIENTS
H/D
0
1
2
3
4
5
6
7
8
9
.00
.01
.02
.03
.04
.000000
.001692
.004ii3
.008742
.0134li
.0000.'53
.0019.52
.005134
.009179
.013919
.000151
.002223
.005503
.009625
.014427
.000279
.002507
.005881
.010076
.014940
.000429
.002800
.006267
.010534
.015459
.000600
.003104
.006660
.010999
.015985
.000788
.003419
.007061
.011470
.016515
.000992
.003743
.007470
.011947
.017052
.001212
.004077
.007886
.012432
.017593
.001445
.004421
.008:HO
.012920
.018141
.05
.06
.07
.08
.09
.018692
.024496
.030772
.037478
.044579
.0192.50
.025103
.031424
.038171
.04.5310
.019813
.02.5715
.032081
.038867
.046043
.020382
.026331
.032740
.039569
.046782
.0209.5.',)
.026952
.033405
.040273
.047523
.021533
.027578
.034073
.040981
.048268
.022115
.028208
.oa4747
.041694
.049017
.022703
.028842
.035423
.042410
.049768
.023296
.029481
.036104
.043129
.050524
.023894
.030124
.036789
.043852
.051283
.10
.11
.12
.13
.14
.052044
.0598.50
.067972
.076393
.085094
.052810 .0.53579 .0.54351
.060648 .061449 .062253
.068802 .069633 .070469
.0772.51 .078112 .078975
.085979 .086866 .087756
.05.5126
.063062
.071307
.079841
.088650
.055905
.063872
.072147
.080709
.089545
.056688
.064687
.072991
.081581
.090443
.057474
.065503
.073836
.082456
.091343
.058262
.066323
.074686
.083332
.092246
.059054
.067147
.07.5539
.084212
.093153
.15
.16
.17
.18
.19
.094061
.103275
.112728
.122403
.132290
.094971
.104211
.113686
.123382
.133291
.095884
.10.'5147
.114646
.124364
.134292
.096799
.106087
.115607
. 12.5:J47
.135296
.097717
.107029
.116.572
.126333
.136302
.098638
.107973
.1.17538
.127321
.137310
.099560
.108920
.118506
.128310
.138320
.100486
.109869
.119477
.129302
.139332
.101414
.110820
.120450
.130296
.140345
.102343
.111773
.121425
.131292
.141361
.20
.21
.22
.23
.24
.142378
.1526.'59
.163120
.173753
.1845.'50
.143398
.153697
.164176
.174825
.185639
.144419
.1.54737
.165233
.175900
.186729
.145443
.155779
.166292
.176976
.187820
.146468 .147494 .148524 .149554
.156822 .157867 .1.'58915 .l!i9963
.167353 .168416 .169480 .170546
.178053 179131 .180212 .181294
.188912 190007 .191102 .192200
.150587
.161013
.171613
.182378
.193299
.151622
.162066
.172682
.18346:1
.194400
.25
.26
.27
.28
.29
.19.5501
.206600
.2li839
.229209
.240703
.196604
.207718
.218970
.230352
.2418.59
.197709
.208837
.220102
.231498
.243016
.198814
.209957
.221235
.232644
.244173
.199922
.211079
.222371
.233791
.245333
.201031 .202141 .203253
.212202 .213326 .214453
.223507 .224645 .225783
.234941 .236091 .237242
.246494 .247655 .248819
.204368
.215580
.226924
.238395
.249983
.205483
.216708
.228065
.239548
.251148
.:30
.31
.2.')231.5
.264039
.253483 .254652 .255822
.265218 .266397 .267578
.256992 .258165 .259338 .260512
.268760 .269942 .271126 .272310
.261687 .262863
.273495 .274682
419
PARTIAL VOLUMES IN HORIZONTAL CYLINDERS COEFFICIENTS (Cont.)
HID
0
1
2
3
4
5
6
7
8
9
.285401 .286598
.297403 .298605
.309492 .310705
.32
.33
.34
.275869 .277058 .278247 .279437
.287795 .288992 .290191 .291390
.299814 .301021 .302228 .3034:38
.280627 .281820
.292591 .293793
.304646 .305857
.35
.:36
.37
.38
.39
.:311918
.324104
.336363
.348690
.:mI082
.313134
.325:326
.337593
.349926
.36232.')
.:314350
.:326550
.338823
.:351164
.363568
.315566
.327774
.340054
.3.'>2402
.364811
.31678a
.328999
.341286
.353640
.366056
.318001
.330225
.342519
.354879
.367300
.:319219
.331451
.343751
.3.'>6119
.:368545
.320439
.332678
.344985
.357359
. 3697!)()
.321660
.333905
.346220
.358599
.371036
.322881
.335134
.3474.'>5
.359840
.372282
.40
,41
,42
,43
.:373530
.:3860:m
.:398.577
,41116:)
.42;m;8
.:374778
.387283
.:m9834
,412426
.42.5052
.376026
.388537
.401092
.413687
,426316
.377275
.389790
.402350
.414949
.427,582
.378,524
.391044
.403608
.416211
.428846
.379774
.392298
.404866
.417473
,4:30112
.:381024
.393M3
.40612.5
.418736
.431:378
.382274
.394808
.407384
.419998
.4:~2645
.383526
.:396063
.408645
.421261
.433911
.384778
.397320
.409904
.422.'52:'5
.43.5li8
.444050
.456741
.469453
.482176
.494906
.445318
.458012
.470725
.483449
,496179
.446587
.459283
.471997
.484722
.497452
.447857
.460554
.473269
.485995
.498726
A4
.283013 .284207
.294995 .296198
.307068 .308280
.45
,46
.47
.48
.49
.43644.5
.44912.')
.461825
.474541
.487269
.437712
.450394
.463096
.475814
o4R8.542
.438979
.451663
.464367
.477086
o48!l814
.440246
.4,52932
.465638
.4783.58
.491087
.441,514
.4.54201
.466910
.479631
.492360
.442782
.455472
.468182
.480903
.493633
.50
.51
.52
.:i3
.54
.500000
.512731
.525459
.53817,5·
.550875
.501274
.514005
.526731
.5:39446
.,5,52143
.502548
..515278
.528003
..540717
.,55a4U
.503821
.5165.51
.52927.5
.541988
.5.54682
..505094
..517824
.530547
..543259
.5.559,50
.506367
.:'510097
.,531818
.,544,528
.:'557218
.507640
.520369
.533090
.545799
.558486
.508913
..521642
.534362
.547068
.559754
.510186
.,522914
.,535633
.548337
.561021
.511458
.524186
.536904
.549606
.562288
.55
.,56
.57
.58
.59
.5635.55
.576212
588835
.601423
.613970
.564822
.577475
.590096
.602680
.615222
.566089
..578739
.591355
.60:3937
.616474
.56n55
..,)80002
.592616
.605192
.617726
..'568622
.581264
.593875
.606447
.618976
.:'569888
..582527
.595134
.607702
.620226
.571154
.583789
.596392
.608956
.621476
..,)72418
.58,5051
.597650
.610210
.622725
.573684
..586313
.598908
.611463
.623974
.574948
.587574
.600166
.612717
.625222
.1i0
.61
62
.63
.1\4
.626470
.638918
.651:UO
.663637
.tl758!l6
.027718
.640160
.652545
.664866
.677119
.628!)64
.1\41401
.6.'i:mm
.6fif!095
.H71n40
.630210 .6:n·I.')i'l .632700
.642641 .64:3~R1 .645121
.6SS01S .65624!l .0."i7481
.607322 .6f>R."i4!l .669775
.G7!)561 .680781 .681!}!}9
.63:J!)44
.646360
.658714
.671001
.683217
.63518!)
.647.')98
.659946
.672226
.fl84434
.636432
.648836
.661177
.673450
.68.')6.'50
.637675
.6.')0074
.662407
.674674
.686866
.fi.'l
.fl6
.H7
.fi8
.fI!)
.688082
.700186
.712205
.724131
.7:W161
.6R929.'5
.701392
.713402
.72.5:318
.7:37137
.GHO!iOS
.702.')97
.7 I 45!)!}
.72650.')
.7:3S31a
.691720
.703802
.69;')3.')4
.707409
.719373
.731240
.74:l00R
.696.'562
.708610
.720.563
.732422
.74417S
.697772
.709809
.721753
.733603
.74.5348
.698979
.711008
.722942
.n4782
.74(i.')17
.70
.71
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.700c)4:l
.80l1S(i
.7.')6984
.768502
.779898
.791163
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.7,')8141
.i6!l64S
.7810:m
.792282
.727690
.7394SR
.6!)2!l32
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.716987
.728874
.740H62
.694143
.706207
.718180
.7300.58
.7.,)IIS1
.7627:)S
.774217
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.826247
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.847341
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.816.')37
.827318
.8:n9:34
.848:m,
.8OGiOI
:817622
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.838987
.84941:\
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.829454
.lW)()37
.8.'>0446
.808898
.819788
.8:l0.520
.84108.')
.8.')14i6
.S0099:!
.R20869
.831584
.842133
.8.'>2.')06
.R11088
.821947
.832647
.843178
.8.5:l532
.R12180
.823024
.8:l3708
.844221
.8.54.5.')7
.813271
.824100
.834767
.845263
.855581
.814361
.825175
.835824
.846303
.856602
.80
.81
.82
.83
.84
.857(i22
.8G7710
.877597
.887272
.896725
.8586:39
.868708
.87857.,>
.888227
.897657
.8.')9655
.8tl9704
.879.'>50
.889180
.898586
.860668
.870698
.880523
.8!}0131
.899514
.861680
.871690
.881494
.891080
.900440
.862690
.872679
.882462
.892027
.901362
.863698
.873667
.883428
.892971
.902283
.864704
.874653
.884393
.893913
.903201
.865708
.875636
.885354
.894853
.904116
.866709
.876618
.886314
.895789
.905029
.8.'>
.86
.87
.88
.89
.905939
.914906
.923607
.932028
.940150
.906847
.915788
.924461
.932853
.940946
.!lO7754 .908657
.916668 .917.544
.925:n4 .926164
.933677 .934497
.941738 .942526
.909557
.918419
.927009
.935313
.943312
.910455
.919291
.927853
.936128
.944095
.911350
.920159
.928693
.936938
.944874
.912244
.921025
.929531
.937747
.945649
.913134
.921888
.930367
.938551
.946421
.914021
.922749
.931198
.939352
.947190
.90
.91
.92
.947956 .948717
.955421 .956148
.962522 .96:-1211
.!l49476 .9S0232
.956871 .957590
.963896 .964577
.950983 .9.'>1732
.958306 .959019
.965253 .965927
.952477 .953218
.959727 .960431
.966595 .967260
.953957 .954690
.961133 .961829
.967919 .968.')76
420
PARTIAL VOLUMES IN HORIZONTAL CYLINDERS COEFFICIENTS (cont.)
HID
.!l3
.94
.9!i
.!)(i
.Hi
.98
. HI)
1.00
0
1
.!If>!l22R .!lIM'il)
.97!i.504 .97f>106
.!lSlaOR
.!lX()58:{
.!lHl2.,)8
.91):;227
.H9S30X
1.000000
.9S18;,)!l
.!lRiOSO
.!l!lHi!)()
.!lH!ii'i7!l
.!I!lk.').'lii
2
3
4
.HiO;")l9 .!lill.')~ .!liI792
.976i04 .!l772!l7 .!lii88.'}
.HX240i
.987.,)6R
.!l!)2114
.!l9i'i923
.!19878B
.982948
.!l88();):{
.H!l2i'j:{O
.996257
.999008
5
.972422
.978467
.98348.') .984015
.988530 .989001
.992939 .9!J3340
.996.,}81 .996896
.999212 .999400
6
7
8
9
.!17:1048 .973669
.97D045 .979618
.974285
.980187
.974897
.980750
.984541
.98946(\
.99:1733
.997200
.999.571
.98.,}573
.990375
.994497
.997777
.999849
.986081
.990821
.994866
.998048
.999947
.985060
.989924
.994119
.997493
.9D9721
421
PARTIAL VOLUMES IN HORIZONTAL CYLINDERS
(pp.rcentage Relation of Diameter to Volume)
10
20
30
40
I
50
I
60
PERCENTAGE OF TOTAL DIAMETER
70
100 HID
80
90
100
422
PARTIAL VOLUMES IN ELLIPSOIDAL HEADS AND SPHERES
~
0
Two 2: 1 Ellipsoidal
Heads on Horizontal
Vessel
Total Volume: 0.2618 D3
D
Q~Q
Two 2: 1 Ellipsoidal
Heads on Vertical Vessel
Total Volume: 2.0944 D3
D
H
O~HO
Sphere
Total Volume: 0.5236 D3
Partial volumes of ellipsoidal heads and spheres equals
total volume x coefficient (found from table below)
EXAMPLE:
D = 10ft., 0 in.
H=2.75 ft.
Find the partial volume of(2) 2: 1 ellipsoidal heads ofa
horizontal vessel. The total volume of the two heads:
0.2618 x D3 = 0.2618 x 103 = 261.8 cu. ft.
Coefficient from table:
HID=2.75110 = .275
Referr to the first two figures (.27) in the column headed
(HID) in the table below. Proceed to the right until the
coefficient is found under the column headed (5) which
is the third digit. The coefficient of .275 is found to be
.185281.
Total volume x coefficient = partial volume
261.8 x 185281 = 48.506 cu. ft.
cu. ft. multiplied by 7.480519 = U.S. Gallon
c.u. ft. multiplied by 28.317016 = Liter
COEFFICIENTS
HID
.00
.01
.02
.03
.04
.000003
.000360
.001304
.002823
.004905
2
.000012
.000429
.001431
.003006
.005144
3
.000027
.000503
.001563
.003195
.005388
0
.000000
.000298
.001184
.002646
.004672
4
.000048
.000583·
.001700
.003389
.005638
5
.000075
.000668
.001844
.003589
.005893
6
.000108
.000760
.001993
.003795
.006153
.05
.06
.07
.08
.09
.007250
.010368
.014014
.018176
.022842
.007538
.010709
.014407
.018620
.023336
.007831
.011055
.014806
.019069
.023835
.008129
.011407
.015209
.019523
.024338
.008433
.011764
.015618
.019983
.024847
.008742
.012126
.016031
.020447
.025360
.10
.11
.12
.13
.14
.028000
.033638
.039744
.046306
.053312
.028542
.034228
.040380
.046987
.054037
.029090
.034822
.041020
.047672
.054765
.029642
.035421
.041665
.048362
.055499
.030198
.036025
.042315
.049056
.056236
.030760
.036633
.042969
.049754
.056978
1
.000146
.000857
.002148
.004006
.006419
8
.000191
.000960
.002308
.004222
.006691
9
.000242
.001069
.002474
.004444
.006968
.009057
.012493
.016450
.020916
.025879
.009377
.012865
.016874
.021390
.026402
.009702
.013243
.017303
.021869
.026930
.010032
.013626
.017737
.022353
.027462
.031326
.037246
.043627
.050457
.057724
.031897
.037864
.044290
.051164
.058474
.032473
.038486
.044958
.051876
.059228
.033053
.039113
.045630
.052592
.059987
7
.15 .060750 .061517 .062288 .063064 .063843 .064627 .065415 .066207 .067003 .067804
.16 .068608 .069416 .070229 .071046 .071866 .072691 .073519 .074352 .075189 .076029
.17 .076874 .077723 .078575 .079432 .080292 .081156 .082024 .082897 .083772 .084652
423
PARTIAL VOLUMES IN ELLIPSOIDAL HEADS AND SPHERES: COEFFICIENTS (Cont.)
HID
0
1
2
3
4
5
6
7
9
8
.18 .085536 .086424 .087315 .. 088210 .089109 .090012 .090918 .091829 .092743 .093660
.19 .094582 .095507 .096436 .097369 .098305 .099245 .1 00189 .101136 .102087 .103042
.20
.21
.22
.23
.24
.104000
.113778
.123904
.134366
.145152
.104962
.114775
.124935
.135430
.146248
.105927
.115776
.125970
.136498
.147347
.106896
.116780
.127008
.137568
.148449
.107869
.117787
.128049
.138642
.149554
.108845
.118798
.129094
.139719
.150663
.109824
.119813
.130142
.140799
.151774
.110808
.120830
.131193
.141883
.152889
.111794
.121852
.132247
.142969
.154006
.112784
.122876
.133305
.144059
.155127
.25
.26
.27
.28
.29
.156250
.167648
.179334
.191296
.203522
.157376
.168804
.180518
.192507
.204759
.158506
.169963
.181705
.193720
.205998
.159638
.171124
.182894
.194937
.207239
.160774
.172289
.184086
.196155
.208484
.161912
.173456
.185281
.197377
.209730
.163054
.174626
.186479
.198601
.210979
.164198
.175799
.187679
.199827
.212231
.165345
.176974
.188882
.201056
.213485
.166495
.178153
.190088
.202288
.214741
.30
.31
.32
.33
.34
.216000
.228718
.241664
.254826
.268192
.217261
.230003
.242971
.256154
.269539
.218526
.231289
.244280
.257483
.270889
.219792
.232578
.245590
.258815
.272240
.221060
.233870
.246904
.260149
.273593
.222331
.235163
.248219
.261484
.274948
.223604
.236459
.249536
.262822
.276305
.224879
.237757
.250855
.264161
.277663
.226157
.239057
.252177
.265503
.279024
.227437
.240359
.253500
.266847
.280386
.35
.36
.37
.38
.39
.281750
.295488
.309394
.323456
.337662
.283116
.296871
.310793
.324870
.339090
.284484
.298256
.312194
.326286
.340519
.285853
.299643
.313597
.327703
.341950
.287224
.301031
.315001
.329122
.343382
.288597
.302421
.316406
.330542
.344815
.289972
.303812
.317813
.331963
.346250
.291348
.305205
.319222
.333386
.347685
.292727
.306600
.320632
.334810
.349122
.294106
.307996
.322043
.336235
.350561
.40
.41
.42
.43
.44
.352000
.366458
.381024
.395686
.410432
.353441
.367910
.382486
.397157
.411911
.354882
.369363
.383949
.398629
.413390
.356325
.370817
.385413
.400102
.414870
.357769
.372272
.386878
.401575
.416351
.359215
.373728
.3-88344
.403049
.417833
.360661
.375185
.389810
.404524
.419315
.362109
.376644
.391278
.406000
.420798
.363557
.378103
.392746
.407477
.422281
.365007
.379563
.394216
.408954
.423765
.45
.46
.47
.48
.49
.425250
.440128
.455054
.470016
.485002
.426735
.441619
.456549
.471514
.486501
.428221
.443110
.458044
.473012
.488001
.429708
.444601
.459539
.474510
.489501
.431195
.446093
.461035
.476008
.491000
.432682
.447586
.462531
.477507
.492500
.434170
.449079
.464028
.479005
.494000
.435659
.450572
.465524
.480504
.495500
.437148
.452066
.467021
.482003
.497000
.438638
.453560
.468519
.483503
.498500
.50
.51
.52
.53
.54
.500000
.514998
.529984
.544946
.559872
.501500
.516497
.531481
.546440
.561362
.503000
.517997
.532979
.547934
.562852
.504500
.519496
.534476
.549428
.564341
.506000
.520995
.535972
.550921
.565830
.507500
.522493
.537469
.552414
.567318
.509000
.523992
.538965
.553907
.568805
.510499
.525490
.540461
.555399
.570292
.511999
.526988
.541956
.556890
.571779
.513499
.528486
.543451
.558381
.573265
.55
.56
.57
.58
.59
.574750
.589568
.604314
.618976
.633542
.576235
.591046
.605784
.620437
.634993
.577719
.592523
.607254
.621897
.636443
.579202
.594000
.608722
.623356
.637891
.580685
.595476
.610190
.624815
.639339
.582167
.596951
.611656
.626272
.640785
.583649
.598425
.613122
.627728
.642231
.585130
.599898
.614587
.629183
.643675
.586610
.601371
.616051
.630637
.645118
.588089
.602843
.617514
.632090
.646559
424
PARTIAL VOLUMES IN ELLIPSOIDAL HEADS AND SPHERES: COEFFICIENTS (Cont.)
1
3
4
5
6
7
HID
0
2
8
9
.60
.61
.62
.63
.64
.648000
.662338
.676544
.690606
.704512
.649439
.663765
.677957
.692004
.705894
.650878
.665190
.679368
.693400
.707273
.652315
.666614
.680778
.694795
.708652
.653750
.668037
.682187
.696188
.710028
.655185
.669458
.683594
.697579
.711403
.656618
.670878
.684999
.698969
.712776
.658050
.672297
.686403
.700357
.714147
.659481
.673714
.687806
.701744
.715516
.660910
.675130
.689207
.703129
.716884
.65
.66
.67
.68
.69
.718250
.731808
.745174
.758336
.771282
.719614
.733153
.746500
.759641
.772563
.720976
.734497
.747823
.760943
.773843
.722337
.735839
.749145
.762243
.775121
.723695
.737178
.750464
.763541
.776396
.725052
.738516
.751781
.764837
.777669
.726407
.739851
.753096
.766130
.778940
.727760
.741185
.754410
.767422
.780208
.719111
.742517
.755720
.768711
.781474
.730461
.743846
.757029
.769997
.782739
.70
.71
.72
.73
.74
.784000
.796478
.808704
.820666
.832352
.785359
.797712
.809912
.821847
.833505
.786515
.798944
.811118
.823026
.834655
.787769
.800173
.812321
.824201
.835802
.789021
.801399
.813521
.825374
.836946
.790270
.802623
.814719
.826544
.838088
.791516
.803845
.815914
.827711
.839226
.792761
.805063
.817106
.828876
.840362
.794002
.806280
.818295
.830037
.841494
.795241
.807493
.819482
.831196
.842624
.75
.76
.77
.78
.79
.843750
.854848
.865634
.876096
.886222
.844873
.855941
.866695
.877124
.887216
.845994
.857031
.867753
.878148
.888206
.847111
.858117
.868807
.879170
.889192
.848226
.859201
.869858
.880187
.890176
.849337
.860281
.870906
.881202
.891155
.850446
.861358
.871951
.882213
.892131
.851551
.862432
.872992
.883220
.893104
.852653
.863502
.874030
.884224
.894073
.853752
.864570
.875065
.885225
.895038
.80
.81
.82
.83
.84
.896000
.905418
.914464
.923126
.931392
.896958
.906340
.915348
.923971
.932196
.897913
.907257
.916228
.924811
.932997
.898864
.908171
.917103
.925648
.933793
.899811
.909082
.917976
.926481
.934585
.900755
.909988
.918844
.927309
.935373
.901695
.910891
.919708
.928134
.936157
.902631
.911790
.920568
.928954
.936936
.903564
.912685
.921425
.929771
.937712
.904493
.913576
.922277
.930584
.938483
.85
.86
.87
.88
.89
.939250
.946688
.953694
.960256
.966362
.940013
.947408
.954370
.960887
.966947
.940772
.948124
.955042
.961514
.967527
.941526
.948836
.955710
.962136
.968103
.942276
.949543
.956373
.962754
.968674
.943022
.950246
.957031
.963367
.969240
.943764
.950944
.957685
.963975
.969802
.944501
.951638
.958335
.964579
.970358
.945235
.952328
.958980
.965178
.970910
.945963
.953013
.959620
.965772
.971458
.90
.91
.92
.93
.94
.972000
.977158
.981824
.985986
.989632
.972538
.977647
.982263
.986374
.989968
.973070
.978131
.982697
.986757
.990298
.973598
.978610
.983126
.987135
.990623
.974121
.979084
.983550
.987507
.990943
.974640
.979553
.983969
.987874
.991258
.975153
.980017
.984382
.988236
.991567
.975662
.980477
.984791
.988593
.991871
.976165
.980931
.985194
.988945
.992169
.976664
.981380
.985593
.989291
.992462
.95
.96
.97
.98
.99
.992750
.995328
.997354
.998816
.999702
.993032
.995556
.997526
.998931
.999758
.993309
.995778
.997692
.999040
.999809
.993581
.995994
.997852
.999143
.999854
.993847
.996205
.998007
.999240
.999892
.994107
.996411
.998156
.999332
.999925
.994362
.996611
.998300
.999417
.999952
.994612
.996805
.998437
.999497
.999973
.994856
.996994
.998569
.999571
.999988
.995095
.997177
.998696
.999640
.999997
1.00 1.000000
425
AREA OF SURFACES
(In Square Feet)
* The area of straight flanges is not included in the figures of the table.
Outside
Diameter
of Vessel
o inches
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
48
54
60
66
72
78
84
90
96
102
108
114
120
126
132
138
144
Cylindrical
Shell per
Lineal Foot
( 7r X D)
2: I
Ellipsoidal
Head*
(1.09 x 0 2)
3.14
3.66
4.19
1.09
1.48
1.94
2.45
3.02
3.66
4.36
5.12
5.92
6.81
7.76
8.75
9.82
10.93
12.11
13.35
17.47
22.09
27.30
33.10
39.20
46.00
53.40
61.20
69.80
78.80
88.25
98.25
109.00
120.11
132.00
144.00
157.00
4.71
5.23
5.76
6.28
6.81
7.32
7.85
8.37
8.90
9.43
9.94
10.47
11.00
12.57
14.14
15.71
17.28
18.85
20.42
21.99
23.56
25.20
26.70
28.27
29.85
31.50
32.99
34.56
36.20
37.70
ASME¥
HemisFlat
Flanged and
pherical
Head*
Dished Head
Head*
(0.918 x 0 2) (1.5708 x 0 2) (0.7854 x 0 2)
0.92
1.25
1.64
2.07
2.56
3.10
3.68
4.32
5.00
5.76
6.53
7.39
8.29
9.21
10.20
11.25
14.70
18.60
23.60
27.80
33.00
38.85
45.00
51.60
58.90
66.25
74.35
83.00
92.00
100.85
111.50
121.50
132.20
1.57
2.14
2.79
3.53
4.36
5.28
6.28
7.08
8.55
9.82
11.17
12.11
14.14
15.75
17.44
19.23
25.13
31.81
39.27
47.52
56.55
66.37
76.97
88.37
100.54
113.43
127.25
141.78
157.08
173.20
190.09
207.76
226.22
0.79
1.07
1.40
1.77
2.18
2.64
3.14
3.69
4.28
4.91
5.58
6.31
7.07
7.88
8.72
9.62
12.57
15.90
19.64
23.76
28.27
33.18
38.49
44.16
50.27
56.25
63.62
70.88
78.87
86.59
95.03
102.00
113.50
426
DECIMALS OF AN INCH
WITH MILLIMETER EQUIVALENTS
Decimal
!U
~6
~
VB
~
~6
~
~
.03125
.0625
.09375
.125
.15625
.1875
.21875
.25
MiIIimeter
.794
1.587
2.381
3.175
3.969
4.762
5.556
6.350
Decimal
~
%'6
l~
VB
l~
h6
1~
Y2
.28125
.3125
.34375
.375
.40625
.4375
.46875
.5
MiIIimeter
7.144
7.937
8.731
9.525
10.319
11.113
11.906
12.700
IJ.i2
~
l~
%
%
l~
23~
3/
/4
Decimal
Mill imeter
.53125
.5625
.59375
.625
13.494
14.287
15.081
15.875
.65625
.6875
.71875
.75
Decimal
Millimeter
.78125
.8125
.84375
.875
19.844
20.637
21.431
22.225
.90625
.9375
.96875
1.
23.019
23.812
24.606
25.400
25~
l~
27Al
Ys
29~
16.669
17.462
18.256
19.050
15,,{6
3~
1
DECIMALS OF A FOOT
INCHES
8
9
10
11
.5833
.5885
.5937
.5989
.6667
.6719
.6771
.6823
.7500
.7552
.7604
.7656
.8333
.8385
.8437
.8489
.9167
.9219
.9271
.9323
.5208
.5260
.5313
.5365
.6041
.6093
.6146
.6198
.6875
.6927
.6980
.7032
.7708
.7760
.7813
.7865
.8541
.8593
.8646
.8698
.9375
.9427
.9480
.9532
.4584
.4636
".4688
.4740
.5417
.5469
.5521
.5573
.6250
.6302
.6354
.6406
.7084
.7136
.7188
.7240
.7917
.7969
.8021
.8073
.8750
.8802
.8854
.8906
.9584
.9336
.9f)88
.9740
.4792
.4844
.4896
.4948
.5625
.5677
.5729
.5781
.6458
.6510
.6562
.6614
.7292
.7344
.7396
.7448
.8125
.8177
.8229
.8281
.8958
.9010
.9062
.9114
.9792
.9844
.9896
.9948
In.
0
1
2
0
.0000
.0052
.0104
.0156
.0833
.0885
.0937
.0989
.1667
.1719
.1771
.1823
.2500
.2552
.2604
.2656
.3333
.3385
.3437
.3489
.4167
.4219
.4271
.4323
.5000
.5052
.5104
.5156
~
~6
~
.0208
.0260
.0313
.0365
.1041
.1093
.1146
.1198
.1875
.1927
.1980
.2032
.2708
.2760
.2813
.2865
.3541
.3593
.3646
.3698
.4375
.4427
.4480
4532
Y2
.0417
.0469
.0521
.0573
.1250
.1302
.1354
.1406
.2084
.2136
.2188
.2240
.2917
.2969
.3021
.3073
.3750
.3802
.3854
.3906
.0625
.0677
.0729
.0781
.1458
.1510
.156:!
.1614
.2292
.2344
.2396
.2448
.3125
.3177
.3229
.3281
.3958
.4010
.4062
.4114
~6
VB
~6
Us
%1
%
1~6
%
1~6
%
l~fI
3
4
5
6
7
427
METRIC SYSTEM OF MEASUREMENT
This system has the advantage that it is a coherent system. Each quantity has only one
unit and all base units are related to each other. The fractions and mUltiples of the units
are made in the decimal system.
UNITS OF METRIC MEASURES
unit
meter
meter2
meter)
gram
second
degree Celsius
Length
Area
Volume
Weight Imassl
Time
Temperature
symbol
m
m2
m3
g
s
°C
equivalent of
39.37 in
1.196 sq.yard
1.310 cu.yard
0.035 oz
second
DoC = 32°F
100°C = + 212°F
MULTIPLES AND FRACfIONS OF UNITS
Symbol
Unit Multiplied by
Prefix
mikro
milli
centi
deci
deka
hekto
kilo
mega
~
m
c
d
D
h
k
M
Name
10-6
millionth
10-)
10- 2
10- 1
10
102
103
106
thousendth
hundredth
tenth
ten
hundred
thousand
million
EXAMPLE: Unit of weight is gram; 1000 gram is one kilogram, 1 kg
en
~
....JEo-<
1 ,OOOm = 1 kilometer, km
~Z
~::J
::J~
::Eo
MEASURES OF LENGTH
UNIT: METER, m
en
Z
9t:
bz
~ ~o_
~
*1 decimeter, dm = O.lm
1 centimeter, cm = 0.01 m
1 millimeter, mm = 0.001 m
*not used in practice
428
METRIC SYSTEM OF MEASUREMENT
1,000,ooom2 = 1 sq. kilometer, km2
10,000 m2 = 1 sq. hectare, ha
100 m2 = 1 sq. are, a *
r:a
......lE-<
Q..-
Z
;:J
6
;:J
:E
~
0
MEASURES OF AREA
UNIT: SQUARE METER, m2
CI)
Z
9E-< t:
Z
~
;:J
*1 sq. decimeter, dm 2 = 0.01m2
1 sq. centimeter, cm 2 = 0.0001m2
1 sq. millimeter, mm 2 = 0.000,00Im2
~
0
*not used in practice
CI)
r..tJ
not used in practice
E-<
~Z
tl ;:J
;:J
:E
~
0
MEASURES OF VOLUME
UNIT: CUBIC METER, m 3
CI)
Z
0 E-<
1= Z
U ;:J
~
g: 0
~
1 hectoliter, hI =
1 liter, -I =
1 cu. centimeter =
1 cu. millimeter =
0.lm 3
0.001m3
0.000,00Im 3
0.OOO,000,00Im3
CI)
1,000,000
100,000
1,000
10
g=
g=
g=
g=
1 ton, t
1 quintal, q
1 kilogram, kg
I dekagram, dg
MEASURES OF WEIGHT
UNIT: GRAM, g
CI)
Z
0
- t:
E-<
u Z
;:J
~~
centigram, cg = 0.01 g
milligram, mg = 0.001 g
r..tJ
......l
Q..
t:
:E
0
z
;:J
6
;:J
~
429
METRIC SYSTEM OF MEASUREMENT
km
1
1
1
1
1
1
1
km
m
dm*
em
mm
J-L
mJ-L
1
10-3
lOA
10-5
10-6
10-9
10- 12
m
MEASURES OF LENGTH
em
mm
dm
103
1
10- 1
10- 2
10-3
10-6
10-9
104
10
1
10- 1
10- 2
10-5
10-8
106
103
102
10
1
10-3
10-6
105
102
10
1
10- 1
lOA
10-7
J-L
mJ-L
109
106
105
104
103
1
10-3
10 12
109
108
107
106
103
1
MEASURES OF AREA
1
1
1
1
1
1
1
km 2
ha
a
m2
dm2
cm2
mm2
km 2
ha
a
m2
dm 2
cm2
mm 2
1
10- 2
lOA
102
1
10- 2
10-6
10-8
10-10
10- 12
lOA
104
102
1
10- 2
10-6
10- 8
10-10
lOA
106
104
102
1
10- 2
10-6
10- 8
lOA
108
106
104
102
1
10- 2
10-6
lOA
1010
108
106
104
102
1
10- 2
10 12
1010
108
106
104
102
1
MEASURES OF VOWME
m3
1
1
1
1
1
1
m
3
hI
I
dm 3
em 3
mm 3
dm 3
em 3
mm 3
103
103
106
102
1
1
10- 3
10-6
10 2
1
1
10- 3
10- 6
105
103
103
1
10- 3
109
108
106
106
103
1
hI
1
10- 1
10- 3
10- 3
10-6
10-9
10
1
10- 2
10- 2
10-5
10-8
MEASURES OF WEIGHT
1 t
~ q
1 kg
1 dg
1 g
1 eg
1 mg
10- 1
10-3
10-5
10-6
lO- B
10-9
q
kg
dg
g
eg
mg
10
1
10- 2
103
10 2
1
10- 2
10-3
10-5
10-6
105
104
102
I
10- 1
10- 3
106
105
103
10
1
10- 2
10-3
108
107
105
103
102
1
10- 1
109
lOB
106
104
103
10
1
lOA
10-5
10- 7
10-B
lOA
EXAMPLE CALCULATION
Weight of the water in a cylindrical vessel of 2,000 mm inside diameter and
10,000 mm length:
3.1416 x 1,0002 X 10,000 = 31,416,000,000 mm 3
31,416 liter, 1
31.416 cu. meter, m
31416 kilogram, kg
(The weight of one liter of pure water at the maximum
density (4°C) equals one kilogram.)
430
METRIC SYSTEM OF MEASUREMENT
RECOMMENDED PRESSURE VESSEL DIAMETERS
Diameter
in inches
Diameter in
millimeters
Diameter
in inches
Diameter in
millimeters
24-30
36
42-48
54-60
630
800
1,000
1,250
66-72
78-90
96-120
126-156
1,600
2,000
2,500
3,150
RECOMMENDED TANK DIAMETERS
Diameters
in API feet
10
15
20
25
30
35-40
45-50
60
Diameters
in meters
Diameters
in API feet
Diameters
in meters
3.15
4.00
5.00
6.30
8.00
10.00
12.50
16.00
70-80
90-100
120
140-163
180-200
220-240
260-300
20.00
25.00
31.50
40.00
50.00
63.00
80.00
The recommended diameters are based on a geometric progression, called Renard
Series (RIO) of Preferred Numbers. *
Dimensions on drawings shall be expressed in millimeters. The symbol for millimeters, mm (no period) need not be shown on the drawings. However, the following note
shall be shown on the darawings: ALL DIMENSIONS ARE IN MILLIMETERS.
Dimensions above 5 digits in millimeters may be expressed in meters ( e.g. 110.75 m)
Scales if Metric Drawings: enlarging the object, 2, 5, 10, 20 times reducing the
object in proportion of 1:2.5, 1:5, 1:10, 1:20, 1:50, 1:100, 1:200, 1:500, 1:1000
* Reference:
Makin!? it with Metric. The National Board of Boiler and Pressure
Vessel Inspectors.
CONVERSION TABLE - LENGTH
INCHES TO MILLIMETERS
(l Inch = 25.4 Millimeters)
IN.
0
1/16
1/8
3/16
1/4
5/16
3/8
7/16
1/2
9/16
5/8
11/16
3/4
13/16
7/8
15/16
0
1
1
3
4
0.0
15.4
50.8
76.1
101.6
1.6
27.0
52.4
77.8
103.1
3.2
28.6
54.0
79.4
104.8
4.8
30.2
55.6
81.0
106.4
6.4
31.8
57.2
82.6
108.0
7.9
33.3
58.7
84.1
109.5
9.5
34.9
60.3
85.7
111.1
11.1
36.5
61.9
87.3
112.7
12.7
38.1
63.5
88.9
114.3
14.3
39.7
65.1
90.5
115.9
15.9
41.3
66.7
92.1
117.5
17.5
42.9
68.3
93.7
119.1
19.1
44.5
69.9
95.3
120.7
20.6
46.0
71.4
96.8
122.2
22.2
47.6
73.0
98.4
123.8
23.8
49.2
74.6
100.0
125.4
5
6
7
8
9
127.0
152.4
177.8
203.2
128.6
128.6
154.0
179.4
204.8
230.2
130.2
155.6
181.0
206.4
231.8
131.8
157.2
182.6
208.0
233.4
133.4
158.8
184.2
209.6
235.0
134.9
160.3
185.7
211.1
236.5
136.5
161.9
187.3
212.7
238.1
138.1
163.5
188.9
214.3
239.7
139.7
165.1
190.5
215.9
241.3
141.3
166.7
192.1
217.5
242.9
142.9
168.3
193.7
219.1
244.5
144.5
169.9
195.3
220.7
246.1
146.1
171.5
196.9
221.3
247.7
147.6
173.0
198.4
223.8
249.2
149.2
174.6
200.0
225.4
250.8
150.8
176.2
201.6
227.0
252.4
10
11
12
13
14
154.0
279.4
304.8
330.2
355.6
255.6
281.0
306.4
331.8
357.2
257.2
282.6
308.0
333.4
358.8
258.8
284.2
309.6
335.0
360.4
260.4
285.8
311.2
336.6
362.0
261.9
287.3
312.7
338.1
363.5
263.5
288.9
314.3
339.7
365.1
265.1
290.5
315.9
341.3
366.7
266.7
292.1
317.5
342.9
368.3
268.3
293.7
319.1
344.5
369.9
269.9
295.3
320.7
346.1
371.5
271.5
296.9
322.3
347.7
373.1
273.1
298.5
323.9
349.3
374.7
274.6
300.0
325.4
350.8
376.2
276.2
301.6
327.0
352.4
377.8
277.8
303.2
328.6
354.0
379.4
15
'16
17
18
19
381.0
406.4
431.8
451.2
482.6
382.6
408.0
433.4
458.8
484.2
384.2
409.6
435.0
460.4
485.8
385.8
411.2
436.6
462.0
487.4
387.4
412.8
438.2
463.6
489.0
388.9
414.3
439.7
465.1
490.5
390.5
415.9
441.3
466.7
492.1
392.1
417.5
442.9
468.3
493.7
393.7
419.1
444.5
469.9
495.3
395.3
420.7
446.1
471.5
496.9
396.9
422.3
447.7
473.1
498.5
398.5
423.9
449.3
474.7
500.1
400.1
425.5
450.9
476.3
501.7
401.6
427.0
452.4
477.8
503.2
403.2
428.6
454.0
479.4
504.8
404.8
430.2
455.6
481.0
506.4
20
21
508.0
533.4
558.8
584.2
609.6
509.6
535.0
560.4
585.8
611.1
511.2
536.6
562.0
587.4
612.8
512.8
538.2
563.6
589.0
614.4
514.4
539.8
565.2
590.6
616.0
515.9
541.3
566.7
592.1
617.5
517.5
542.9
568.3
593.7
619.1
519.1
544.5
569.9
595.3
620.7
520.7
546.1
571.5
596.9
622.3
522.3
547.7
573.1
598.5
623.9
523.9
549.3
574.7
600.1
625.5
525.5
550.9
576.3
601.7
627.1
527.1
552.5
577.'1
603.3
628.7
528.6
554.0
579.4
604.8
630.2
530.2
555.6
581.0
606.4
631.8
531.8
557.2
582.6
608.0
633.4
12
23
24
~
w
.....
MEASURES
~
W
tv
INCHES TO MILLIMETERS (con't.)
IN.
0
1/16
1/8
3/16
1/4
5/16
3/8
7/16
1/2
9/16
5/8
11/16
3/4
13/16
7/8
15/16
25
26
27
28
29
635.0
660.4
685.8
711.2
736.6
636.6
662.0
687.4
712.8
738.2
638.2
663.6
689.0
714.4
739.8
639.8
665.2
690.6
716.0
714.4
641.4
666.8
692.2
717.6
743.0
642.9
668.3
693.7
719.1
744.5
644.5
669.9
695.3
720.7
746.1
646.1
671.5
696.9
722.3
747.7
647.7
673.1
698.5
723.9
749.3
649.3
674.7
700.1
725.5
750.9
650.9
676.3
701.7
727.1
752.5
652.5
677.9
703.3
728.7
754.1
654.1
679.5
704.9
730.3
755.7
655.6
681.0
706.4
731.8
757.2
657.2
682.6
708.0
733.4
758.8
658.8
684.2
709.6
735.0
760.4
30
31
32
33
34
762.0
787.4
812.8
838.2
863.6
763.6
789.0
814.4
839.8
865.2
765.2
790.6
816.0
841.4
866.8
766.8
792.2
817.6
843.0
868.4
768.4
793.8
819.2
844.6
870.0
769.9
795.3
820.7
846.1
871.5
771.5
796.9
822.3
847.7
873.1
773.1
798.5
823.9
849.3
874.7
774.7
800.1
825.5
850.9
876.3
776.3
801.7
827.1
852.5
877.9
777.9
803.3
828.7
854.1
879.5
779.5
804.9
830.3
855.7
881.1
781.1
806.5
831.9
857.3
882.7
782.6
808.0
833.4
858.8
884.2
784.2
809.6
835.0
860.4
885.8
785.8
811.2
836.6
862.0
887.4
35
36
37
38
39
889.0
914.4
939.8
965.2
990.6
890.6
916.0
941.4
966.8
992.2
892.2
917.6
943.0
968.4
993.8
893.8
919.2
944.6
970.0
995.4
895.4
920.8
946.2
971.6
997.0
896.9
922.3
947.7
973.1
998.5
898.5
923.9
949.3
974.7
1000.1
900.1
925.5
950.9
976.3
1001.7
901.7
927.1
952.5
977.9
1003.3
903.3
928.7
954.1
979.5
1004.9
904.9
930.3
955.7
981.1
100&.5
906.5
931.9
957.3
982.7
1008.1
"908.1
933.5
958.9
984.3
1009.7
909.6
935.0
%0.4
985.8
1011.2
911.2
936.6
962.0
987.4
1012.8
912.8
938.2
963.6
989.0
1014.4
40
41
42
43
44
1016.0
1041.4
1066.8
1092.2
1117.6
1017.6
1043.0
1068.4
1093.8
1119.2
1019.2
1044.6
1070.0
1095.4
1120.8
1020.8
1046.2
1071.6
1097.0
1122.4
1022.4
1047.8
1073.2
1098.6
1124.0
1023.9
1049.2
1074.7
1100.1
1125.5
1025.5
1050.9
1l01.7
1127.1
1027.1
1052.5
1077.9
1103.3
1128.7
1028.7
1054.1
1079.5
1104.9
Il30.3
1030.3
1055.7
1081.1
1106.5
Il31.9
1031.9
1057.3
1082.7
1108.1
1133.5
1033.5
1058.9
1084.3
1l09.7
1135.1
1035.1
1060.5
1085.9
1111.3
1136.7
1036.6
1062.0
1087.4
IIl2.8
1138.2
1038.2
1063.6
1089.0
1114.4
1139.8
1039.8
1065.2
1090.6
1116.0
1141.4
45
46
47
48
49
1143.0
1161>.4
1193.8
1219.2
1244.6
1144.6
1170.0
1195.4
1220.8
1246.2
1146.2
Il71.6
1197.0
1222.4
1247.8
1147.8
1173.2
1198.6
1224.0
1249.4
1149.4
Il74.8
1200.2
1225.6
1251.0
1150.9
1176.3
1201.7
1227.1
1252.5
1152.5
1177.9
1203.3
1228.7
1254.1
1154.1
1179.5
1204.9
1230.3
1255.7
1155.7
1181.1
1206.5
1231.9
1257.3
1157.3
1182.7
1208.1
1233.5
1258.9
1158.9
Il84.3
1209.7
1235.1
1260.5
1160.5
1185.9
1211.3
1236.7
1262.1
1162.1
1187.5
1212.9
1238.3
1263.7
1163.6
1189.0
1214.4
1239.8
1265.2
1165.2
Il90.6
1216.0
1241.4
1266.8
Il66.8
1192.2
1217.6
1243.0
1268.4
50
1270.0
1271.6
1273.2
1274.8
1276.4
1277.9
1279.5
1281.1
1282.7
1284.3
1285.9
1287.5
1289.1
1290.6
1292.2
1293.8
~076.3
CONVERSION TABLE - LENGTH
MILLIMETERS TO INCHES
(1 Millimeter = 0.0394 Inch)
Millimeters
0
1
2
3
4
5
6
7
8
9
Millimeters
0
10
20
30
40
0.00
0.39
0.79
1.18
1.57
0.039
0.43
0.83
J.22
1.61
0.079
0.47
0.87
1.26
1.65
0.118
0.51
0.91
1.30
1.69
0.157
0.55
0.94
1.34
1.73
0.197
0.59
0.98
1.38
1.77
0.236
0.63
1.02
1.42
1.81
0.276
0.67
1.06
1.46
1.85
0.315
0.71
1.10
1.50
1.89
0.354
0.75
1.14
1.54
1.93
0
10
20
30
40
50
60
70
80
90
1.97
'2.36
2.76
3.15
3.54
2.01
2.40
2.80
3.19
3.58
2.05
2.44
2.83
3.23
3.62
2.09
2.48
2.87
3.27
3.66
2.13
2.52
2.91
3.31
3.70
2.17
2.56
2.95
3.35
3.74
2.20
2.60
2.99
3.39
3.78
2.24
2.64
3.03
3.43
3.82
2.28
2.68
3.07
3.46
3.86
2.32
2.72
3.11
3.50
3.90
50
60
70
80
90
100
110
120
130
140
3.94
4.33
4.72
5.12
5.51
3.98
4.37
4.76
5.16
5.55
4.02
4.41
4.80
5.20
5.59
4.06
4.45
4.84
5.24
5.63
4.09
4.49
4.88
5.28
5.67
4.13
4.53
4.92
5.31
5.71
4.17
4.57
4.96
5.35
5.75
4.21
4.61
5.00
5.39
5.79
4.25
4.65
5.04
5.43
5.83
4.29
4.69
5.08
5.47
5.87
100
110
120
130
140
150
160
170
180
190
5.91
6.30
6.69
7.09
7.48
5.94
6.34
6.73
7.13
7.52
5.98
6.38
6.77
7.17
7.56
6.02
6.42
6.81
7.20
7.60
6.06
6.46
6.85
7.24
7.64
6.10
6.50
6.89
7.28
7.68
6.14
6.54
6.93
7.32
7.72
6.18
6.57
6.97
7.36
7.76
6.22
6.61
7.01
7.40
7.80
6.26
6.65
7.05
7.44
7.83
160
170
180
190
200
210
220
230
240
7.87
8.27
8.66
9.06
9.45
7.91
8.31
8.70
9.09
9.49
7.95
8.35
8.74
9.13
9.53
7.99
8.39
8.78
9.17
9.57
8.03
8.43
8.82
9.21
9.61
8.07
8.46
8.86
9.25
9.65
8.11
8.50
8.90
9.29
9.69
8.15
8.54
8.94
9.33
9.72
8.19
8.58
8.98
9.37
9.76
8.23
8.62
9.02
9.41
9.80
200
210
220
230
240
250
260
270
280
290
9.84
10.24
10.63
11.02
11.42
9.88
10.28
10.67
11.06
11.46
9.92
10.31
10.71
11.10
11.50
9.96
10.35
10.75
11.14
11.54
10.00
10.39
10.79
11.18
11.57
10.04
10.43
10.83
11.22
11.61
10.08
10.47
10.87
11.26
11.65
10.12
10.51
10.91
11.30
11.69
10.16
10.55
10.94
11.34
11.73
10.20
10.59
10.98
11.38
11.77
250
260
270
280
290
MEASURES
I
I
ISO
~
V.)
V.)
+0W
+0-
MILLIMETERS TO INCHES (con't.)
8
9
6
11.97
12.36
12.76
13.15
13.54
12.01
12.40
12.80
13.19
13.58
12.05
12.44
12.83
13.23
13.62
12.09
12.48
12.87
13.27
13.66
12.13
12.52
12.91
13.31
13.70
12.17
12.56
12.95
13.35
13.74
300
310
320
330
13.90
14.29
14.69
15.08
15.47
13.94
14.33
14.n
15.1:2
15.51
13.98
14.37
14.76
15.16
15.55
14.02
14.41
14.80
15.20
15.59
14.06
14.45
14.84
15.24
15.63
14.09
14.49,
14.88
15.28
15.67
14.13
14.53
14.92
15.31
15.71
350
360
370
380
390
15.83
16.22
16.61
17.01
17.40
15.87
16.26
16.65
17.05
17.44
15.91
16.30
16.69
17.09
17.48
15.94
16.34
16.73
17.13
17.52
15.98
16.38
16.77
17.17
17.56
16.02
16.42
16.81
17.20
17.60
16.06
16.46
16.85
17.24
17.64
16.10
16.50
16.89
17.28
17.68
400
440
17.76
18.15
18.54
18.94
19.33
17.80
18.19
18.58
18.98
19.37
17.83
18.23
18.62
19.02
19.41
17.87
18.27
18.66
19.06
19.45
17.91
18.31
18.70
19.09
19.49
17.95
18.35
18.74
19.13
19.53
17.99
18.39
18.78
19.17
19.57
18.03
18.43
18.82
19.21
19.61
18.07
18.46
18.86
19.25
19.65
450
460
470
480
490
19.69
20.08
20.47
20.87
21.26
19.72
20.12
20.51
20.91
21.30
19.76
20.16
20.55
20.94
21.34
19.80
20.20
20.59
20.98
21.38
19.84
20.24
20.63
21.02
21.42
19.88
20.28
20.67
21.06
21.46
19.92
20.31
20.71
21.10
21.50
19.96
20.35
20.75
21.14
21.54
20.00
20.39
20.79
21.18
21.58
20.04
20.43
20.83
21.22
21.61
500
510
520
530
540
21.65
22.05
22.44
22.83
23.2-3
21.69
22.09
22.48
22.87
23.27
21.73
22.13
22.52
22.91
23.31
21.77
22.17
22.56
22.95
23.35
21.81
22.20
22.60
22.99
23.39
21.85
22.24
22.64
23.03
23.43
21.89
22.28
22.68
23.07
23.46
21.93
22.32
22.72
23.11
23.50
21.97
22.36
22.76
23.15
23.54
22.01
22.40
22.80
23.19
23.58
550
560
570
580
590
0
1
2
3
300
310
320
330
340
11.81
12.20
12.60
12.99
13.39
11.85
12.24
12.64
13.03
13.43
11.8'
12.28
12.68
13.07
13.46
11.93
12.32
12.72
13.11
13.50
350
360
370
380
390
13.78
14.17
14.57
14.96
15.35
13.82
14.21
14.61
15.00
15.39
13.86
14.25
14.65
15.04
15.43
400
440
15.75
16.14
16.54
16.93
17.32
15.79
16.18
16.57
16.97
17.36
450
460
470
480
490
17.72
18.11
18.50
18.90
19.29
500
510
520
530
540
550
560
570
580
590
410
420
430
7
5
Millimeters
4
Millimeters
340
410
420
430
MILLIMETERS TO INCHES (con't.)
Millimeters
0
1
2
3
4
5
6
7
8
9
Millimeters
600
640
23.62
24.02
24.41
24.80
25.20
23.66
24.06
24.45
24.84
25.24
23.70
24.09
24.49
24.88
25.28
23.74
24.13
24.53
24.92
25.31
23.78
24.17
24.57
24.96
25.35
23.82
24.21
24.61
25.00
25.39
23.86
24.25
24.65
25.04
25.43
23.90
24.29
24.68
25.08
25.47
23.94
24.33
24.72
25.12
25.51
23.98
24.37
24.76
25.16
25.55
610
620
630
640
650
660
670
680
690
25.59
25.98
26.38
26.77
27.17
25.63
26.02
26.42
26.81
27.20
25.67
26.06
26.46
26.85
27.24
25.71
26.10
26.50
26.89
27.28
25.75
26.14
26.54
26.93
27.32
25.79
26.18
26.57
26.97
27.36
25.83
26.22
26.61
27.01
27.40
25.87
26.26
26.65
27.05
27.44
25.91
26.30
26.69
27.09
27.48
25.94
26.34
26.73
27.13
27.52
650
660
670
680
690
700
710
720
730
740
27.56
27.95
28.35
28.74
29.13
27.60
27.99
28.39
28.78
29.17
27.64
28.03
28.43
28.82
29.21
27.68
28.07
28.46
28.86
29.25
27.72
28.11
28.50
28.90
29.29
27.76
28.15
28.54
28.94
29.33
27.80
28.19
28.58
28.98
29.37
27.83
28.23
28.62
29.02
29.41
27.87
28.27
28.66
29.06
29.45
27.91
28.31
28.70
29.09
29.49
700
710
720
730
740
750
760
770
780
790
29.53
29.92
30.31
30.71
31.10
29.57
29.96
30.35
30.75
31.14
29.61
30.00
30.39
30.79
31.18
29.65
30.04
30.43
30.83
31.22
29.68
30.08
30.47
30.87
31.26
29.72
30.12
30.51
30.91
31.30
29.76
30.16
30.55
30.94
31.34
29.80
30.20
30.59
30.98
31.38
29.84
30.24
30.63
31.02
31.42
29.88
30.28
30.67
31.06
31.46
750
760
770
780
790
800
810
820
830
840
31.50
31.89
32.28
32.68
33.07
31.54
31.93
32.32
32.72
33.11
31.57
31.97
32.36
32.76
33.15
31.61
32.01
32.40
32.80
33.19
31.65
32.05
32.44
32.83
33.23
31.69
32.09
32.48
32.87
33.27
31.73
32.13
32.52
32.91
33.31
31.77
32.17
32.56
32.95
33.35
31.81
32.20
32.60
32.99
33.39
31.85
32.24
32.64
33.03
33.43
800
810
820
830
850
860
870
880
890
33.46
33.86
34.25
34.65
35.04
33.50
33.90
34.29
34.68
35.08
33.54
33.94
34.33
34.72
35.12
33.58
33.98
34.37
34.76
35.16
33.62
34.02
34.41
34.80
35.20
33.66
34.06
34.45
34.84
35.24
33.70
34.09
34.49
34.88
35.28
33.74
34.13
34.53
34.92
35.31
33.78
34.17
34.57
34.96
35.35
33.82
34.21
34.61
35.00
35.39
850
860
870
880
890
600
610
620
630
840
~
~
Vl
MEASURES
+:0W
0'1
MILLIMETERS TO INCHES (con't.)
Millimeters
0
1
2
3
4
S
6
7
8
9
Millimeters
35.43
35.83
36.22
36.61
37.01
35.47
35.87
36.26
36.65
37.05
35.51
35.91
36.30
36.69
37.09
35.55
35.94
36.34
36.73
37.13
35.59
35.98
36.38
36.77
37.17
35.63
36.02
36.42
36.81
37.20
35.67
36.06
36.46
36.85
37.24
35.71
36.10
36.50
36.89
37.28
35.75
36.14
36.54
36.93
37.32
35.79
36.18
36.57
36.97
37.36
910
920
930
980
990
37.40
37.80
38.19
38.58
38.98
37.44
37.83
38.23
38.62
39.02
37.48
37.87
38.27
38.66
39.06
37.52
37.91
38.31
38.70
39.09
37.56
37.95
38.35
38.74
39.13
37.60
37.99
38.39
38.78
39.17
37.64
38.03
38.43
38.82
39.21
37.68
38.07
38.46
38.86
39.25
37.72
38.11
38.50
38.90
39.29
37.76
38.15
38.54
38.94
39.33
950
960
970
980
990
1000
39.37
39.41
39.45
39.49
39.53
39.57
39.61
39.65
39.68
39.72
1000
900
910
920
930
940
950
960
970
------
-----
900
940
SQUARE FEET TO SQUARE METERS
Square Feet
0
10
20
30
40
50
60
70
80
90
0
0.000
0.929
1.858
2.787
3.716
4.645
5.574
6.503
7.432
8.361
1
0.093
1.022
1.951
2.880
3.809
4.738
5.667
6.596
7.525
8.454
3
2
4
0.279
1.208
2.137
3.066
3.995
4.924
5.853
6.782
7.711
8.640
0.186
1.115
2.044
2.973
3.902
4.831
5.760
6.689
7.618
8.547
0.372
1.301
2.230
3.159
4.088
5.017
5.946
6.875
7.804
8.733
5
0.465
1.394
2.323
3.252
4.181
5.110
6.039
6.968
7.897
8.826
6
0.557
1.486
2.415
3.345
4.274
5.203
6.132
7.061
7.990
8.919
=
1 Sq. Ft.
7
8
0.650
1.579
2.508
3.437
4.366
5.295
6.225
7.154
8.083
9.012
0.743
1.672
2.601
3.530
4.459
5.388
6.317
7.246
8.175
9.105
0.0929034
Square Meters
9
0.836
1.765
2.694
3.623
4.552
5.481
6.410
7.339
8.268
9.197
I
SQUAR~
METERS TO SQUARE FEET
1 Sq. M
=
10.76387
Square Feet
I
Square Meters
0
10
20
30
40
50
60
70
80
90
0
1
0.00
107.64
215.28
322.92
430.56
538.19
645.83
753.47
861.11
968.75
10.76
118.40
226.04
333.68
441.32
548.96
656.60
764.23
871.87
979.51
2
21.53
129.17
236.81
344.44
452.08
559.72
667.36
. 775.00
882.64
990.28
3
32.29
139.93
247.57
355.21
462.85
570.49
678.12
785.76
893.40
1001.04
4
43.06
150.69
258.33
365.97
473.61
581.25
688.89
796.53
904.17
1011.80
5
53.82
161.46
269.10
376.74
484.37
592.01
699.65
807.29
914.93
1022.57
MEASURES
6
7
8
9
64.58
172.22
279.86
387.50
495.14
602.7R
710.42
818.05
925.69
1033.33
75.35
182.99
290.62
398.26
505.90
613.54
721.18
828.82
936.46
1044.10
86.11
193.75
301.39
409.03
516.67
624.30
731.94
839.58
947.22
1054.86
96.87
204.51
312.15
419.79
527.43
635.07
742.71
850.35
957.98
1065.62
I
~
Vl
-..l
oj::.
W
00
CONVERSION TABLE - WEIGHTS
POUNDS TO KILOGRAMS
(1 pound = 0.4536 kilogram)
Pounds
0
0
10
20
30
40
50
60
70
80
90
0.00
4.54
9.07
13.61
18.14
22.68
27.22
31.75
36.29
40.82
1
0.45
4.99
9.53
14.06
18.60
23.13
27.67
32.21
36.74
41.28
2
3
0.91
5.44
9.98
14.52
19.05
23.59
28.12
32.66
37.20
41.73
1.36
5.90
10.43
14.97
19.50
24,04
28.58
33.11
37.65
42.18
5
4
1.81
6.35
10.89
15.42
19.96
24.49
29.03
33.57
38.10
42.64
2.27
6.80
11.34
15.88
20.41
24.95
29.48
34.02
38.56
43.09
6
8
7
2.72
7.26
11.79
16.33
20.87
25.40
29.94
34.47
39.01
43.55
9
3.18
7.71
12.25
16.78
21.32
25.86
30.39
34.93
39.46
44.00
3.63
8.16
12.70
17.24
21.77
26.31
30.84
35.38
39.92
44.45
4.08
8.62
13.15
17.69
12.23
26.76
31.30
35.83
40.37
44.91
KILOGRAMS TO POUNDS
(1 kilogram = 2.2046 pounds)
Kilograms
0
10
20
30
40
50
60
70
80
90
0
1
2
3
4
5
6
7
8
9
0.00
22.05
44.09
66.14
88.18
110.23
132.28
154.32
176.37
198.41
2.20
24.25
46.30
68.34
90.39
112.43
134.48
156.53
178.57
200.62
4.41
26.46
48.50
70.55
92.59
114.64
136.69
158.73
180.78
202.82
6.61
28.66
50.71
72.75
94.80
116.84
138.89
160.94
182.98
205.03
8.82
30.86
52.91
74.96
97.00
119.05
141.09
163.14
185.19
207.23
11.02
33.07
55.12
77.16
99.21
121.25
143.30
165.35
187.39
209.44
13.23
35.27
57.32
79.37
101.41
123.46
145.50
167.55
189.60
211.64
15.43
37.48
59.52
81.57
103.62
125.66
147.71
169.75
191.80
213.85
17.64
39.68
61.73
83.77
105.82
127.87
149.91
171.96
194.00
216.05
19.84
41.89
63.93
85.98
108.03
130.07
152.12
174.16
196.21
218.26
--
--
-
L - ..
-----
--
-
-
'--------
~
----
---
-
--
-
'-
-
I
U. S. GALLONS TO LITERS
Gallon
0
10
20
30
40
50
60
70
80
90
1
u. S. Gallon
= 3.785329 Liter
0
1
2
3
4
5
6
7
8
9
0
37.85
75.71
113.56
151.41
189.27
227.12
264.97
302.83
340.68
3.79
41.64
79.49
117.35
155.20
193.05
230.91
268.76
306.61
344.46
7.57
45.42
13.28
121.13
158.98
196.84
234.69
272.54
310.40
348.25
11.36
49.21
87.01
124.92
162.77
200.62
238.48
276.33
314.18
352.04
15.14
52.99
90.85
128.70
166.55
204.41
242.26
280.11
317.97
355.82
18.93
56.78
94.63
132.49
170.34
208.19
246.05
283.90
321.75
359.60
22.71
60.57
98.42
136.27
174.13
211.98
249.83
287.69
325.54
363.39
26.50
64.35
102.20
140.06
177.91
215.76
253.62
291.47
329.32
367.18
30.28
68.14
105.99
143.84
181.70
219.55
257.40
295.26
333.11
370.96
34.07
71.92
109.77
147.63
185.48
223.33
261.19
299.04
336.89
374.75
:
LITER TO U. S. GALLON
Liter
0
10
20
30
40
50
60
70
80
90
~
0
0
2.64
5.28
7.93
10.57
13.21
15.85
18.49
21.13
23.78
1
0.26
2.91
5.55
8.19
10.83
13.47
16.11
18.76
21.40
24.04
2
0.53
3.17
5.81
8.45
11.10
13.74
16.38
19.02
21.66
24.30
3
0.79
3.43
6.08
8.72
11.36
14.00
16.64
19.28
21.93
24.57
4
1.06
3.70
6.34
8.98
11.62
14.27
16.91
19.55
22.19
24.83
5
1.32
3.96
6.60
9.25
11.89
14.53
17.17
19.81
22.45
25.10
- -
MEASURES
1 Liter = 0.264168 U. S. Gallon
6
1.59
4.23
6.87
9.51
12.15
14.79
17.44
20.08
22.72
25.36
7
1.85
4.49
7.13
9.77
12.42
15.06
17.70
20.34
22.98
25.62
8
2.11
4.76
6.60
10.04
12.68
15.32
17.96
20.61
23.25
25.89
9
2.38
5.02
7.66
10.30
12.94
15.59
18.23
20.87
23.51
26.15
~
W
\0
~
~
CONVERSION TABLE - PRESSURE
o
POUNDS PER SQUARE INCH TO KILOGRAMS PER SQUARE CENTIMETER
(1 pound per square inch = .0703066 kilogram per square centimeter)
1 to 30
Lbs. Per Kg. Per
Sq. In.
Sq. em.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
.07
.14
.21
.28
.35
.42
.49
.56
.63
.70
.77
.84
.91
.98
1.05
1.12
1.20
1.27
T.34
1.41
1.48
1.55
1.62
1.69
1.76
1.83
1.90
1.97
2.04
2.11
31 to 60
Lbs. Per Kg. Per
Sq. In.
Sq. em.
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
2.18
2.25
2.32
2.39
2.46
2.53
2.60
2.67
2.74
2.81
2.88
2.95
3.02
3.09
3.16
3.23
3.30
3.37
3.45
3.52
3.59
3.66
3.73
3.80
3.87
3.94
4.01
4.08
4.15
4.22
61 to 90
Lbs. Per Kg. Per
Sq. In.
Sq. em.
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
4.29
4.36
4.43
4.50
4.57
4.64
4.71
4.78
4.85
4.92
4.99
5.06
5.13
5.20
5.27
5.34
5.41
5.48
5.55
5.62
5.69
5.77
5.84
5.91
5.98
6.05
6.12
6.19
6.26
6.33
91 to 200
205 to 400
Lbs. Per
Sq. In.
Kg. Per
Sq. em.
Lbs. Per
Sq. In.
Kg. Per
Sq. em.
91
92
93
94
95
96
97
98
99
100
105
110
115
120
125
130
135
140
145
150
155
160
165
170
175
180
185
190
195
200
6.40
6.47
6.54
6.61
6.68
6.75
6.82
6.89
6.96
7.03
7.38
7.73
8.09
8.44
8.79
9.14
9.49
9.84
10.19
10.55
10.90
11.25
11.60
11.95
12.30
12.66
13.01
13.36
13.71
14.06
205
210
215
220
225
230
235
240
245
250
255
260
265
270
275
280
285
290
295
300
310
320
330
340
350
360
370
380
390
400
14.41
14.76
15.12
15.47
15.82
16.17
16.52
16.87
17.23
17.58
17.93
18.28
18.63
18.98
19.33
19.69
20.04
20.39
20.74
21.09
21.80
22.50
23.20
23.90
24.61
25.31
26.01
26.72
27.42
28.12
410 to 700
710 to 1000
1010to 1500
Lbs. Per Kg. Per
Sq. In.
Sq. em.
Lbs. Per Kg. Per
Sq. In.
Sq. em.
Lbs. Per Kg. Per
Sq. em.
Sq. In.
410
420
430
440
450
460
470
480
490
500
510
520
530
540
550
560
570
580
590
600
610
620
630
640
650
660
670
680
690
700
28.83
29.53
30.23
30.93
31.64
32.34
33.04
33.75
34.45
35.15
35.86
36.56
37.26
37.97
38.67
39.37
40.07
40.78
41.48
42.18
42.89
43.59
44.29
45.00
45.70
46.40
47.11
47.81
48.51
49.21
710
720
730
740
750
760
770
780
790
800
810
820
830
840
850
860
870
880
890
900
910
920
930
940
950
960
970
980
990
1000
49.92
50.62
51.32
52.03
52.73
53.43
54.14
54.84
55.54
56.25
56.95
57.65
58.35
59.06
59.76
60.46
61.17
61.87
62.57
63.28
63.98
64.68
65.39
66.09
66.79
67.49
68.20
68.90
69.60
70.31
1010
1020
1030
1040
1050
1060
1070
1080
1090
1100
1120
1140
1160
1180
1200
1220
1240
1260
1280
1300
1320
1340
1360
1380
1400
1420
1440
1460
1480
1500
71.01
71.71
72.42
73.12
73.82
74.52
75.23
75.93
76.63
77.34
78.74
80.15
81.56
82.96
84.37
85.77
87.18
88.59
89.99
91.40
92.80
94.21
95.62
97.02
98.43
99.84
101.24
102.65
104.05
105.46
441
CONVERSION TABLE - DEGREE
DEGREES TO RADIANS
1 DEGREE = 180 = 0.01745 RADIANS
Degrees
i
Minutes
Seconds
0°
1
2
3
4
0.0000000
0.01745 H
0.03490 66
0.05235 99
0.06981 32
60°
61
62
63
64
1.0471976
1.0646508
1.0821041
1.09955 74
I.Il701 07
120°
121
122
123
124
2.09439 51
2.11184 84
2.12930 17
2.1467550
2.16420 83
0
1
2
3
4
0.0000000
0.00029 09
0.00058 18
0.0008727
0.0011636
0
1
2
3
4
0.0000000
0.0000048
0.00000 97
0.00001 45
0.00001 94
5
6
7
8
9
0.08726
0.10471
0.12217
0.13962
0.15707
65
98
30
63
96
65
66
67
68
69
1.1344640
1.1519173
1.16937 06
1:1868239
1.2042772
125
126
127
128
129
2.18166 16
2.1991149
2.21656 82
2.23402 14
2.2514747
5
6
7
8
9
0.00145
0.00174
0.00203
0.00232
0.00261
80
5
6
7
8
9
0.0000242
0.00002 91
0.00003 39
0.0000388
0.00004 36
70
71
72
73
74
1.22173 05
1.2391838
1.25663 7 I
1.27409 04
1.29154 36
130
14
0.17453 29
0.1919862
0.20943 95
0.22689 28
0.2443461
132
133
134
2.26892 80
2.28638 13
2.30383 46
2.3212879
2.3387412
10
11
12
13
14
0.0029089
0.0031998
0.00349 07
0.00378 15
0.00407 24
10
11
12
13
14
0.00004
0.00005
0.00005
0.00006
0.00006
I5
16
17
18
19
0.26179 94
0.2792527
0.29670 60
0.31415 93
0.33161 26
75
76
77
78
79
1.30899 69
1.32645 02
1.3439035
1.36135 68
1.37881 01
135
136
137
138
139
2.3561945
2.37364 78
2.39110 11
2.40855 44
2.4260077
15
16
17
18
19
0.00436 33
0.0046542
0.00494 51
0.00523 60
0.00552 69
15
16
17
18
19
0.0000727
0.00007 76
0.00008 24
0.00008 73
0.00009 21
20
21
22
23
24
0.34906 59
0.36651 91
0.38397 24
0.4014257
0.41887 90
80
81
82
83
84
1.39626 34
1.41371 67
1.4311700
1.44862 H
1.46607 66
140
141
142
143
144
2.44346 10
2.46091 42
2.47836 75
2.49582 08
2.5132741
20
21
22
23
24
0.00581
0.00610
0.00639
0.00669
0.00698
78
87
95
04
13
20
21
22
23
24
0.00009
0.00010
0.00010
0.00011
0.00011
25
26
27
28
29
0.43633 23
0.45378 56
0.4712389
0.48869 22
0.5061455
85
86
87
88
89
1.48352 99
1.5009832
1.51843 64
I. 53588 97
1.55334 30
145
146
147
148
149
2.53072
2.54818
2.56563
2.58308
2.60054
74
07
40
73
06
25
26
27
28
29
0.0072722
0.00756 31
0.00785 40
0.0081449
0.00843 58
25
26
27
28
29
0.0001212
0.00012 61
0.00013 09
0.00013 57
0.0001406
30
31
32
33
34
0.5235988
0.5410521
0.55850 54
0.5759587
0.59341 19
90
91
92
93
94
1.57079 63
1. 58824 96
1.6057029
1.62315 62
1.64060 95
150
151
152
153
154
2.61799
2.63544
2.65290
2.67035
2.68780
39
72
OJ
38
70
30
31
32
33
34
0.00872 66
0.00901 75
0.00930 84
0.00959 93
0.0098902
30
31
32
33
34
0.0001454
0.00015 03
0.00015 51
0.0001600
0.0001648
35
36
37
38
39
0.61086 52
0.62831 85
0.64577 18
0.66322 51
0.6806784
95
96
97
98
99
1.6580628
1.67551 61
1.69296 94
1.7104227
1.72787 60
155
156
157
158
159
2.70526 03
2.72271 36
2.74016 69
2.7576202
2.7750735
35
36
37
38
39
0.01018
0.01047
0.01076
0.01105
0.01134
II
20
29
38
46
35
36
37
38
39
0.0001697
0.0001745
0.0001794
0.0001842
0.00018 91
40
41
42
43
44
0.69813 17
0.71558 50
0.7330383
0.75049 16
0.76794 49
100
101
102
103
104
1.7453293
1.76278 25
1.78023 58
1.79768 91
1.81514 24
160
161
162
163
164
2.79252
2.80998
2.82743
2.84488
2.86234
68
01
34
67
00
40
41
42
43
44
0.0116355
0.0119264
0.01221 73
0.0125082
0.01279 91
40
41
42
43
44
0.00019 39
0.00019 88
0.0002036
0.00020 85
0.00021 33
45
46
47
48
49
0.78539
0.80285
0.82030
0.83775
0.85521
82
15
47
80
13
105
106
107
108
109
1.83259
1.85004
1.86750
1.88495
1.90240
57
90
23
56
89
165
166
167
168
169
2.87979 H
2.89724 66
2.9146999
2.9321531
2.9496064
45
46
47
48
49
0.01309 00
0.01338 09
0.01367 17
0.01396 26
0.0142535
45
46
47
48
49
0.00021 82
0.00022 30
0.00022 79
0.0002327
0.00023 76
50
51
52
53
54
0.8726646
0.89011 79
0.90757 12
0.92502 45
0.94247 78
IIO
III
112
113
II4
1.91986 22
1.93731 55
1.9547688
1.9722221
1.9896753
170
171
172
173
174
2.96705
2.98451
3.00196
3.01941
3.03687
97
30
63
96
29
50
51
52
53
54
0.0145444
0.01483 53
0.01512 62
0.01541 71
0.01570 80
50
51
52
53
54
0.00024 24
0.00024 73
0.0002521
0.00025 70
0.00026 18
55
56
57
58
59
0.95993 II
.09773844
0.99483 77
1.01229 10
1.02974 43
II5
116
II7
II8
119
2.007/2
2.02458
2.04203
2.05948
2.07694
86
19
52
85
18
175
176
177
178
179
3.05432
3.07177
3.08923
3.10668
3.12413
62
95
28
61
94
55
56
57
58
59
0.01599 89
0.01628 97
0.0165806
0.01687 15
0.0171624
55
56
57
58
59
0.00026
0.00027
0.00027
0.00028
0.00028
60
1.0471976
120
2.0943951
180
3.14159 27
60
0.01745 H
60
0.00029 09
10
II
12
13
HI
44
53
62
7I
85
33
82
30
79
70
18
67
15
64
66
15
63
12
60
442
CONVERSION TABLE - DEGREE
RADIANS TO DEGREES
=
1 RADIAN
Radians
1
2
3
4
5
6
7
8
9
57° 17' •• ".8
11.°35'29".6
171°51'14".4
229 ° 10' 59".2
286°28'44".0
343°46'28".8
401 ° 4'13",6
458°21'58" ••
.515°39'.3",3
1:0 = 57.29578 DEGREES
Tenths
Hundredths
Thousandths
5°41'46".5
11°27'JJ".0
17°11'19".4
22°55'05".9
28 ° 38' 52 ",4
34°22'38",9
40° 6'25".4
45°50'11".8
51°33'58".3
0°3. '22".6
1 ° 8'.5",1
1°41'Q7",.9
2° 17'10".6
2°51'53".2
3°26'15",9
4° 0'38".5
4°35'01".2
5° 9'23",8
0° 3'26".3
0° 6'52".5
0°10'18".8
0°0'45".1
0° 17' II ".1
0°20'17",6
0°24'03".9
0°27'30".1
0°30"6",.
EXAMPLES
1.
Change 87 0 26' 34" to radian
Solution: From table on opposite page
87 0
26'
34"
=
=
=
87 0 26' 34"
2.
1.5184364
0.0075631
0.0001648
radians
radians
radians.
1.5261643
radians
Change 1.5262 radians to degrees
Solution: From table above
1
radian
0.5
0.02
0.006
0.0002
1.5262
=
=
=
=
=
=
=
57 0 17' 44.8"
28 0 38' 52.4"
10 8' 45.3"
0 0 20' 37.6"
0 0 0' 41.3"
86 0 83' 221.4"
87 0 26' 41.4"
Tenthousandths
0° 0'20",6
0° 0'.1 ".3
0° 1'01 ".9
0° 1'22".5
0° 1'41".1
0° 2'03".8
0° 2'24".4
OC 2'45".0
0°3'05".6
443
CONVERSION TABLE - DEGREE
MINUTES AND SECONDS TO
DECIMALS OF A DEGREE
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
,
0.0000
0167
0333
0500
0667
0.0833
1000
1167
1333
1500
0.1667
1833
2000
2167
2333
0.2500
2667
2833
3000
3167
0.3333
3500
3667
3833
4000
0.4167
4333
4500
4667
4833
0.5000
5167
5333
5500
5667
0.5833
6000
6167
6333
6500
0.6667
6833
7000
7167
7333
0.7500
7667
7833
8000
8167
0.8333
8500
8667
8833
9000
0.9167
9333
9500
9667
9833
1.000
0
DECIMALS OF A DEGREE TO
MINUTES AND SECONDS
0
"
'and"
0
0.000
60
0.00000
028
056
083
III
0.00139
167
194
222
250
0.00278
306
333
361
389
0.00417
444
472
500
528
0.00556
583
611
639
667
0.00694
722
750
778
806
0.00833
861
889
917
944
0.00972
01000
028
056
083
0.01111
139
167
194
222
0.01250
278
306
333
361
0.01389
417
444
472
500
0.01528
556
583
611
639
0.01667
"
0
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
001
002
003
004
0.005
006
007
008
009
0.00
01
02
03
04
0.05
06
07
08
09
0.10
11
12
13
14
0.15
16
17
18
19
0.20
21
_22
23
24
0.25
26
27
28
29
0.30
31
32
33
34
0.35
36
37
38
39
0.40
41
42
43
44
0.45
46
47
48
49
0.50
0'
0'
0'
0'
0'
0'
0'
0'
0'
0'
0'
0'
I'
I'
2'
3'
3'
4'
4'
5'
6'
6'
7'
7'
8'
9'
9'
10'
10'
II'
12'
12'
13'
13'
14'
IS'
IS'
16'
16'
17'
18'
18'
19'
19'
20'
21'
21'
22'
22'
23'
24'
24'
25'
25'
26'
27'
27'
28'
28'
29'
30'
0"
4"
7"
11 "
14"
18"
22"
25"
29"
32"
0"
36"
12"
48"
24"
0"
36"
12"
48"
24"
0"
36"
12"
48"
24"
0"
36"
12"
48"
24"
0"
36"
12"
48"
24"
0"
36"
12"
48"
24"
0"
36"
12"
48"
24"
0"
36"
12"
48"
24"
0"
36"
12"
48"
24"
0"
36"
12"
48"
24"
0"
• and"
0
'and ..
0.50
2.00
30' 0"
30' 36"
31' 12"
31' 48"
32' 24"
33' 0"
33' 36"
34' 12"
34' 48"
35' 24"
36' 0"
36' 36"
37' 12"
37' 48"
38' 24"
39' 0"
39' 36"
40' 12"
40' 48"
41' 24"
42' 0"
42' 36"
43' 12"
43' 48"
44' 24"
45' 0"
45' 36"
46' 12"
46' 48"
47' 24"
48' 0"
48' 36"
49' 12"
49' 48"
50' 24"
51' 0"
51' 36"
52' 12"
52' 48"
53' 24"
54' 0"
54' 36"
55' 12"
55' 48"
56' 24"
57' 0"
57' 36"
58' 12"
58' 48"
59' 24"
60' 0"
66' 0"
72' 0"
78' 0"
84' 0"
90' 0"
96' 0"
102' 0"
108' 0"
114' 0"
120' 0"
0
'and"
51
52
53
54
0.55
56
57
58
59
0.60
61
62
63
64
0.65
66
67
68
69
0.70
71
72
73
74
0.75
76
77
78
79
0.80
81
82
83
84
0.85
86
87
88
89
0.90
91
92
93
94
0.95
96
97
98
99
1.00
10
20
30
40
1.50
60
70
80
90
~
~
~
CONVERSION TABLE - TEMPERATURE
CENTIGRADE - FAHRENHEIT
5
9
(FO + 40) -40
Degrees Cent., Co
Degrees Fahr., FO
(CO + 40) -40
9
NOTE: The numbers in boldface refer to the temperature either in degrees, Centigrade or Fahrenheit which it is desired to convert into
the other scale. If converting from Fahrenheit to Centigrade degrees, the equivalent temperature will be found in the left column; while
if converting from degrees Centigrade to degrees Fahrenheit, the answer will be found in the column on the right.
=-
Centigrade
Fahrenheit
Fahrenheit
Centigrade
-15.6
-15.0
4
5
39.2
41.0
-14.4
-13.9
-13.3
-12.8
-12.2
-11.7
-11.1
-10.6
6
7
8
9
10
13
42.8
44.6
46.4
48.2
50.0
51.8
53.6
55.4
-10.0
-9.4
-8.9
-8.3
-7.8
-7.2
-6.7
-6.1
14
15
16
17
18
19
20
21
-73.3
-67.8
-62.2
-59.5
-56.7
-53.9
-51.1
-48.4
-100
-90
-80
-75
-70
-65
-60
-55
-148.0
-130.0
-112.0
-103.0
-94.0
-85.0
-76.0
-67.0
-45.6
-42.8
-40.0
-37.2
-34.4
-31.6
-28.8
-26.1
-50
-45
-40
-35
-30
-25
-20
-15
-58.0
-49.0
-40.0
-31.0
-22.0
-13.0
-4.0
5.0
-23.3
-20.6
-17.8
-17.2
-16.7
-16.1
-10
-5
0
1
2
3
14.0
23.0
32.0
33.8
35.6
37.4
-5.6
-5.0
-4.4
-3.9
11
12
22
23
24
25
="5
Fahrenheit
Centigrade
Centigrade
Fahrenheit
-3.3
-2.8
-2.2
-1.7
26
27
28
29
78.8
80.6
82.4
84.2
9.4
10.0
10.6
11.1
49
50
51
52
120.2
122.0
123.8
125.6
57.2
59.0
60.8
62.6
64.4
66.2
68.0
69.8
-1.1
-0.6
0.0
0.6
1.1
1.7
2.2
2.8
3.3
3.9
4.4
5.0
5.6
6.1
6.7
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
86.0
87.8
89.6
91.4
93.2
95.0
96.8
98.6
100.4
102.2
104.0
105.8
107.6
109.4
111.2
11.7
12.2
12.8
13.3
13.9
14.4
15.0
15.6
53
54
55
56
57
58
59
60
127.4
129.2
131.0
132.8
134.6
136.4
138.2
140.0
71.6
73.4
75.2
77.0
7.2
7.8
8.3
8.9
16.1
16.7
17.2
17.8
18.3
18.9
19.4
20.0
61
62
63
64
65
66
67
68
141.8
143.6
145.4
147.2
149.0
150.8
152.6
154.4
20.6
21.1
69
70
156.2
158.0
45
46
47
48
113.0
114.8
116.6
118.4
i
I
I
I
CENTIGRADE - FAHRENHEIT (con't.)
Centigrade
Fahrenheit
Fahrenheit
Centigrade
Fahrenheit
54
60
65
71
76
130
140
150
160
170
266
284
302
320
338
226
232
238
243
249
440
450
460
470
480
824
842
860
878
896
83
88
93
99
100
104
110
115
180
190
200
210
212
220
230
240
356
374
392
410
413
428
446
464
185.0
186.8
188.6
190.4
192.2
194.0
195.8
121
127
132
138
143
149
154
160
250
260
270
280
290
300
310
320
482
500
518
536
554
572
590
608
254
260
265
271
276
282
288
293
299
304
310
315
321
326
332
490
500
510
520
530
540
550
560
570
580
590
600
610
620
630
914
932
950
968
986
1004
1022
1040
1058
1076
1094
1112
1130
1148
1166
92
93
94
95
96
97
98
99
197.6
199.4
201.2
203.0
204.8
206.6
208.4
210.2
165
171
177
182
188
193
199
204
330
340
350
360
370
380
390
400
626
644
662
680
698
716
734
752
100
110
120
212.0
230
248
210
215
221
410
420
430
770
788
806
21.7
22.2
22.8
23.3
23.9
24.4
71
72
73
74
75
76
159.8
161.6
163.4
165.2
167.0
168.8
25.0
25.6
26.1
26.7
27.2
27.8
28.3
28.9
77
78
79
80
81
82
83
84
170.6
172.4
174.2
176.0
177.8
179.6
181.4
183.2
29.4
30.0
30.6
31.1
31.7
32.2
32.8
85
86
87
88
89
90
91
33.3
33.9
34.4
35.0
35.6
36.1
36.7
37.2
37.8
:§
Centigrade
338
343
349
354
360
365
371
376
640
650
660
670
680
690
700
710
1184
1202
1220
1238
1256
1274
1292
1310
382
387
393
399
404
720
730
740
750
760
1328
1346
1364
1382
1400
MEASURES
Centigrade
Fahrenheit
410
415
421
770
780
790
1418
1436
1454
426
432
438
443
449
454
460
465
800
810
820
830
840
850
860
970
1472
1490
1508
1526
1544
1562
1580
1598
471
476
482
487
493
498
504
510
880
890
900
910
920
930
940
950
1616
1634
1652
1670
1688
1706
1724
1742
515
520
526
532
538
565
593
620
960
970
980
990
1000
1050
1100
1150
1760
1778
1796
1814
1832
1922
2012
2102
648
675
704
734
760
787
815
1200
1250
1300
1350
1400
1450
1500
2192
2282
2372
2462
2552
2642
2732
I
~
~
VI
446
CONVERSION FACTORS
(For conversion factors meeting the standards of the SI metric system, refer to ASTM E380-72)
MULTIPLY
BY
TO OBTAIN
centimeters ....................................... .
3.28083 x 10-2
feet
centimeters ....................................... .
inches
.3937
6.102 x 10-2
cubic centimeters .............................. .
cubic inches
cubic feet .......................................... .
2.8317 x 10-2
cubic meters
cubic feet .......................................... .
6.22905
gallons, British Imperial
cubic feet ......................................... ..
liters
28.3170
cubic inches ..................................... ..
16.38716
cubic centimeters
cubic meters .................................... ..
35.3145
cubic feet
cubic meters .................................... ..
1.30794
cubic yards
cubic yards ....................................... ..
.764559
cubic meters
degrees angular ................................ .
.0174533
radians
foot pounds ...................................... ..
.13826
kilogram meters
feet .....................................................
centimeters
30.4801
.160538
gallons, British Imperial .................... .
cubic feet
gallons, British Imperial ................... ..
1.20091
gallons, U.S.
4.54596
liters
gallons, British Imperial .................... .
.832702
gallons, British Imperial
gallons, U.S ...................................... .
.13368
cubic feet
gallons, U.S ...................................... .
gallons, U.S ..................................... ..
3.78543
liters
grams, metric ................................... ..
2.20462 x 10- 3
pounds, avoirdupois
horse-power, metric .......................... .
.98632
horse-power, U.S.
1.01387
horse-power, metric
horse-power, U.S ............................. ..
inches ................................................ .
2.54001
centimeters
2.20462
pounds
kilograms ........................................... .
kilograms per sq. centimeter ........... ..
14.2234
pounds per sq. inch
.62137
miles, statute
kilometers ......................................... .
.26417
gallons, U.S.
liters ...................................................
meters .............................................. ..
,3.28083
feet
39.37
inches
meters ................................................
meters ................................................
1.09361
yards
miles, statute .................................... .
1.60935
kilometer
feet
milimeters ......................................... .
3.28083 x 10-3
milimeters ......................................... .
3.937 x 10- 2
inches
kilograms
pounds avoirdupois ........................... .
.453592
kilograms per sq. meter
pounds per square foot .................... ..
4.88241
pounds per square inch .................... .
7.031 x 10-2
kilograms per sq. centimeter
degrees angular
radians ...............................................
57.29578
square centimeters ........................... .
.1550
square inches
6.45163
square centimeters
square inches ................................... .
1.19599
square yards
square meters .................................. ..
square kilometers
square miles .................................... ..
2.590
.83613
square meters
square yards .................................... ..
1016.05
kilograms
tons, long .......................................... .
2240.
pounds
tons, long ......................................... ..
2204.62
pounds
tons, metric ....................................... .
.98421
tons, long
tons, metric ...................................... ..
tons, short
tons, metric ....................................... .
1.10231
tons, short ......................................... .
.892857
tons, long
tons, metric
tons, short ........................................ ..
.907185
.914402
yards ................................................ ..
meters
447
PART IV.
DESIGN OF STEEL STRUCTURES
1.
Stress and Strain Formulas .. ..... .... .... .... .... .... .... .... .... .... .... ... ....... ..... ...... 448
2.
Properties of Sections ........................................................................... 450
3.
Center of Gravity .................................................................................. 452
4.
Beam Formulas ..................................................................................... 455
5.
Design of Welded Joints ....................................................................... 458
6.
Example of Calculations ....................................................................... 461
7.
Bolted Connections .... .... ............ .................... .... .... ........ ................ .... ... 463
448
STRESS AND STRAIN FORMULAS
= Bending stress, psi
= Shear stress, psi
DEFINITION OF SYMBOLS
A
= Cross sectional area, in 2•
AR = Required cross sectional Area, in 2
1
=Moment of inertia, in 4
M
= Moment, in-lb
MA = Allowable moment, in-Ib
P
=Force, Ib
PA
= Allowable force. Ib
S
= Tensile or compressive stress, psi
= Allowable tensile or compressive
stress, psi
= Allowable bending stress, psi.
= Allowable shear stress, psi.
== Distance from neutral axis to
extreme fiber, in
= Section modulus, in3
TYPE OF LOADING
P..f. ~--8-P
A'
TENSION
0- P
tt
P~"·U-·i--~
4
A'
COMPRESSION
P
~~Single
P/2.~
S =
AR
Double
A
= -P (.102)
SA
~ (psi)
A
PA = ASA (Ib)
P (. 2)
AR == - m
SA
S =
Ss
=
.!.. (psi)
A
PA = ASSA (lb)
P (. 2)
AR = - 10
SSA
S
PA
P/2-
~ (psi)
PA = ASA (Ib)
S
~p
EXAMPLES
=.!.(psi)
2A
= 2ASSA
(lb)
A =P- (.10 2)
M == PI (in-Ib)
MA = ZSA (in-Ib)
M (. 3)
ZR = - 10
SSA
S
DIW
LLb=cJ
SECTION MODULUS
S = P = 5,000 = 10 000 psi
A
0.5
'
To support a load of 11 ,000 lbs. in
compression, the required area of steel
bar made from SA 285C steel is:
AR =
1:...
SA
= 11.000 = 0.5 in2
22,000
The required area of bolt made from
SA-307 B steel to support a load of
15,000 lbs. in double shear:
AR
=L
2SA
=
.
15.000 = 0.75 in 2
2x 10,000
2SSA
SHEAR
BENDING
The stress in a 2 x Y4 in. bar made from
SA 285-C steel due to 5,000 lb. tensional
load is:
Area, A == 2 X Y4 = 0.5 in 2 ;
=
SA =
The maximum bending moment at the
support of a cantilever beam due to a
load of 1,000 lbs. acting at a distance of
60 inches from the support:
M = PI == 1,000 x 60 = 60,000 in-lb.
M (psi)
Z
~ (psi)
Section modulus
Zmin
If dimension b =2 in. and d=4 in,
axis of moment on the base. 1=42.67.
Z==lly == 42.67/4 = 1O.67in3
axis of moment through center, 1= 10.67,
Z=lly = 10.67/2 = 5.335 in3
1
Z== Y
449
ALLOWABLE STRESSES
FOR NON PRESSURE PARTS OF VESSELS AND OTHER STRUCTURES
TYPE OF STRESS
& JOINT
ALLOW ABLE STRESS
STEEL
Bearing
Shear
Compression
Tension (except pin connection)
Bending
Shear
Bearing (on projected area of bolts
in shear on connection)
1. 60 x} The values of
0.80 x tables UCS-23
0.60x }
O.6Ox
0.66x
0.40x
1.5 x
Specified
minimum
yield stress
Min. tensile
strength
SOURCE
CODE
UCS-23
Notes
American
Institute
of Steel
Construction
WELDED JOINT OF STEEL
Full penetration groove weld
tension, compression, shear
Partial penetration groove weld
1. tension transverse to axis of weld,
shear on throat
2. tension parallel to axis of weld or
compression on throat
same as for the
steel welded
13,600 psi
same as for the
steel welded
Fillet weld, shear on throat
13,600 psi
(using throat dimension)
9,600 ('si
(usmg leg dimension)
Plug or slot weld
same as fillet weld
American
Welding
Society
450
PROPERTIES OF SECTIONS
DEFINITION OF SYMBOLS
r
y
= Area, in. 1
= Moment of inertia, in.4
A
I
fa
/.
0
=
y
IIJ
I/~ 0
1= 0112
l = oj6
I.
./
= 0.289
r
y
=0
I
=
=
l
=
r
= 0.577
r
./
= bdy3
=
Y~
r
=
A
I.
0.2890
b2
02_
1.=0!;4- b )/12
Z
=(04- b4 )/6a
r
=
0.289.J 0 2 + b 2
= '~
=(04 -
b~)/ 12
=(O.118a4-b4Vo
, = 0.289,j
A
= bd
~
/.
Z
r
=
=
bd/6
0.289 d
./
02 + b 2
d[ffJ?
I..
j
b
.S\'
' .
:'
~
d
Y
hk.1
bd - hk
bd
2
bd /24
=
= 0.236 d
Y
=d
I
= bd 3/12
= bd112
Z
, = 0.408
d
A = d(a+ bJ/2
Y '" d(o + 2b)/3(a + b)
d,1 (a 2 + -I ab + b 2)
I = -3-6-(a +b)2
d (a 2 + -I ab + b 2)
Z = ----:-;-12 (a+2b)
A
=..J/iA
= 0.7854d 2
y =
d/2
.
...•.".".'::.'."'."'."..'...•' '••..............
.•..•..•.....'.'. :
...•.•.•. : .•... .•..::•..
......
I bdJ -
v'
r
r
~
: ~'."~;'\"
",
I = bd-;12
b
0.289
hk J )/6 d
1= bdo/36
.1
b
n
= 0.7070
l
hk 3 )/12
-
Y=¥:ld
Z
4
I
3
Z =(Pd] -
y='I2 0
Y
d
bd-hk
I =(bd
0.1180 3
=
A
.1
=d
Z
ai'3
I = 04/12
b
Y
bd
y = V2d
= 02
= 0.7070
y
I
=
1= bd/3
r=0.5770
A
ITa
b
= 0'l3
Z
1
0
0
A
A
{OJ
I.
Z
Radius of gyration, viTIA
Distance from neutral axis to extreme fiber, in.
Section modulus, l/y, in. 3
I = 0.049 d
=
, =
Z
0.098d
d/4
4
3
451
PROPERTIES OF SECTIONS
DEFINITION OF SYMBOLS
r
A
y
I
Area, in.l
Moment of inertia, in.·
Z
V
Radius of gyration,
II A
Distance from neutral axis to extreme fiber, in.
J
Section modulus, Jly, in.
""TT"I
y'" D/2
I
=
Z
='
0.049 (d-d~
0.098(D~-d~)/D
r ",...[fii+Ci1/ 4
:f9
Section of thin walled
cylinder when R > /01
A = 2R1Tt
Y=R
I = R-'I7T
Z = R'17T
1
r = 0.707R
A '" ((2 a-I)
~l.~I
I.
Y
=a_
I
= 1,-)( ly 3+ a(a_y)3
- (a - I) (a -
a
A '" I(a+b-I)
=
.1
=
Z
1.5708 (Rl_ r/)
Y", b/2
1=(2 sb J +h(.1)/12
Z =(2 sb J +h(.1)/6 b
=.../T!A
r
r = V7[A
A '" bd-h(b-I)
y '" a
Y = d/2
I '" 0.7854 alb
I ",!Pd J -h.1(b-O]/12
z
r
A
= 0.7854 a'b
=
a/2
I
Z ",.[bdJ_hJ(b_I)]
, '"
= bs +
_ d
y -
h(
d'( + s'(b-I)
2(bs+ hi)
=
VJ (ly.1+ b(d-yJl
-(b-I)(d-y-s).1)
Z = f/y
r
VTiA
A '" bd-h(b-I}
Ily
= 3.1416 ab
6d
r =
R+r,
A
I/y
bd'-hYb-l)
J
1= 0.1098 (R~-r,'
_ 0.283 Ri 'l' (R-r, )
=
=
=.JliA
y = dl2
y = O. 424(RJ - r;)j(Ri - rn
Z
Z
r
I '" [bd·~h.1(b-l)] /12
r = 0.132 d
A
1(2d + a) + d'
A = bd - h (b - I)
0.007 d 4
Z '" 0.024 d
b_
2(d+a)
1= y,(ly 3+ a(b_y).1
_(a_l)(b_y_I)')
y=O.l88d
I
=
Y
0.393 d '
A =
=VTiA
r
~ll~
a
y - In
Z =//y
til
I~
a'+al-('
2(2 a-I)
=..JTTA
.j
/6d
bdJ-h)(b-O
12(M-h(b-l))
A = bd-h(b-t)
Y - b
-
2 b' s+ hi'
2 bd-2h(b-l)
I ={2sb 3 + h/J)!3 -A(b-y)·'
Z
r
=
lIy
=.J17A
452
CENTER OF GRAVITY
The center of gravity of an area or body is the point through which about any axis the
moment of the area or body is zero. If a body of homogenous material at the center of
gravity were suspended it would be balanced in all directions.
The center of gravity of symmetrical areas as square, rectangle, circle, etc. coincides with
the geometrical center of the area. For areas which are not symmetrical or which are
symmetrical about one axis only, the center of gravity may be determined by calculation.
The center of gravity is located on the centerline of
symmetry. (Axis y - y)
To determine the exact location of it:
1. Divide the area into 3 rectangles and calculate the
area of each. (A, B, C)
2. Determine the center of gravity of the rectangles
and determine the distances a, band c to a
selected axis (x-x) perpendicular to axis y-y.
3. Calculate distance y to locate the center of gravity
by the formula:
y = Aa+Bb+Cc
A+B+C
y
,r-
-+ ~f +----,. C
c.g.
x lflo....-A_--I-----'-t-->--'-x
y
Assuming for areas of rectangles: A = 16, B = 14
and C = 12 square inches and for the distances of
center of gravities: a= 1, b=5 and c=9 inches.
EXAMPLE #1
y = 16 xl + 14 x 5 + 12 x 9 = 4.62 in.
16+ 14+ 12
The area is not symmetrical about any axi:s. The
center of gravity may be determined by calculating
the moments wIth reference to two selected axes. To
determine the distances of center of gravity to these
axes:
1. Divide the area into 3 rectangles and calculate the
areas of each. (A, B, C)
2. Determine the center of gravity of the rectangles
and the distances, a, band c to axis x-x and the
distances aJ, bJ, c, to axis y-y.
3. Calculate distances x and y by the formulas:
y
x = Aal + Bb l + CCl
A+B+C
c
b
X
X
Y
y
EXAMPLE #2
x
=
16x4+14x1+12x3
16+ 14+ 12
=
= Aa+Bb+Cc
A+B+C
Assuming for areas of rectangles: A = 16, B = 14
and C = 12 square inches and for distances of
center of gravities: a=l, b=5, c=9: a,=4, b,=l
and c,=3
16 x 1 + 14 x 5 + 12 x 8 = 4.62 in.
2.71 in.
y
16+14+12
453
CENTER OF GRAVITY
TRIANGLE
The center of gravity is at the intersection of lines AD and BE,
which bisect the sides Be and A C. The perpendicular distance
from the center of gravity to anyone of the sides is equal to onethird the height perpendicular to that side. Hence, a = h ..;- 3.
TRAPEZOID
The center of gravity is on the line joining the middle points of
parallel lines AB and DE.
h(a+2b)
d=h(2a+b)
c=
3 (a + b)
3 (a + b)
a 2 + ab + b 2
e=
3 (a + b)
SECTOR OF CIRCLE
Distance b from center of gravity to center of circle is:
2
b = 2 rc = r c = 38 197 r sin 0:
31
3A
.
0:
in which A = area of sector, and 0: is expressed in degrees.
For the area of a half-circle:
b = 4 r";- 3 Tr = 0.4244 r
For the area of a quarter circle:
b= 4
X r ..;- 3 Tr = 0.6002 r
For the area of a sixth of a circle:
b
2 r";- Tr 0.6366 r
J2
=
=
SEGMENT OF CIRCLE
The distance of the center of gravity from the center of the circle
is:
c3
2
r3 sin 3 0:
b = 12 A = 3 X
A
in which A = area of segment.
PART OF CIRCULAR RING
Distance b from center of gravity to center of circle is:
3
Angle
0:
b = 38.197 (R3 - r ) sin 0:
(R2 - r2) 0:
is expressed in degrees.
FRUSTUM OF CONE
For a solid frustum of a circular cone the formula:
h (R2 + 2 Rr + 3 r 2)
a=
4 (R2 + Rr+ r2)
The location of the center of gravity of the conical surface of a
frustum of a cone is determined by:
h (R + 2 r)
a=3(R+r)
454
CENTER OF GRAVITY
EXAMPLES
t--_ _ _ _ _ _ _ _ _I:.;:oo~·-.....;0:;....- - - - - - - _ + - 1 f + . 3 · -0"
A
70'-0"
2'-0"
80lbs
75000 Ibs
2·6.. -t--t-4------------...:..:..--------.....,1+-t--2· -0"
x
weight: 75000 Ib
80lb
1800 Ib
800lb
600lb
600 Ib
78880 Ib
75000
x
l<
50' + 80 x 2' + 1800 x 70' + 800 x
102' + 600 x 2'-6" + 600 x 97'-6"
78880 Ibs
= 4,017,760 = 50,935' = 50' -11-1/4"
78,880
56'-0"
U7000 Ibs)
"I
2'-0"
1000 Ibs
1400 Ibs
weight:
107'-0"
X
2400 x 3' + 24000 x 27' + 1000 x 49' + 17000 x 78' + 1400x lOT + 1900 x II'
=~~------~-.....:~--~--~--~~~~~~~~-------
47,700 Ibs.
2200,900
III
= - - - = 46.14' = 46'-1 116"
47,700
2400 Ih
24000lh
1000 Ib
17000lb
1400 Ib
1900lb
477001b
455
BEAM FORMULAS
DEFINITION OF SYMBOLS
= Modulus of elasticity,
= Moment of inertia, in.
= Length, in.
= Moment of force, in. lb.
p = Force of concentrated load, lb.
R = Reaction, lb.
W
fSi.
E
I
/
M
v
=
=
=
w
==
V
x
10ad,lb.
Total shear, lb.
Unit shear, Ib.lin.
unifonnly distributed load Ib.lin.
Distance parallel to axis X, in.
Deflection, in.
Angle of deflection, radians
=
=
=
.:1
e
Cantilever fixed at one end - Concentrated load at free end
p
l__________~
LUI
r=
R
.I
=
=
V
P
At support, Mmax = PI
Mx = Px
R
At free end, ~max
=
PI3
3EI
P
6EI
~x = - - (2P - 3f2x
+
x 3)
Cantilever fixed at one end - Concentrated load at any point
2
R = V = P
At support,
Whenx>a
Mmax = Pb
Mx = P(x - aj
At free end,
~max =
Whenx<a
2
~~ _ Pb (31 - 3x - b)
6EI
A
3
I
.1
(31 - b)
~
_ P - xj2 (3b - I + x)
3EI
x -
Uniform load over entire span
R = V = wi
~
Vx = wx
(IIIIIIIIIIIIIIIIIII~R
~
3
6EI
Whenx>a
-
Cantilever fixed at one end -
wi
Pb
At support,
A
At free end, '-lomax
=
Mmax
=
wi·
8EI
--
~
wf2
Mx=
2
_ ~ (r - 4Px
x -
24EI
2
+ 3f4)
4 Cantilever fixed at one end - Load increasing uniformly from free end to support
R = V= W
w=
A
2
Vx=W~
At support,
WP
At free end, ~ max = 15EI
Wf2
At free end, 0 = + - - 12EI
12
Mmax =
Mx =
Wx 3
3f2
WI
3
~x = ~
60EIP
(.x'-5f4x+41')
456
BEAM FORMULAS
s
Supported at both ends Concentrated load at mid-span
RJ = R2 = V = PI2
PI
Mx= Px
At load, Mmax = - When x < I 12
RJ~----------~R2
4
2
PI'
A
d
PI2
At load, ~max = 48EI
ten, (JJ = - 16£1 = - (h
A
Px
I 12 ~x = - - (312 - 4XZ)
48EI
<
When x
Supported at both ends Concentrated load at any point
Pab
Max when a < b RI = VI = Pb At load, Mmax = - -
6
P
M ax when a>b R2
=
V2
Whenx<a
I
..
I
Pbx
I
Pa 2 b 2
At load, A = - 3EII
I
= -~-
RJ ~---.&..- R2 when a> b
=
Mx
Whenx<a
At ends,
7
RI
Supported at both ends Two unequal concentrated loads, equally spaced from ends
R = V =P
Mmax = Pa
Whenx<.a Mx = Px
Pa
At center, A max = 24EI (3P - 4a 2)
~_...._____.. R2
~ x = Px (31a - 3a2
When x <a
6EI
Pa
6EI (31x -
Whenx>a ~ _
but x «I-a) x At ends, 6
-
r)
2
3r - a)
Pa 2EI (I - a)
=
8 Supported at both ends Two equal concentrated loads, unequally spaced from ends
RI = VI
PI(I- a) + P2b
R2 = V2=Pla + P2(/ - b)
P
P
I
R/~---......-
.. R2
When x>a
but x </1 _ bl V
I'
'/
When x<a
Whenx>a
but x < (I - b)
9
Supported at both ends
R =V
=
I
Max when RI<PI MI
= RI - PI
Max when R2<P2 M2
Mx = RI x
Mx
= RI X
= R2 b
(x - a)
+-
Uniform load over entire span
V =w(
;1
wP
At center, Mmax =-8
5w/ J
At center, ~max = 384EI
At ends,
-
= RI a
6
=
wf3
24EI
x )
wx
Mx = - ( 1 - x)
2
~x =
2
2;;1 (P - 21x + xl)
457
BEAM FORMULAS
10
Supported at both ends Uniform load partially distributed over span'
wb
Max when a<c RI = VI = - - (2c + b)
21
Max when a>c R2 = V = wb (2a + b)
21
When x>a but x «a + b) Vx = RI - w(x - a)
Mmax = RI
(a+~
2w)
When x <a
Atx = a
+~
w
Mx =RlX
W
Whenx>a butx«a+b) Mx =Rlx- 2" (x - aj2
When x>(a+ b) Mx = R'l(1 - x)
11
Fixed at both ends Concentrated load at mid-span
I
t----'--_+--1-/2---<~
R =V = P
At center and Mmax = ~
.~
0.2
at ends,
8
2f
~
R0; j - - -....~ x
'I
I
~
......
.1
I.
11
R
2
When x <112
Mx
0::
At center,
A max
=
P (4x - I)
8
= -PP-
Ax =
192£1
Pr (31 - 4x)
48EI
Fixed at both ends Uniform load over entire span
V
= ~l
I1111111111 i I! 11111 t§R
I~~
~ ~ A tend s,
lYlmaX
'-
~
~
I
I
t - - - - - ' - - -..~
13
x
a
II'
=
AI
Vx
=
=W
12/2
W /
1
po
a
(
~
A
-
x)
t center,
Mx = W /12 (61x - 12 - 6x2).
A
_
wi
t center,
~ max 384£1
Both ends are overhanging Uniform load
R = VI + V2 = w(a + 112)
WXl 2
For overhang, Mxl = - 2
Between
supports,
Mx
=
III III ill I III
n
II
R
M -_ wll /24
r/
2
"x __ ~
....
24EI
(I
_
x)
2
over entire beam
Vxl = WXI Vx = w(x - 112)
wa 2
At support, M = - 2
w
2
(Ix -
X2
-
At center, Me.= ~ (12 - 4 a 2)
8
When a = .207 x total length or A = .3541
wf2
M=Mc. =
16
a 2)
458
DESIGN OF WELDED JOINTS
FOR STRUcruRAL MEMBERS
GROOYE-WELD
Groove welds are usually a continuation of the base metal. For groove welds the same
strength is ascribed as for the members that they join.
FlLJ.,ETWELD
Size of weld
I ~h~at
The size of an equal-leg fillet weld is the leg
dimension of the largest 450 right triangle inscribed
in the cross section of the weld.
eg
The size of an unequal-leg fillet weld is the
shortest distance from the root to the face of the
fillet weld.
~~
~root
Throat dimension
= 0.707
x leg dimension
Minimum Weld size·
Thickness of the thicker plate, in.
Y2
¥4
Y2
Minimum fillet weld size, in.
¥16
Y4
0/16
2Y4
3fs
6
Y2
over
6
5fs
* Weld size need not to exceed the thickness of the thinner part joined
Economy of fillet welding
1. Use the minimum size of fillet weld required for the desired strength.
Increasing the size of a fillet weld in direct proportion, the volume (and costs) of it
will increase with the square of its size.
2. Locate weld to avoid eccentricity, to be readily accessible, and in down-welding
position.
3. Apply fillet weld transversely to the force to achieve greater strength.
~ PARALLEL
P'
WELD
~
TRANSVERSE
~
WELD
Allowable Load
The strength of the welds is a function of the welding procedure and the electrode used.
For carbon steel joints commonly used maximum allowable static load 9,600 (9.6 kips) Ibs
per 1 square inch of the fillet weld leg-area, or 600 Ibs on a Y16" leg x 1" long fillet weld.
For example: the allowable load on a Y4" x 1" long fillet weld 4 x 600 = 2,400 lbs.
Combined Loads
Shear stress and bending or torsional stresses due to eccentric loadings may be combined
vectorially. It is based on the elastic theory and provides a simplified and conservative
method.
459
DESIGN OF WELDED JOINTS
FOR STRUcrURAL MEMBERS
subjected to bending moment, in 2
V = Vertical shear, kips
w = Fillet weld leg dimension, in
W = Load on fillet weld, kips per
lineal inch of weld
W,r = Average vertical shear on fillet
weld, kips per lin. inch of weld
Wb = Bending force on weld, kips per
lin. inch of weld
DEFINmON OF SYMBOLS
Aw = Length of weld, in.
t = Allowable
load on weld, 9.6 kips
per in2 • le~-area
M = Bending moment, kips
P = Allowable concentrated axial
load, kips
Sw = Section Modulus of weld lines
FORMULAS FOR FORCES ON WELD
Ws
TENSION OR
COMPRESSION
VERTICAL
RESULTANT FORCE: W = YW,2 +
wi
= -V
Aw
SH~AR
BENDING
+ W/
EXAMPLE #1
Determine the required size of fillet weld. The length of the weld is all around 8.5
inches and the tensional load 20 kips.
20,000 lbs.
W
= ~ ='~=
w
= ~ = 29~: = 0.24; use~"
Aw
8.5
2.35 kips per lin. in.
fillet weld
EXAMPLE #2
Determine the required size of fillet weld. The length of the weld 12 inches (6" each
side) and the load 9 kips.
9,000 lbs
Section modulus, (from table)
Bending Force,
~
=
Sw
Shear Force Ws =
~
12
Sw
Fillet weld size,
W
62
12 in'
= 2.25 kips per lin. inch
~w = ~ = 0.75 kips per lin. inch
Resultant force, W =oJWb2 + W/
vi
tf
= 3"= 3"=
= 2.37 kips per lin.
+
=
=2.37 = .247"; use W' fillet weld
W
t
0.752
=
2.25 2
9.6
inch.
460
DESIGN
OF
WELDED
JOINTS
PROPERTIES OF WELD OUTLINES
d~t_-x
cf
Sw = -6
d2
SW = 3
Sw
Sw (top)
= bd
d (4b
=
6
+ d)
d 3 (4b+d)
Sw (bottom) = 6 (2b + d)
(max.stress at bottom)
S
w
=
d2
bd -+6
_ d (2b + d)
Sw ( top ) 3
Sw
=
d2 (2b+ d)
(bottom) 3 (b + d)
(max. force at bottom)
2
'TT d
Sw =4-
461
EXAMPLE CALCULATIONS
EXAMPLE #1
A platform is supported by 3 equally
spaced channels bolted to lugs. The
floor load is 125 Ibs per square feet.
The other design data are shown in the
figures.
Determine the stresses in the channels
and bolts.
One half of the total load is supported
by the middle channel, thus the stress
conditions only of this channel shall be
investigated.
Area supported by the middle channel:
~ .7854 (li-5 2 )= 15.577 sq. ft.
360
=
Load: 15.577 x 125
1947 lbs
Center of gravity (see page 434):
3
b = 38.197 (R -,J) sin oc =
(R2 -,z) oc
3
3
38.197 (6 - 2.5 ) 0.500
(62 - 2.5 2 ) 30
4.28
Moment:
1947 x 2.28 x 12 = 53,270 in-lb
Moment of inertia:
I
xx
Ixx
4"1
_ bd 3
12
.b I d? _
12-
_
-
2 X 123
12
= -- -
1.75 X 11.53
12
66.206
Section modulus:
Z
= : = 66 206 = 11.034
6
Stress in channel at the support:
53,270
S = 11.034 = 4828
- --
::
N
::
~
.
pSI
Stress in bolts: (center on bolts pattern)
load on one bolt:
53,270
8
.
try '/11
bolt; A =0.6013 in 2
6659
S
= 6659 lb.
= 0.6013 =
11074 psi.
462
EXAMPLE CALCULATIONS
EXAMPLE #2
A vertical vessel is supported by two
beams.
The weight of the vessel is 20,000 lbs
I = 120 in
Assume pin joint
The load on one beam:
Moment:
M == PI = 10,000 x 120 =
4
4
10'·0"
300,000 in.lb
Required section modulus:
--
Z=M
SA
Assuming for allowable stress, SA: 20,000
psi,
Section modulus:
I
I
I
I
Z
= 300,000
= 15 in 3
20,000
The section modulus of a wide flange
WF 8 X 20 is 17 in3
Moment of inertia: 69.2
Stress at the center of wide flange:
S
10,0001bs
..
!
=M
Z
= 300,000 = 17,647 psi
17
Deflection:
.6.
= PP
==
48£1
3
10,000 X 120
48 x 29,000,000 x 69.2
.1794 in -
3/16
in.
463
BOLTED CONNECTIONS
FOR STRUCTURAL MEMBERS
REQUIRED LENGTH OF BOLTS
NOMINAL
REQUIRED BOLT LENGTH =
BOLT
GRIP + DIMENSIONS BELOW, inches
DIAMETER NO WASHERS 1 WASHER 2 WASHERS
m.
718
11!J6
Ih
I
5/8
V8
IV16
IY16
I
~
15/16
I Vi6
718
IV8
IV4
IV2
1%
I
1V8
IV4
IVs
IV2
15fI6
]7/16
I 1V16
r-
IV16
'-
10/)6
1Vi6
11Sf16
I~
113/16
115/16
IVs
2V16
2Y16
~~~b
--~B~~~~GRIP
21!J6
MINIMUM EDGE DISTANCE AND SPACE
The minimum distance from the center of bolt hole to any edge
BOLT
DIAMETER
in
MINIMUM EDGE DISTANCE
AT SHEARED
EDGES
AT ROLLED OR
GAS CUT EDGES
718
~
~
IYs
IV,
V8
IV2
Vs
I
I Vs
IV4
IIh
1%
P/8
V2
VB
I
lY4
IYs
IV,
2
2l,4
IIh
2%
vvl""
('<")
('<")
0
Z
-ill-
- - t-O
~II-
QS
--t-tf)
('<")
('<")
-1,.-. 1"'--l-
-t-
-i LEDGE
DISTANCE
BOLT HOLES shall be Y16" larger than bolt diameter.
ALLOWABLE LOADS in kips
SA 307 unfinished bolts and connected material: SA 283C, SA 285C, SA 36
Nominal Diameter
of Bolt
%
Tensile Stress
Area, in
718
I
IV8
1l,4
IVs
I V2
0.2260 0.3345 0.4617 0.6057 0.7633 0.9691 1.1549 1.4053
Allowable Loads
in Tension
Allowable
Loads in
Shear
~
4.52
6.69
9.23
12.11
15.27
19.38
23.10
28.11
Single
3.07
4.42
6.01
7.85
9.94
12.27
14.85
17.67
Double
6.14
8.84
12.03
15.71
19.88
24.54
29.70
35.34
-------------NOTES
465
PARTV.
MISCELLANEOUS
1.
Abbreviations......... ............................................................................... 466
2.
Codes, Standards, Specifications .......................................................... 470
3.
Boiler and Pressure Vessel Laws.......................................................... 474
4.
List of Organizations Sponsoring or Publishing Codes,
Standards or Specifications Dealing with Pressure Vessels ................. 476
5.
Literature............................................................................................... 479
6.
Definitions ................................. ............................... .... ........ .... ............ 483
7.
Index ..................................................................................................... 494
466
ABBREVIATIONS
COMPILED: From 1. ASA Z32.13-1950 ABBREVIATIONS FOR USE
ON DRAWINGS
2. ASA ZlO.1-1941 ABBREVIATIONS FOR
SCIENTIFIC & ENGINEERING TERMS
ADDED:
AB
AISC
ALLOW
ANSI
ASA
API
APPROX
ASB
ASME
ASTM
AVG
bbl
BC
BEV
BLD
BOP
BOT
BRKT
btu
BW
BWG
C
CA
ABBREVIATIONS GENERALLY USED ON
VESSEL & PIPING DRAWINGS
Anchor Bolt
American Institute
of Steel Construction
Allowance
Allowable
American National
Standards Institute
American Standard
Association
American Petroleum
Institute
Approximately
Asbestos
American Society of
Mechanical Engineers
American Society
for Testing Mat'ls.
Average
Barrel
Bolt Circle
Bevel
Blind
Bottom of Pipe
Bottom
Bracket
British Thermal
Unit
Bevel Weld
Birmingham Wire
Gauge
Degree Centigrade
Corrosion Allowance
CCW
cfm
CFW
CG
CG
cm
CO
CONC
CPLG
CORR
ALLOW
COUP
CRS
CS
C to C
CTR
cu
cu. ft.
CW
CWT
DC
DEH
DET
DIA
DIAM
DIM
DP
Counter Clockwise
Cubic Foot per
Minute
Continuous Fillet
Weld
Commercial Grade
Center of Gravity
Centimeter
Centerline
Centerline to
Centerline
Company
Concentric
Coupling
Corrosion Allowance
Coupling
Cold Rolled
Steel
Carbon Steel
Cen ter to Cen ter
Center
Cubic
Cubic Foot
Clockwise
Hundred Weight
Downcomer
Double Extra
Heavy
Detail
Diameter
Diameter
Dimension
Design Pressure
467
ABBREVIATIONS (cant.)
i
DT'L
DWG
EA
EH
EL
ELEV
ELL
ELLIP
EQ
ETC
EXT
F
F-F
F&D
FF
FIG
FIN
FLG
FS
ft
FT3
FW
g
GA
GALV
gal
GG
GOL
gpd
gpm
GR
HVY
HD
HEMIS
HEX
HH
HL
Detail
Drawing
Each
Extra Heavy
Elevation
Elevation
Elbow
Ellipse, Elliptical,
Ellipsoid
Equal, Equally
Et Cetera
External
Fahrenheit
Face to Face
Flanged & Dished
Flat Face
Figure
Finish
Flange
Far Side, Forged
Steel
Foot, Feet
Cubic Foot
Fillet Weld
Gram
Gage
Galvanized
Gallon
Gage Glass
Gage of Outstanding
Leg
Gallon per Day
Gallon per Minute
Grade
Heavy
Head
Hemispherical
Hexagonal
Handhole
Hole
HLA
HLL
HLSD
HR
HT
ID
in
INCL
INS
INT
JE
kg
I
lb
lbf
lbs
LC
LeV
LG
LG
Lin. ft.
LLA
LLC
LLSD
LR
LS
LWN
m
MB
MK
MAT'L
MAWP
MAX
MH
MIN
MK'D
High Level Alarm
High Liquid Level
High Level Shut
Down
Hot Rolled
Heat Treatment
Inside Diameter
inches
Including, Included
hlspection
Internal
J oint Efficiency
Kilogram
Liter
Pound
Pound Force
Pounds
Level Control
Liquid Control Valve
Long
Level Gage
Lineal Foot (Feet)
Low Level Alarm
Liquid Level Control
Low Level Shut
Down
Long Radius
Low Stage
Long Welding Neck
Meter
Machine Bol t
Mark
Material
Maximum Allowable
Working Pressure
Maximum
Manhole
Minimum
Marked
468
ABBREVIATIONS (cont.)
mm
MMSCF
MSCF
MW
N
N&C
NLL
NO
NOM
NPS
NPT
NS
NTS
OA
OD
OR
OSHA
oz
ozs
P
PBE
PC
PeS
PCV
PI
It
PROJ
PSE
psi
psia
psig
Millimeter
Million Standard
Cubic Feet
Thousand Standard
Cubic Feet
Manway
North
New & Cold
Normal Liquid Level
Number
Nominal
National Pipe Size
American National
Taper Pipe Thread
Near Side
Not to Scale
Overall
Ou tside Diameter
Ou tside Radius
Occupational Safety and
Health Administration
Ounce
Ounces
Pressure
Plain Both Ends
Pressure Control
Pieces
Pressure Control
Valve
Pressure Indicator
Plate
Projection
Plain Small End
Pound per Square
Inch
Pound per Square
Inch Absolute
Pound per Square
Inch Gage
RAD
REF
REINF
REPAD
REQ'D
RF
RJ
RTJ
RV
S
SIC
SCF
SCH
SCR
SCR'D
SDV
SERV
Sht.
SF
SHT
SM
SMLS
SO
SPA
SPEC
SPGR
SQ
SR
SS
S-S
SIS
STD
STL
STR
SUPT
SYM
T&B
TC
TBE
Radial
Reference
Reinforcing
Reinforcing Pad
Required
Raised Face
Ring Joint
Ring Type Joint
Relief Valve
Schedule
Shop Coat
Standard Cubic Foot
Schedule
Screw
Screwed
Shu tdown Valve
Service Sheet
Straight Flange
Sheet
Seam
Seamless
Slip On
Spacing
Specification
Specific Gravity
Square
Short Radius
Stainless Steel
Seam to Seam
Standard
Steel
Straddle
Support
Symmetrical
Top & Bottom
Temperature Control
Threaded Both Ends
469
ABBREVIATIONS (cont.)
PSV
R
TEMA
THD
THK
TI
TLE
TOC
TOS
TS
TSE
T-T
TW
TW
Pressure Safety Valve
Radius
Tubular Exchanger
Manufacturers
Association
Threaded, Thread
Thick
Temperature
Indicator
Threaded Large End
Top of Concrete
Top of Steel
Tube Sheet
Threaded Small End
Tangent to Tangent
Tack Weld
Thermowell
TYP
USAS
VA
VOL
WI
WG
WN
W/OUT
WP
WT
XH
XXH
XXSTG
Typical
United States of America Standards Institute
Valve
Volume
With
Water Gallon
Welding Neck
Without
Working Pressure
Weight
Extra Heavy
Double Extra
Heavy
Double Extra
Strong
470
CODES, STANDARDS, SPECIFICATIONS
PRESSURE VESSELS, BOILERS
ASME
I
II
III
IV
V
VI
VII
VIII
IX
X
XI
Boiler and Pressure Vessel Code, 2001
Power Boilers
Materials
Nuclear Power Plant Components
Heating Boilers
Nondestructive Examination
Recommended Rules for Care and Operation of Heating
Boilers
Recommended Rules for Care of Power Boilers
Pressure Vessels - Division 1,
Division 2 and 3 Alternate Rules
Welding and Brazing Qualifications
Fiberglass-Reinforced Plastic Pressure Vessels
Rules for Inservice Inspection of Nuclear Power Plant
Components
British Standards Institution (BSI)
1500 - Fusion Welded Pressure Vessels for Use in the Chemical,
Petroleum and Allied Industries
1515 -Fusion Welded Pressure Vessels for Use in the Chemic.al,
Petroleum and Allied Industries (advanced design and con
struction)
Canadian Standards Association (CSA)
B-51-MI991- Code for the Construction and Inspection of Boilen
and Pressure Vessels
TANKS
American Petroleum Institute (API)
Spec 12B Specification for Bolted Tanks for Storage of Production
Liquids, 1990
Spec 12D Specification for Field Welded Tanks for Storage of Production Liquids, 1982
471
CODES, STANDDARDS, SPECIFICATIONS
(Continued)
Spec 12F Specification for Shop Welded Tanks for Storage of Production Liquids,
1988
Std. 620 Recommended Rules for Design and Construction of Large Welded, LowPressure Storage Tanks, 1990
Std. 650 Welded Steel Tanks for Oil Storage, 1988
Underwriters Laboritories, Inc. (UL)
No. 142
No. 58
Steel Aboveground Tanks for Flammable and Combustible Liquids
Steel Underground Tanks for Flammable and Combustible Liquids
American Water Works Association (A WW A)
No. 30
No. 58
No. 59
Flammable & Combustible Liquids Code
Liquified Petroleum Gases, Storage and Handling
Liquified Petroleum Gases at Utility Gas Plants
PWING
American National Standards Institute (ANSI)
831.1-1998
831.2-1968
831.3-1999
831.4-1998
831.5-2000
83l.8--1999
Power Piping
Fuel Gas Piping
Chemical Plant and Petroleum Refinery Piping
Liquid Petroleum Transportation Piping Systems
Refrigeration Piping with 1978 Addenda
Gas Transmission and Distribution Piping Systems
HEAT EXCHANGERS
Expansion Joint Manufacturers Association, Inc.
Standards, 5th Edition with 1985 Addenda and Practical Guide to Expansion Joints
PWES
American National Standarsa Institute (ANSI)
ANSI 836.19-1976 Stainless Steel Pipe
ANSI! ASME 836.1 OM- 1985 Welded and Seamless Wrought Steel Pipe
472
CODES, STANDARDS, SPECIFICATIONS
FITI1NGS, FLANGES, AND VALVES
American National Standards Institute (ANSI)
ANSI B16.25-1992 Buttwelding Ends
ANSI B 16.1 0-1992 Face-to-Face and End-to-End Dimensions of
Ferrous Valves
ANSI B16.9-1993 Factory-Made Wrought Steel Buttwelding
Fittings
ANSI B 16.14-1991 Ferrous Pipe Plugs, Bushings, and Locknuts
with Pipe Threads
ANSI B16.11-1991 Forged Steel Fittings, Socket-Welding and
Threaded
ANSI B16.5 1988 Pipe Flanges and Flanged Fittings, Steel, Nickel'
Alloy and Other Special Alloys
ANSI B16.20-1993 Ring-Joint Gaskets and Grooves for Steel Pipe
Flanges
MATERIALS
The American Society for Testing and Materials (ASTM)
1989 Annual Book of ASTM Standards, Section 1 Iron and Steel
Products
Volume Ol.OllSteel Piping, Tubing and Fittings, 131 Standards
Volume 01.03/Steel Plate, Sheet, Strip, and Wire, 95 Standards
Volume 01.04/Structural Steel, _Concrete Reinforcing Steel,
Pressure Vessel Plate and Forgings, Steel Rails,
Wheels, and Tires - 135 Standards
MISCELLANEOUS
International Conference of BuDding Officials (ICBO)
Uniform Building Code - 1991
Steel Structures Painting CouncU (SSPC)
Steel Structures Painting Manual
Volume 1, Good Painting Practice
Volume 2, Systems and Specifications
Uniform BoUer and Pressure Vessel Laws Society
Synopsis of Boiler and Pressure Vessel Laws, Rules and Regulations
by States, Cities, Counties and Provinces (United States and Canada)
-1990,
473
CODES, STANDARDS, SPECIFICATIONS
Environment Protection
Code of Federal Regulations, Protection of Environment, 1988 40-Parts 53
to 60 (Obtainable from any Government Printing Office).
American Society of Civil Engineers (ASCE)
Minimum Design Loads for Buildings and Other Structures
ANSIIASCE 7-95 (Formerly ANSIIASCE 7-93)
474
TABULATION OF THE
BOILER AND PRESSURE VESSEL LAWS
OF THE UNITED STATES AND CANADA
JURISDICTION
r
ill N
Alabama
Alaska
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
Florida'Y
Georgia
Hawaii
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massach usetts
Michigan
Minnesota
Mississippi
Missouri
Montana
Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Puerto Rico
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
Y Y
Y Y
N Y
Y Y
Y Y
Y Y
Y Y
Y Y
N Y
Y Y
N Y
Y Y
Y Y
Y Y
Y Y
Y Y
Y Y
N Y
Y Y
Y Y
Y Y
Y Y
Y Y
N Y
Y Y
N Y
N Y
N Y
N Y
Y Y
N Y
N Y
Y Y
N Y
Y Y
N Y
Y Y
Y Y
Y Y
Y Y
N N
N Y
Y Y
Y Y
Y Y
N Y
Y Y
~II(l) ~III(2)
Y
N
N
Y
Y
Y
N
Y
N
Y
Y
Y
Y
Y
Y
Y
Y
N
Y
Y
Y
y*
Y
Y
Y
N
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
N
Y
N
Y
Y
Y
Y
Y
N
Y
Y
Y3
N
Y3
N
Y
Y
Y3
Y
Y
Y3
Y3
Y
N
Y3
Y3
N
N
Y
N
Y3
N
Y3
Y
Y
Y
N
N
Y
Y3
Y
Y
Y
Y
Y
Y
N
N
Y3
N
Y3
Y
Y
XI
Y
N
N
Y
Y
Y
N
Y
N
Y
N
Y
Y
Y
N
Y
N
N
Y
Y
Y
Y
Y
N
Y
N
N
N
Y
Y
N
N
Y
N
Y
N
Y
Y
Y
Y
N
N
Y
Y
Y
N
Y
EXPLANATION
The column headings indicate the Sections and
Divisions of ASME Boiler
and Pressure Vessel Code.
I -Power Boilers
H - Nuclear Components
IV
VIII(1)
Vill(2)
IX
-Heating Boilers
-Pressure Vessels
-Pressure Vessels
-Inservice Inspection
Nuclear
Y - Design and construction shall conform to the
appropriate code section.
Y3 - Denotes Section VIII,
Division 2 and 3.
N - Design and construction is not covered by law.
* - Only portions of code.
SOURCE:
This condensed tabulation
of data is taken from the
Synopsis of Boiler and
Pressure Vessel Laws,
Rules and Regulations,
Copyright 1998, Uniform
Boiler and Pressure Vessel
Laws Society.
It dies not list all the exemption and variances in
the many laws and regulations. More detailed information is available under
the Society's Synopsis.
Further information may
be obtained from the jurisdictional authority or from
the society.
I
475
TABULA TION OF THE
BOILER AND PRESSURE VESSEL LAWS
OF THE UNITED STATES AND CANADA
(Continued)
I
JURISDICTION
Washington
West Virginia
Wisconsin
Wyoming
Alberta
British Columbia
Manitoba
New Brunswick
New Foundland
& Labrador
Northwest Territories
Nova Scotia
Ontario
Prince Edward Island
Quebec
Saskatchewan
Yukon Territory
Albuquerque
Buffalo
Chicago
Denver
Des Moines
Detroit
Los Angeles
Miami
Milwaukee
New Orleans
New York
Omaha
St. Joseph
Seattle
Spokane
Tacoma
Tucson
Tulsa
University City
Dade County
Jefferson Parish
St. Louis County
District of Columbia
I
Y
Y
Y
N
Y
Y
Y
Y
m
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
N
N
Y
Y
Y
Y
N
N
Y
Y
Y
N
Y
Y
Y
Y
Y
N
N
Y
Y
N
Y
N
N
N
N
Y
Y
Y
IV VIll(l) VIll(2) XI
Y
Y
Y Y
Y3
N
Y Y
N
N
Y Y
Y
Y
Y3
N N
Y
N
N
Y Y
Y
Y
Y
Y Y
Y
Y3
Y
Y Y
Y
Y
Y
Y
Y
Y Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y3
Y
Y
Y
Y
N
N
Y
Y
N
Y
Y
Y
Y
Y
N
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
N
N
Y
N
N
Y
N
N
N
Y
Y
N
Y
N
N
N
Y
N
N
N
Y
N
N
N
N
N
N
N
N
Y
EXPLANATION
The column headings indicate the Sections and
Divisions of ASME Boiler
and Pressure Vessel Code.
I -Power Boilers
n -NuclearComponents
N
VIII(l)
VIII(2)
IX
- Heating Boilers
-Pressure Vessels
-Pressure Vessels
-Inservice Inspection
Nuclear
Y - Design and construction shall conform to the
appropriate code section.
Y 3 - Denotes Section VIII,
Division 2 and 3.
N - Design and construction is not covered by law.
* - Only portions of code.
SOURCE:
This condensed tabulation
of data is taken from the
Synopsis of Boiler and
Pressure Vessel Laws,
Rules and Regulations,
Copyright 1998, Uniform
Boiler and Pressure Vessel
Laws Society.
It dies not list all the exemption and variances in
the many laws and regulations. More detailed information is available under
the Society's Synopsis.
Further information may
be obtained from the jurisdictional authority or from
the society.
476
LIST OF ORGANIZATIONS
SPONSORING OR PUBLISHING CODES AND STANDARDS OR
SPECIFICATIONS DEALING WITH PIPING AND PRESSURE VESSELS
T = Telephone· F = Fax • E = e-mail· W = Website
ABS
American Bureau of Shipping
Two World Trade Center, I 06th Floor
New York, NY 10048 USA
T
F
E
W
212-839-5016
212-839-5208
devans@eagle.org
www.eagle.org
AISG
American Insurance Services Group, Inc.
85 John Street
New York, NY 10038
T
212-669-0427
ANSI
American National Standards Institute
11 West 42nd Street
New York, NY 10026
API
American Petroleum Institute
1220 L. Street Northwest
Washington, D.C. 20005
F 212-669-0550
E rthonnings@aisg.org
W www.aisg.org
T
212-642-4900
F 212-302-1286
E quote@ansi.org
W www.ansi.org
T
202-682-8375
F 202-962-4776
E publications@api.org
W www.api.org
T
800-548-2723
ASCE
The American Society of Civil Engineers
1801 Alexander Bell Drive
Reston, V A 20191-4400
E marketing@asce.org
W www.pubs.asce.org
ASME
T
The American Society of Mechanical Engineers
3 Park A venue
New York, NY 10016-5980
F 973-882-1717
ASTM
American Society for Testing and Material
100 Barr Harbor Drive
West Conshohocken, P A 19428
AWWA
American Water Works Association
6666 West Quincy Avenue
Denver, CO 80235
AWS
American Welding Society
P.O. Box351040
Miami, FL 33135
BSI
British Standards Institution
389 Chiswick High Road
London W44AL
*British Standard Publications are available from
The American National Standards Institute
F 703-295-6333
800-843-2763
E infocentral@asme.org
W www.asme.org
T
610-832-9500
F 610-832-9555
E service@astm.org
W www.astm.org
T
303-794-7711
F 303-347-0804
E
W www.awwa.org
T
800-334-9353
F 305-443-7559
E
W www.aws.org
T 181-996-7474
F 181-996-7048
E
W www.bsi.org.uklbsi
477
LIST OF ORGANIZATIONS
SPONSORING OR PUBLISHING CODES AND STANDARDS OR
SPECIFICATIONS DEALING WITH PIPING AND PRESSURE VESSELS
(Continued)
CSA
Canadian Standards Association
178 Rexdale Blvd.
Etobicoce (Toronto)
ON Canada M9W IR3
T 800-463-6727
F 416-747-2475
E sales@csa.ca
W
Commercial Union Insurance Company
of America
I Beacon Street
Boston, MA 02108
T 617-725-7309
F 617-725-6094
E
W www.cuusa.com
CGA
Compressed Gas Association, Inc.
1725 Jefferson Davis Highway, Ste. 1004
Arlington, VA 22202
T
F
E
W
703-412-0900
703-412-0128
customerservice@cganet.com
www.cganet.com
EJMA
Expansion Joint Manufacturers Assoc.
25 North Broadway
Terrytown, NY 10591
T
F
E
W
914-332-0040
914-332-1541
ejma@ejma.org
www.ejma.org
HEI
Heat Exchange Institute, Inc.
1300 Summer Avenue
Cleveland, OH 44115
T
F
E
W
216-241-7333
216-241-0105
hei@taol.com
www.taol.com/hei
ICBO
International Conference of Building Officials
5360 Workman Mill Road
Whittier, CA 90601
T 800-284-4406
F 888-329-4226
E
W www.icbo.org
National Board of Boiler and
Pressure Vessel Inspectors
1055 Crupper A venue
Columbus, OH 43229
T
F
E
W
614-888-2463
614-847-1147
orders@nationalboard.org
www.nationalboard.org
NFPA
National Fire Protection Association
P.O. Box 91 01, Batterymarch Park
Quincy, MA 02269
T
800-344-3555
800-593-6372
F
E
W
Occupational Safety & Health Administration
200 Constitution Avenue, N.W.
Washington, D.C.
T 202-219-4667
F 202-219-9266
E
W
PVRC
Pressure Vessel Research Council
(formerly: Welding Research Council)
3 Park A venue, 27th Floor
New York, NY 10016
T 212-705-7956
F 212-371-9622
E wrc@forengineers.org
W www.forengineers.org/wrc
478
LIST OF ORGANIZATIONS
SPONSORING OR PUBLISHING CODES AND STANDARDS OR
SPECIFICATIONS DEALING WITH PIPING AND PRESSURE VESSELS
(Continued)
Steel Tank Institute
570 Oakwood Road
Lake Zurich, IL 60047
T
F
E
W
TEMA
Tubular Exchanger Manufacturers
25 North Broadway
Terrytown, NY 10591
T 914-332-0040
F 914-332-1541
E tema@tema.org
W www.tema.org
SSPC
The Society for Protective Coatings
(formerly: Steel Structure Painting Council)
40 24th Street, 6th Floor
Pittsburgh, PA 15222
T
F
E
W
412-281-2331
412-281-9992
books@sspc.org
www.sspc.org
lL
Underwriters Laboratories, Inc.
333 Pfingsten Road
Northbrook, IL 60062
T
F
E
W
847-272-8800
847-509-6235
walkerd@ul.com
www.ul.com
T
UBPVLS
Uniform Boiler and Pressure Vessel Laws Society F
E
308 Evergreen Road, Ste. 240
W
Louisville, KY 40243
502-244-6029
502-244-6030
ray@uboiler.com
www.uboiler.com
847-438-8265
847-438-8766
ankiefer@interaccess.com
www.steeltank.com
United States Coast Guard
2100 Second Street S. W.
Washington, D.C. 20593
T 202-267-2967
F 202-267-4816
E comd.uscg.mil
W
US EPA Headquaarters Information Resources
Center Public Access
Ariel Rios Building
1200 Pennsylvania Ave., N.W. (3404)
Washington, D.C. 20460
T 202-260-5922
F 202-260-6257
E E-pu bl ic-access@epa.gov
W www.epa.gov
479
LITERATURE
1.
S. Timoshenko, Strength of Materials, 1955, D. Van Nostrand Co., New York.
2.
S. P. Timoshenko, Theory ofPlates and Shells, 1959, McGraw-Hill Book Co.,
New York.
3.
R. J. Roark and W. C. Young, Formulas for Stress and Strain, 5th Edition,
1975, McGraw-Hill Book Co., New York.
4.
K. K. Mahajan, Design of Process Equipment, 2nd Edition, 1985, Pressure
Vessel Handbook Publishing, Inc., Tulsa, OK.
5.
L. E. Brownell and R. H. Young, Process Equipment Design: Vessel Design,
1956, John Wiley and Sons, New York. (Out of print.)
6.
M. B. Bickel and C. Ruiz, Pressure Vessel Design and Analysis, 1967, Mcmillan
Publishing Co., Inc., New York.
7.
H. H. Bednar, Pressure Vessel Design Handbook, 2nd Edition, 1986, Van
Nostrand Reinhold Co., New York.
8.
S. S. Gill, The Stress Analysis of Pressure Vessels and Pressure Vessel Components, 1970, Pergamon Press, New York.
9.
J. F. Harvey, Theory and Design of Modern Pressure Vessels, 2nd Edition,
1974, Van Nostrand Reinhold Co., New York.
10. Pressure Vessels and Piping: Design and Analysis, (Collected Papers), Volume 1, Analysis, 1972, ASME.
11. Pressure Vessels and Piping: Design and Analysis, (Collected Papers), Volume II, Components and Structural Dynamics, 1972, ASME.
12. Pressure Vessels and Piping: Design and Analysis, (Collected Papers), Volume III, Materials and Fabrication, 1976, ASME.
13.
W. Soedel, Vibrations of Shells and Plates, 1981, Marcel Dekker, Inc., New
York.
14.
W. Flligge, Stresses in Shells, 2nd Edition, 1973, Springer - Verlag, New
York.
15.
R. Szilad, Theory and Analysis ofPlates, 1974, Prentice-Hall, Inc., Englewood
Cliffs, NJ.
480
16. M. Hetenyi, Beams on Elastic Foundation, 1974, The University of Michigan Press, Ann Arbor.
17. Foundation Design Handbook (Collected Papers), 1968, Hydrocarbon Processing, Houston, TX.
18. Design of Flanges for Full Face Gaskets, Bulletin No. 45, Taylor Forge &
Pipe Works, Chicago, IL.
19. M. L. Betterley, Sheet Metal Drafting, 1961, McGraw-Hill Book Co., Inc.,
New York.
20. M. H. Jawad & J. R. Farr, Structural Analysis and Design ofProcess Equipment. 1984, John Wiley & Sons, New York.
21. Kohan, Anthony Lawrence, Pressure Vessel Systems, 1987 , McGraw-Hill Book
Company, New York, NY.
22. Moss, Dennis R., Pressure Vessel Design Manual, 1987, Gulf Publishing Co.,
Houston, TX.
481
SUBJECTS
COVERED BY THE WORK(S) LISTED UNDER LITERATURE
(The numbers refer to the work(s) dealing with the subject)
Bending Of Cylindrical Shells -14
Bends, Analysis of Smooth - 6
Bins, Design of- 22
Blind Flanges with Openings - 22
Bolted Joints - 9
Brittle Fracture, Low Stress - 6
Buckling, - 6,10
of Flat and Curved Plates - Formulas-3
Buckling of Shells- 6
Cast Iron Pressure Vessels - 9
Collapse, Fatigue and Incremental- 6
Composite Materials - 12
Computer Analysis of Pressure Vessels- 8
Concrete for Pressure Vessels - 12
Cone, Conical Section when Half Apex
Angle is Greater than 30° - 7
Conical Heads and Reducers - 6
Corrosion - 6,12
Corrosion Resistant Materials - 12
Cracks, Development of - 6
Creep Effects - 8
Cylindrical Shells, Analysis of, - 6
Dead Loads - 7
Deformations in Pressure Vessels, - 3
Design of Flanges - 4
Rectangular Tanks - 4
Tall Stacks - 4
Tall Towers - 7
Discontinuity Stresses - 7, 9
Division 2 of ASME Code Comparison
to Division 1 - 4
Dynamic Stability - 11
Dynamic and Temperature
Stress Formulas - 3
Earthquake Loads -7,22
Economics of Design andConstruction - 9
Elastic Stability - 8
Plates and Shells - Formulas - 3
Elastic Stress Analysis - 6
Elevated Temperature Effects -10,12
Elliptical Opening Stress
Concentration - 9
Expansion Joints, Flanged and Flued - 4
Pipe Segment - 4
External Loads -10
External Pressure; Stress Analysis - 8
Fatigue - 9, 10, 12
Fatigue and Incremental Collapse - 6
Filament-Wound Pressure Vessels - 9
Flange Design - 4
Flange Design & Analysis - 8
Flanged and Flued Expansion Joints - 4
Flanges and Closures - 11
Flanges with Full Face Gasket -18
Flat Closure Plate - 6
Flat Plates - Formulas - 3
Stresses in,- 9
Floating Heads, Stress Analysis of, - 4
Foundation Design - 17
Fracture - 6
Fracture Mechanics -10
Fracture Properties of Materials -12
Heads, Stress Analysis of, - 8, 11
Heat Exchangers, Shell and Tube - 4
High Temperature Materials - 12
Hub Flanges, Rotation of, - 4
Hydrogen Embrittlement - 12
Large Openings in Flat Heads - 22
Large Openings in Cylindrical Shells - 22
Leg Support for Vertical Vessels - 4, 22
Ligament Stresses, Analysis of, - 8
Limit Analysis and Plasticity -10
Lobed Pressure Vessels - 9
Local Loading, Stress Analysis of, - 8, 11
Local Stresses in Vessels - 7, 22
Low Stress Brittle Fracture - 6
Low Temperature Materials -12
Lug Support for Vertical Vessels - 4, 22
Material Selection - 22
Materials for Vessels - 6,7,9
Membrane Stresses - 7, 9
Mitered Bends, Analysis of - 6, 8
Modular Construction - 9
Non-Bolted Closures - 9
Nozzles-11
Nozzles, Intersection Stress Analysis - 8
482
SUBJECTS (continued)
Nozzle Thennal Sleeves - 9
Oblique Nozzles - 6
Perforated Plates and Shells - 11
Pipe Bends, Stress Analysis of, - 8
Pipe Segment Expansion Joints - 4
Pipe Supports at Intervals - Fonnulas - 3
Pipe Loads - 7
Piping Systems, Stress Analysis of, - 6, 11
Plasticity - 10
Plastic Collapse - 6
Plates, Theory and Analysis of - 18
Prestressed Concrete Vessels - 9
Rectangular Tanks, Design of, - 4
Reinforcement of Openings - 7
Ring Support - 22
Rotation of Hub Flanges - 4
Saddle, Design of, - 7
Seismic Analysis - 11
Seismic Design. Vessels Supported by
Legs, Rings, Lugs, - 22
Selection of Materials - 6
Shallow Shells - 14
Sheet Metal Drafting - 19
Shell and Tub Heat Exchangers - 4
Shells of Revolution, Analysis of, - 6
Sliding Supports for Horizontal and
Vertical Vessels - 7
Spherical Shells, Analysis of, - 6
Stress and Strain Due to Pressure on or
Between Elastic Bodies - Fonnulas - 3
Stress Concentration - 9
Stress in Horizontal Vessels Supported
by Two Saddles (Zick) - 7
Stresses in Flat Plates - 9
Stresses in Vessels - 8, 14
Fonnula - 3
Stacks, Designs of Tall, - 4
Structural Dynamics - 11
Support of Vessels by Legs - 4, 7
Support of Vessels by Lugs - 4, 7
Support Lugs, Stresses Exerted
in Vessels by, - 24
Tall Stacks, Design of, - 4
Tall Towers, Vibration of, - 4
Tanks, Design of Rectangular, - 4
Temperature, Effects of Elevated, -10
Temperature Stresses - Fonnulas, - 3
Thennal Stresses, - 7, 9
Thick Cylinder - 9
Thick Shells, Analysis of, - 6
Tube Sheet Design, Fixed, - 4
Vertical Vessels Supported by Lugs - 4
Vibration -11,13
Analysis of Tall Towers - 4
Induced by Flow - 11
Weld Design - 7
Welded Joints, Design of, - 6,9
Welding, - 12
Wind-Induced Deflection of Towers - 7
Wind-Induced Vibration of Towers -7
Wind Loads - 7
483
DEFINITIONS
Abnsion - The removal of surface material
from any solid through the frictional action of
another solid, a liquid, or a gas or combination
thereof.
Absolute Pressure - The pressure above the
absolute zero value of pressure that theoretically obtains in empty space or at the absolute
zero of temperatre, as distinguished from gage
pressure.
Alloy - Any of a large number of substances
having metallic properties and consisting of
two or more elements; with few exceptions, the
components are usually metallic elements.
Angle Joint - A joint between two members
located in intersecting planes between zero (a
butt joint) and 90 deg. (a corner joint). (Code
UA-60)
Angle Valve - A valve, usually of the globe
type, in which the inlet and outlet are at right
angles.
Annealing - Annealing generally refers to the
heating and controlled cooling of solid material
for the purpose of removing stresses, making it
softer, refining its structure or changing its
ductility, toughness or other properties.
Specific heat treatments covered by the term
annealing include black annealing, blue annealing, box annealing, bright annealing, full
annealing, graphitizing, maleabilizing and process annealing.
Arc Welding - A group of welding processes
wherein coalescence is produced by heating
with an electric arc, with or without the
application of pressure and with or without the
use of filler metal.
Automatic Welding - Welding with equipment which performs the entire welding operation without constant observation and adjustment of the controls by an operator. The
equipment mayor may not perform the
loading and unloading of the work.
Ba«:king -
Material backing up the joint
during welding to facilitate
obtaining a sound weld at
the root.
Backing Strip is a backing
in a form of a strip.
Brittle Fra«:ture - The tensile failure with
negligible plastic deformation of an ordinary
ductile metal.
Brittleness - Materials are said to be brittle
when they show practically no permanent
distortion before failure.
Bushing - A pipe fitting for connecting a pipe
with a female fitting of larger size. It is a
hollow plug with internal and external threads.
Butt Weld -
on
A weld joining two members
lying approximately in the
same plane. Butt welded
joints in pressure vessel
construction shall have
complete penetration and
fusion.
Types of butt welded joints:
Single or Double Beveled
Joint, Square Butt Joint.
Full Penetration, Partial
Penetration Butt Joints.
Butt Joints with or without
backing strips.
484
Centroid of an Area (Center of Gravity of an
Area) - That point in the plane of the area
about any axis through which the moment of
the area is zero; it coincides with the center of
gravity of the area materialized as an infinitely
thin homogeneous and uniform plate.
Chain Intermittent Fillet Welds - Two lines of
intermittent fillet welding in
a tee or lap joint, in which
the increments of welding in
one line are approximately
opposite to those in the
other line.
Check Valve - A valve
designed to allow a fluid to
pass through in one direction only. A common type
has a plate so suspended
that the reverse flow aid~
gravity in forcing the plate
against a seat, shutting off
reverse flow.
Chipping - One method of removing surface
defects such as small fissures or seams from
partially worked metal. If not eliminated, the
defects might carry through to the finished
material. If the defects are removed by means
of a gas torch the term "deseaming" or "scarfing" is used.
Clad Vessel - A vessel made from plate having
a corrosion resistant material integrally bonded
to a base of less resistant material. (Code
UA-60)
Complete Fusion - Fusion which has occurred over the entire base-metal surfaces exposesd for welding.
Complete Penetration - Penetration which extended completely through the joint.
Corner Joint - A welded joint at the junction
of two parts located approximately at right
angles to each other.
Corrosion - Chemical erosion by motionless
or moving agents. Gradual destruction of a
metal or alloy due to chemical processes such
as oxidation or the action of a chemical agent.
Corrosion Fatigue - Damage to or failure of a
metal due to corrosion combined with fluctuating fatigue stresses.
Coupling - A threaded sleeve used to connect
two pipes. They have internal threads at both
ends to fit external threads un pipe.
Creep - Continuous increase in deformation
under constant or decreasing stress. The term is
usually used with reference to the behavior of
metals under tension at elevated temperatures.
The similar yielding of a material under compressive stress is usually called plastic flow or
flow.
Damaging Stress - The least unit stress, of a
given kind and for a given material and condition of service, that will render a member unfit
for service before the end of its normal life. It
may do this by producing excessive set, or by
causing creep to occur at an excessive rate, or
by causing fatigue cracking, excessive strain
hardening, or rupture.
Deformation (Strain) - Change in the form or
in the dimension of a body produced by stress.
Elongation is often used for tensile strain, compression or shortening for compressive strain,
and detrusion for shear strain. Elastic deformation is such deformation as disappears on
removal of stress; permanent deformation is
such deformation as remains on removal of
stress.
Design Pressure - The pressure used in determining the minimum permissible thickness or
physical characteristics of the different parts of
the vessel. (Code UA-60)
Design Temperature - The mean metal
temperature (through the thickness) expected
under operating conditions for the part considered. (Code UG-20)
Discontinuity, Gross Structural - A source of
stress or strain intensification which affects a
relatively large portion of a structure and has a
significant effect on the overall stress or strain
pattern or on the structure as a whole. Examples
of gross structural discontinuities are head-toshell and flange-to-shell junctions, nozzles, and
junctions between shells of different diameters or
thicknesses.
485
Discontinuity, Local Structural - A source of
stress or strain intensification which affects a
relatively small volume of material and does not
have a significant effect on the overall stress or
strain pattern or on the structure as a whole.
Examples are small fillet radii, small
attachments, and partial penetration welds.
Double-Welded Butt Joint - A butt joint
welded from both side.
Double-Welded Lap Joint - A lap joint in
which the overlapped edges
of the members to be joined
are welded along the edges
of both members.
Ductility - The ability of a metal to stretch
and become permanently deformed without
breaking or cracking. Ductility is measured by
the percentage reduction in area and percentage elongation of test bar.
Eccentricity - A load or component of a load
normal to a given cross section of a member is
eccentric with respect to that section if it does
not act through the centroid. The perpendicular distance from the line of action of the
load to either principal central axis is the eccentricity with respect to that axis.
Efficiency of a Welded Joint - The efficiency
of a welded joint is expressed as a numerical
quantity and is used in the design of a joint as a
multiplier of the appropriate allowable stress
value. (Code UA-60)
Elastic - Capable of sustaining stress without
permanent deformation; the term is also used
to denote conformity to the law of stress-strain
proportionality. An elastic stress or elastic
strain is a stress or strain within the elastic
limit.
Elastic Limit The least stress that will cause
permanent set.
Electroslag Welding - A welding process in
which consumable electrodes aIt fed into a
joint containing flux; the current melts the
flux, and the flux in turn melts the faces of the
joint and the electrodes, allowing the weld
metal to form a continuously cast ingot between the joint faces. Used in pressure vessel
construction when back of the welding is not
accessible. All butt welds joined by electroslag
welding shall be examined radiographically for
their full length. (Code UW-ll) (a) (6)
Endurance Limit (Fatigue Strength) - By
endurance limit of a material is usually meant
the maximum stress which can be reversed an
indefinitely large number of times without producing fracture.
Erosion-Corrosion - Attack on a metal surface resulting from the combined effects of
erosion and corrosion.
Expansion Joint - A joint whose primary purpose is not to join pipe but to absorb that
longitudinal expansion in the pipe line due to
heat.
Factor of Safety - The ratio of the load that
would cause failure of a member or structure,
to the load that is imposed upon it in service.
Fatigue - Tendency of materials to fracture
under many repetitions of a stress considerably
less than the ultimate static strength.
Fiber Stress - A term used for convenience to
denote the longitudinal tensile or compressive
stress in a beam or other member subject to
bending. It is sometimes used to denote this
stress at the point or points most remote from
the neutral axis, but the term stress in extreme
fiber is preferable for this pupose. Also, for
convenience, the longitudinal elements or
filaments of which a beam may be imagined as
-composed are called fibers.
Fillet Weld -
[¥:OU
1tks
A weld of approximately triangular cross section joining two surfaces approximately at right angles to
each other.
The effective stress-carrying
area of a fillet weld is
assumed to be the product
of the throat dimension
and the length of the weld.
Fillet welds are specified
by their leg dimension.
486
The throat dimension of an equal legged fillet
weld is 0.707 times the leg dimension.
Fillet welds may be employed as strength welds
for pressure parts of vessels within the limitations given in Table UW-12 of the Code. The
allowable load on fillet welds shall equal the
product of the weld area (based on minimum
leg dimension), the allowable stress value in
tension of the material being welded, and a
joint efficiency of 55010. (Code UW-18) The
allowable stress values for fillet welds attaching
nozzles and their reinforcements to vessels are
(in shear) 49010 of stress value for the vessel
material. (Code (UW-lS)
Filler Metal - Material to be added in making
a weld.
Full Fillet Weld - A fillet weld whose size is
equal to the thickness of the thinner member
joined.
Gage Pressure - The amount by which the
total absolute pressure exceeds the ambient atmospheric pressure.
GaIYanizinR - Applying a coating of zinc to
ferrous articles. Application may be by hot dip
process or electrolysis.
Gas Welding - A group of welding processes
wherein coalescence is produced by heating
with a gas flame with or without application of
pressure and with or without the use of filler
metal.
Gate Valve - A valve employing
a gate, often wedge-shaped,
allowing fluid to flow when the
gate is lifted from the seat. Such
valves have less resistance to flow
than globe valves.
Globe Valve - One with a
somewhat globe shaped body
with a manually raised or
lowered disc which when closed
rests on a seat so as to prevent
passage of a fluid.
Graphitization - Precipitation of carbon in
the form of graphite at grain boundaries, as occurs if carbon steel is in service long enough
above 775°F, and C-MQ steel above 875°F.
Graphitization appears to lower steei strength
by removing the strengthening effect of finely
disperse iron carbides (cementite) from grains.
Fine-grained, aluminum-killed steels seem to
be particularly susceptible to graphitization.
Groove Weld -
A weld made by depositing
filler metal in a groove between two members to be
joined.
Standard shapes of grooves:
V, U and J. Each may be
single or double.
Stress values for groove
welds in tension 74010 and in
shear 60010 of the stress
value of vessel material
joined by the weld. (Code
UW-lS)
Head - The end (enclosure) of a cylindrical
shell. The most commonly used types of heads
are hemispherical, ellipsoidal, flanged and
dished (torispherical), coniCal and flat.
Heat Treatment - Heat treating operation
performed either to produce changes in
mechanical properties of the material or to
restore its maximum corrosion resistance.
There are three principal types of heat treatment; annealing, normalizing, and post-weld
heat treatment.
High-Alloy Steel - Steel containing large
percentages of elements other than carbon.
Hydrogen Brittleness - Low ductility of a
metal due to its absorption of hydrogen gas,
which may occur during an electrolytic process
or during cleaning. Also known as acid brittleness.
Hydrostatic Test - The completed vessel filled
with water shall be subjected to a test pressure
which is equal to 1Y:z times the maximum
allowable working pressure to be marked on
the vessel or 1Y:z times the design pressure by
agreement between the user and the manufacturer. (Code UG-99)
Impact Stress - Force per unit area imposl.;d to
material by a suddenly applied force.
Impact Test - Determination of the degree of
487
resistance of a material to breaking by impact,
under bending, tensile and torsion loads; the
energy absorbed is measured by breaking the
material by a single blow.
Intermittent Weld - A weld whose continuity
is broken by unwelded spaces.
Isotropic - Having the same properties in all
directions. In discussions pertaining to strength
of materials, isotropic usually means having
the same strength and elastic properties
(modulus of elasticity, modulus of rigidity,
Poisson's ratio) in all directions.
Joint Efficiency - A numerical value expressed as the ratio of the strength of a riveted,
welded, or brazed joim to the strength of the
parent metal.
Joint Penetration - The minimum depth a
groove weld extends from its face into a joint,
exclusive of reinforcement.
Killed Steel - Thoroughly deoxidized steel,
(for example, by addition of aluminum or
silicon), in which the reaction between carbon
and oxygen during solidification is suppressed.
This type of steel has more uniform chemical
composition and properties as compared to
other types.
Lap Joint ...
A welded joint in which two
overlapping metal parts are
.. '? joined by means of a fillet,
plug or slot welds.
Layer or Laminated Vessel - A vessel having a
shell which is made up of two or more separate
layers. (Code UA-60)
Leg -
See under Fillet Weld.
Letbal Substances - Poisonous gases or liquids of such a nature that a very small amount
of the gas or of the vapor of the liquid is
dangerous to life when inhaled. It is the responsibility of the user of the vessel to determine
that the gas or liquid is lethal. (Code UW-2)
Ligament - The section of solid material in a
tube sheet or shell between adjacent holes.
Lined Vessel - A vessel having a corrosion
resistant lining attached intermittently to the
vessel wall. (Code UA-60)
Liquid Penetrant Examination (PT). A method
of nondestructive examination which provides
for the detection of discontinuities open to the
surface in ferrous and nonferrous materials
which are nonporous. Typical discontinuities
detectable by this method are cracks, seams,
laps, cold shuts, and laminations. (Code
UA-60)
Loading - Loadings (loads) are the results of
various forces. The loadings to be considered
in designing a vessel: internal or external
pressure, impact loads, weight of the vessel,
superimposed loads, wind and earthquake,
local load, effect of temperature gradients.
(Code UG-22)
Low-Alloy Steel - A hardenable carbon steel
generally containing not more than about 1070
carbon and one or more of the following
alloyed components: < (less than) 2070
manganese, < 4070 nickel, < 2070 chromium,
0.6070 molybdenum, and < 0.2070 vanadium.
Magnetic Particle Examination (MT). A
method of detecting cracks and similar discontinuities at or near the surface in iron and the
magnetic alloys of
Malleable Iron - Cast iron heat-treated to
reduce its brittleness. The process enables the
material to stretch to some extent and to stand
greater shock.
Material Test Report - A document on which
the material manufacturer records the resufts
of tests examinations, repairs, or treatments required by the basic material specification to be
reported. (Code UA-60)
Maximum Allowable Stress Value - The maximum unit stress permissible for any specified
material that may be used in the design formulas given in the Code. (UG-23)
Maximum Allowable Working Pressure - The
maximum gage pressure permissible at the top
of a completed vdisel in its operating position
for a designated temperature. This pressure is
based on the weakest element of the vessel using norminal thicknesses exclusive of allowances for corrosion and thickness required for
loadings other than pressure. (Code UA-60)
488
Membrane Stress - The component of normal
stress which is uniformly distributed and equal
to the average value of stress .across the
thickness of the section under consideration.
Metal Arc Welding - An arc welding process
in which the electrode supplies the filler metal
to the weld.
Modulus of Elasticity (Young's Modulus) The rate of change of unit tensile or compressive stress with respect to unit tensile or
compressive strain for the condition of uniaxial
stress within the proportional limit. For most,
but not all materials, the modulus of elasticity
is the same for tension and compression. For
nonisotropic materials such as wood, it is
necessary to distinguish between the moduli of
elasticity in different directions.
Modulus of Rigidity (Modulus of Elasticity in
Shear) - The rate of change of unit shear
stress with respect to unit shear strain, for the
condition of pure shear within the proportional
limit.
Moment of Inertia of an Area (Second
Moment of an Area) The moment of inertia of
an area with respect to an
axis is the sum of the
products obtained by multiplying each element of the
area by the square of its .
distance from the axis.
The Moment of Inertia (I)
for thin walled cylinder
about its transverse axis; I = 'If r't
where r = mean radius of cylinder
t = wall thickness
Needle Valve - A valve provided with a long
tapering point in place of the ordinary valve
disk. The tapering point permits fine graduation of the opening.
Neutral Axis - The line of zero fiber stress in
any given section of a member subject to bending; it is the line formed by the intersection of
the neutral surface and the section.
Neutral Surface - The longitudinal surface of
zero fiber stress in a member subject to bend-
ing; it contains the neutral axis of every
section.
Nipple - A tubular pipe fitting usually threaded on both ends and under 12 inches in length.
Pipe over 12 inches long is regarded as cut pipe.
Non-Pressure Welding - A group of welding
processes in which the weld is made without
pressure.
Normalizing - Heating to about 100° F.
above the critical temperature and cooling to
room temperature in still air. Provision is often
made in normalizing for controlled cooling at a
slower rate, but when the cooling is prolonged
the term used is annealing.
Notch Sensitivity - A measure of the reduction in strength of a metal caused by the
presence of a notch.
Notch Strength - The ratio of maximum tensional load required to fracture a notched
specimen to the original minimum crosssectional area."
Notch Test - A tensile or creep test of a metal
to determine the effect of a surface notch.
Operating Pressure - The pressure at the top
of a pressure vessel at which it normally
operates. It shall not exceed the maximum
allowable working pressure and it is usually
kept at a suitable level below the setting of the
pressure relieving devices to prevent their frequent opening. (Code UA-60)
Operating or Working Temperature - The
temperature that will be maintained in the
metal of the part of the vessel being considered
for the specified operation of the vessel (see
UG-20 and UG-23). (Code UA-60)
Oxidation or scaling of metals occurs at high
temperatures and access of air. Scaling of carbon steels from air or steam is negligible up to
l000°F. Chromium increases scaling resistance
of carbon steels. Decreasing oxidation
resistance makes austenitic stainless steels unsuitable for operating temperatures above
1500oF.
489
P-Number - The number of welding procedure-group. The classification of materials
based on hardenability characteristic and the
purpose of grouping is to reduce the number of
weld procedures. (Code Section IX)
All carbon steel material listed in the Code
(with the exception of SA-612) are classified as
P-No. I.
Pass - The weld metal qeposited by one progression along the axis of a weld.
Plasticity - The property of sustaining appreciable (visible to the eye) permanent deformation without rupture. The term is also used
to denote the property of yielding or flowing
under steady load.
Plug Valve - One with a short section of a
cone or tapered plug through which a hole is
cut so that fluid can flow through when the
hole lines up with the inlet and outlet, but when
the plug is rotated 90°, flow is blocked.
Plug Weld - A weld made in a circular hole
in one member of a lap
joint. The hole mayor may
not be partially or comppletely filled with weld
metal.
For pressure vessel construction plug welds may be
used in lap joints in rein~
forcements around openings, in non pressure structural attachments (Code UW-17) and for attachment of heads with certain restrictions.
(Code Table UW-12)
r$J
condition of uniform and uniaxial longitudinal
stress within the proportional limit.
Porosity - Gas pockets or voids in metal.
(Code UA-60)
Postweld Heat Treatment - Heating a vessel
to a sufficient temperature to relieve the
residual stresses which are the result of
mechanical treatment and welding.
Pressure vessels and parts shall be postweld
heat treated:
When the vessels are to contain lethal
substances, (Code UW-2)
Unfired Steam Boilers (UW-2)
Pressure vessels and parts subject to direct firing when the thickness of welded joints exceeds
5/8 in. (UW-2)
When the carbon (P-No. I) steel material
thickness exceeds 1Yl in. at welded connections
and attachments (see Code Table UCS-56 for
exceptions) .
Preheating - Heat applied to base metal prior
to welding operations.
Pressure Relief Valve - A valve which relieves
pressure beyond a specified limit and recloses
upon return to normal operating conditions.
Pressure Vessel - A metal container generally
cylindrical or spheroid, capable of withstanding various loadings.
I
.r-?h
"
Pneumatic Test - The completed vessel may
be tested by air pressure in lieu of hydrostatic
test when the vessel cannot safely be filled with
water or the traces of testing liquid cannot be
tolerated (in certain services). The pneumatic
test pressure shall be 1.25 times the maximum
allowable working pressure to be stamped on
the vessel. (Code UG-H)()
Poisson's Ratio - The ratio of lateral unit
strain t4i) longitudinal unit strain, under the
Pressure Welding - A group of welding processes wherein the weld is completed by use of
pressure.
Primary Stress - A normal stress or a shear
stress developed by the imposed loading which is
necessary to satisfy the simple laws of
equilibrium of external and internal forces and
moments. The basic characteristics of a primary
stress is that it is not self-limiting. Primary
stresses which considerably exceed the yield
strength will result in failure or at least, in gross
distortion. A thermal stress is not classified as a
primary stress. Primary membrane stress is
divided into .. general" and "local" categories. A
general primary membrane stress is one which is
so distributed in the structure that no
redistribution of load occurs as a result of
yielding. Examples of primary stress are: general
490
membrane stress in a circular cylindrical or a
spherical shell due to internal pressure or to
distributed live loads; bending stress in the
central portion of a flat head due to pressure.
Quench Annealing - Annealing an austenitic
ferrous alloy by heating followed by quenching
from solution temperatures. Liquids used for
quenching are oil, fused salt or water, into
which a material is plunged.
Radiographing - The process of passing electronic radiations through an object and obtaining a record of its soundness upon a sensitized
film. (Code UA-60)
Radius of Gyration - The radius of gyration
of an area with respect to a given axis is the
square root of the quantity obtained by
dividing the moment of inertia of the area with
respect to that axis by the area.
Random Lengths - A term indicating no
specified minimum or maximum length with
lengths falling within the range indicated.
Refractory - A material of very high melting
point with properties that make it suitable for
such uses as high-temperature lining.
Residual Stress - Stress remaining in a structure or member as a result of thermal or
mechanical treatment, or both.
Resistance Welding - A pressure welding process wherein the heat is produced by the
resistance to the flow of an electric current.
teristic of a secondary stress is that it is self-limiting.
Local yielding and minor distortions can satisfy the
conditions which cause the stress to occur and
failure from one application of the stress is not to be
expected. Examples of secondary stress are: general
thennal stress; bending stress at a gross structural
discontinuity.
Section Modnlu - The term pertains to the
cross section of a beam. The section modulus
with respect to either principal central axis i5
the moment of inertia with respect to that axis
divided by the distance from that axis to the
most remote point of the section. The section
modulus largely determines the flexural
strength of a beam of given material.
Section Modulus (Z) of a
thin walled cylinder (r>IOt)
about its transverse axis:
Z=r1Tt
where r = mean radius of
cylinder, in.
t = wall thickness,
in.
SbeD - Structural element made to enclose
some space. Most of the shells are generated by
the revolution of a plane curve.
In the terminology of this book shell is the
cylindrical part of a vessel or a spherical vessel
is called also a spherical shell.
Shear Stress - The component of stress
tangent to the plane of reference.
Scale - An iron oxide formed on the surface
of hot steel, sometimes in the form of large
sheets which fall off when the sheet is rolled.
Shielded Metal-Arc Welding An arc
weldingprocess wherein coalescence is produced by heating with an electric arc between a
covered metal electrode and the work.
Shielding is obtained from decomposition of
the electr6de covering. Pressure is not used and
filler metal is obtained from the electrode.
Scarf - Edge preparation; preparing the contour on the edge of a member for welding.
Single-Welded Butt Joint - A butt joint welded from one side only.
Root of Weld - The bottom of the weld.
tightness.
Single-Welded Lap Joint - A lap joint in
which the overlapped edges of the members to
be joined are welded along the edge of one
member.
Secondary Stress - A nonnal stress or a shear
stress developed by the constraint of adjacent parts
or by self-constraint of a structure. The basic charac-
Size of Weld penetration.
Seal Weld - Seal weld used primarily to obtain
Groove Weld: The depth of
491
Equal Leg Fillet Weld: the
leg length of the largest
isosceles right-triangle
which can be inscribed
within the fillet weld cross
section.
Unequal Leg Fillet Weld:
The leg length of the largest
right triangle which can be
inscribed within the fillet weld cross section.
Slag - A result of the action of a flux on nonmetallic constituents of a processed ore, or on
the oxidized metallic constituents that are
undesirable. Usually consist of combinations
of acid oxides and basic oxides with neutral oxides added to aid fusibility.
Slenderness Ratio - The ratio of the length of
a uniform column to the least radius of gyration of the cross section.
Slot Weld - A weld made in an elongated hole
(slot) in one member of a
lap joint, joining that member to that portion of the
surface of the other member which is exposed
through the hole. The hole
f i ;.
mayor may not be filled
completely with weld metal.
Din
I'
Specific GnYity - The ratio of the density of a
material to the density of some standard
material, such as water at a specified
temperature, for example, 4°C or 60°F. or (for
gases) air at standard conditions of pressure
and temperature.
Spot Welding - Electric-resistance welding in
which fusion is limited to a small area directly
between the electrode tips.
Stability -of Vessels - (Elastic Stability) The
strength of a vessel to resist buckling or wrinkling due to axial compressive stress. The stability of a vessel is severely affected by out of
roundness.
Stagsrered Intermittent Fillet Welds - Two
lines of intermittent fillet weldin~ in a tee
or lap joint, in which the increments of
welding in one line are
staggered with respect to
those in the other line.
Static Head - The pressure of liquids that is
not moving, against the vessel wall, is due solely to the "Static Head", or height of the liquid.
This pressure shall be taken into consideration
in designing vessels.
Stmn - Any forced change in the dimensions
of a body. A stretch is a tensile strain; a
shortening is a compressive strain; an angular
distortion is a shear strain. The word strain is
commonly used to connote unit strain.
Stress - Internal force exerted by either of two
adjacent parts of a body upon the other across
an imagined plane of separation. When the
forces are parallel to the plane, the stress is called shear stress; when the forces are normal to
the plane the stress is called normal stress;
when the normal stress is directed toward the
part on which it acts it is called compressive
stress; when it is directed away from the part
on which it acts it is called tensile stress.
Stresses In Pressure Vessels - Longitudinal
(meridional) S, stress
Circumferential (hoop) S1
stress
S, and S1 called membrane
(diaphragm) stress for vessels having a figure of
revolution
Bending stress
Shear stress
Discontinuity stresses at an
abrupt change in thickness
or shape of the vessel.
Stud - A threaded fastener without a head,
with threads on one end or both ends, or
threaded full length. (Code UA-60)
Submerged Arc Welding - An arc welding
process wherein coalescence is produced by
heating with an arc or arcs between a bare
metal electrode or electrodes and the work. The
welding is shielded by a blanket of granular,
fusible material on the work. Pressure is not
used and filler metal is obtained from the electrode and sometimes from a supplementary
492
welding rod.
Tack Weld - A weld made to hold parts of a
weldment in proper alignment until the final
welds are made.
Tee Joint - A welded joint at the junction of
two parts located approximately at right angles
to each other in the form of aT.
(see UO-25).
3. The "nominal thickness" is the thickness
selected as commercially availble, and as supplied to the manufacturer; it may exceed the
design thickness. (Code UA-60)
Throat - See under Fillet Weld.
Tensile Stress - Stress developed by a material
bearing tensile load.
Tolerances - For plates the maximum permissible undertolerance is the smaller value of
0.01 in. or 6% of the design thickness. (Code
UO-16)
The manufacturing undertolerance on wall
thickness of heads: pipes and pipefittings shall
be taken into account and the next heavier
commercial wall thickness may then be used.
Test - Trial to prove that the vessel is suitable
for the design pressure.
See Hydrostatic test, Pneumatic test.
U.M. Plate - Universal Mill Plate or plate
rolled to width by vertical rolls as well as to
thickness by horizontal rolls.
Tensile Strength - The maximum stress a
material subjected to a stretching load can
withstand without tearing.
Test Pressure - The requirements for determining the test pressure based on calculations
are outlined in UO-99(c) for the hydrostatic
test and in UO-lOO(b) for the pneumatic test.
The basis for calculated test pressure in either
of these paragraphs is the highest permissible
internal pressure as determined by the design
formulas, for each element of the vessel using
nominal thicknesses with corrosion allowances
included and using the allowable stress values
for the temperature of the test. (Code UA-60)
Thermal Fatigue - The development of cyclic
thermal gradients producing high cyclic thermal stresses and subsequent local cracking of
material.
Thermal Stress - A self-balancing stress produced by a nonuniform distribution of
temperature or by differing thermal coefficients of expansion. Thermal stress is
developed in a solid body whenever a volume
of material is prevented from assuming the size
and shape that it normally should under a
change in temperature.
Thickness of Vessel Wan
I. The "required thickness' is that computed by the formulas in this Division, before
corrosion allowance is added (see UO-22).
2. The "design thickness' is the sum of the
required thickness and the corrosion allowance
Ultrasonic Examination (UT) - a nondestructive means for locating and identifying internal
discontinuitis by detecting the reflections they
produce of a beam of ultrasonic vibrations
(Code UA-60)
Undercut - A groove melted into the base
metal adjacent to the toe of a weld and left unfilled by weld metal.
Unit Strain - Unit tensile strain is the elongation per unit length; unit compressive strain is
the shortening per unit length; unit shear strain
is the change in angle (radians) between two
lines originally at right angles to each other.
Unit Stress - The amount of stress per unit of
area.
Vessel- A container or structural envelope in
which materials are processed, treated, or
stored; for example, pressure vessels, reactor
vessels, agitator vessels, and storage vessels
(tanks).
Weaving - A technique of depositing weld
metal in which the electrode is oscillated from
side to side.
Weld - A localized coalescence of metal produced by fusion with or without use of filler
metal, and with or without application of
pressure.
493
Weld Metal - The metal resulting from the fusion of the base metal and the filler metal.
Welding - The metal joining process used in
making welds.
In the construction of vessels the welding processes are restricted by the Code (UW -27) as
follows:
1. Shielded metal are, submerged are, gas
metal arc. gas tungsten are, plasma are, atomic
hydrogen metal are, oxyfuel gas welding, electroslag, and electron beam.
2. Pressure welding processes: flash, induction, resistance, pressure thermit, and pressure
gas.
Welding Procedure - The materials, detailed
methods and practices involved in the production of a welded joint.
Welding Rod -
Filler metal, in wire or rod
form, used in the gas welding process, and in
those arc welding processes wherein the electrode does not furnish the deposited metal.
Wrought Iron - Iron refined to a plastic state
in a puddling furnace. It is characterized by the
presence of about 3 per cent of slag irregularly
mixed with pure iron and about 0.5 per cent
carbon.
Yield Point - The lowest stress at which strain
increases without increase in stress. For some
purposes it is important to distingish between
the upper yield point, which is the stress at
which the stress-strain diagram first becomes
horizontal, and the lower yield point, which is
the somewhat lower and almost constant stress
under which the metal continues to deform.
Only a few materials exhibit a true yield point;
for some materials the term is sometimes used
as synonymous with yield strength.
494
INDEX
Abbreviations ..................................... 466
Abrasion ............................................. 483
Absolute pressure .............................. 483
Access opening, tickness of.. ............. 140
Allowable load on saddle .................. 110
Allowable pressure ........................ 18-25
Allowable pressure, flanges ................ 28
Allowable stresses for
non-pressure parts ........................ 449
Allowances of plate bending ............. 236
Alloy .................................................. 483
Anchor bolt design ........................ 77-84
Angle joint ......................................... 483
Angle valves ...................................... 366
definition ...................................... 483
Annealing ........................................... 483
API 650 tanks .................................... 204
API 12F tanks .................................... 203
Appurtenances,
Preferred locations ....................... 241
Arc welding ....................................... 483
Area of circles .................................... 300
Planes ............................................ 258
Area of surface,
Cylindrical shell head ................... 425
ASME flanged and dished
head, allowable pressure .......... 20-24
Dimension of .............:.................. 335
External pressure ............................ 34
Internal pressure ....................... 20-24
Automatic welding ............................ 483
Backing .............................................. 483
Base ring design ............................ 79-83
Beam formulas ................................... 455
Bend allowances
of steel plate ................................. 236
Bending of pipe and tube .................. 234
Bent pipe ............................................ 280
Boiler and pressure
vessel laws .................................... 474
Bolted connections ............................ 463
Bolts, weight of ................................. 412
Brittle fracture ................................... 483
Brittleness .......................................... 483
Bushing .............................................. 483
Butt Weld ........................................... 483
Capacities of fabrication .................... 232
Carbon steel, properties of ................ 186
Center of gravity ................................ 452
Centigrade, conversion
to fahrenheit .................................. 444
Centroid of an area ............................ 484
Chain intermittent
fillet weld ...................................... 484
Check list for inspectors ................... 255
Check valves ..................................... 367
Definition ..................................... 484
Chemical plant piping ....................... 208
Chemical resistance
of gaskets ..................................... 224
Metals ........................................... 224
Paints ........................................... 253
Chipping ............................................ 484
Circles, circumferences
and areas of, ................................ 300
Circles, division of.. .......................... 289
Segments of ................................ 290
Circular plate, weight of ................... 404
Circumferences and areas
of circles ...................................... 300
Circumferential stress ......................... 14
Clad vessel ........................................ 484
Code rules related to
Services ....................................... 181
Thicknesses ................................. 182
Codes ................................................. 470
Combination of stresses ...................... 69
Combustible liquids .......................... 184
Common errors
Detailing vessels .......................... 242
Complete fusion ................................ 484
Cone, allowable pressure,
Internal .................................... 20, 24
External pressure ........................... 36
Frustrum of .................................. 276
To cylinder reinforcemenL ......... 159
Wall thickness for
internal pressure ................. 20, 24
Conical section,
Allowable pressure .................. 20, 24
External pressure ........................... 36
Wall thickness ......................... 20,24
Construction of vessels,
Specification ................................ 195
Contraction of
Horizontal vessels ......................... 99
Conversion, decimals
of a degree ................................... 443
Degrees to radains ....................... 441
Factors ......................................... 446
Gallons to liters ........................... 439
Inches to millimeters ................... 431
Kilograms to pounds ................... 438
Liters to gallons ........................... 439
Millimeters to inches ................... 433
Pounds per sq. in. to kilograms per sq. centimeter ........ 440
Pounds to kilograms .................... 438
Radians to degrees ...................... 442
495
Sq. feet to sq. meters ................... 437
Sq. meters to sq. feet ................... 437
Corner joint ....................................... 484
Corrosion ................................... 215,484
Fatigue ......................................... 484
Corrosion resistant materials ............. 222
Creep .................................................. 484
Couplings .......................................... 468
Definition ..................................... 484
Length of .............................. 138, 139
Weight of ..................................... 413
Welding ........................................ 361
Cylinders, .
partial volume of .................. 418,421
Cylindrical shell allowable
Pressure .................................... 18,22
Area of surface ............................. 425
External pressure ........................... 32
Thickness for internal
pressure ............................... 18, 22
Weight .......................................... 375
Damaging stress ................................ 484
Davit .................................................. 312
Decimals of a degree,
conversion .................................... 443
Decimals of an inch ........................... 426
Decimals of a foot ............................. 426
Definitions ......................................... 483
Deflection ............................................ 68
Deformation, strain ........................... 484
Degrees to radians, conversion ......... 441
Description of materials .................... 192
Design pressure, definition ............... 484
internal ........................................... 15
external .......................................... 31
Design specification .......................... 195
steel structures ............................. 447
temperature .................................. 484
tall towers ....................................... 52
welded joints ........................ 174, 448
Detailing of pressure vessels ............. 240
Dimensions of heads ......................... 335
pipe ............................................... 330
Discontinuity .................. ........... 484, 485
Division of circles ............................. 289
Double welded butt joint ................... 485
lap joint ........................................ 485
Drop at intersection of nozzle
and shell ....................................... 291
Ductility ............................................. 485
Earthquake ........................................... 61
map, of seismic zones .................... 64
Eccentric cone frustum ...................... 279
Eccentric load ...................................... 66
Eccentricity ........................................ 485
Efficiency of welded joint ................. 485
Elastic ................................................ 485
Elastic limit ........................................ 485
Elastic stability .................................... 67
Electroslag welding ........................... 485
Ellipsoidal head allowable
pressure .................................... 18, 22
area of surface .............................. 425
dimensions of ............................... 335
external pressure ............................ 34
locating point on ...... .................... 293
partial volume of .......................... 422
wall thickness for
internal pressure .................. 18, 22
Endurance limit ................................. 485
Engagement of pipe .................... ....... 235
Erosion ................................... ............ 485
Examination of welded joints ............ 177
Expansion joint .................................. 485
of horizontal vessels ...................... 99
of metals ....................................... 191
Extension of openings ....................... 128
External pressure ................................. 31
charts ........................................ 42-47
stiffening ring ................................. 40
Fabricating capacities ........................ 232
Fabrication tolerances ........................ 200
Factors, conversion ............................ 446
Factor of safety .................................. 485
Fahrenheit, conversion to
centigrade ..................................... 444
Fatigue ............................................... 485
Fiber stress ......................................... 485
Filler metal ......................................... 486
Fillet weld .......................................... 486
Fittings ....................................... 126-127
welding ......................................... 361
dimensions ................................... 361
weight ........................................... 390
Flammable liquids ............................. 184
Flanged and dished head,
allowable pressure .................... 20, 24
area of surface .............................. 425
dimensions of ............................... 335
external pressure ............................ 34
thickness for internal
pressure ............................... 20, 24
Flanged fittings, pressuretemperature rating .......................... 28
Flange
dimensions ................................... 341
pressure-temperature rating ........... 28
weight of ................................ ...... 395
496
Flat head wall thickness ...................... 26
Frustrum of concentric cone .............. 276
eccentric cone .............................. 279
Fuel gas piping .................................. 208
Full fillet weld ................................... 486
Gage pressure ..................................... 486
Gallons to liters, conversion .............. 439
Galvanized Sheet, weight of.. ............ 399
Galvanizing ........................................ 486
Gas transmission piping .................... 210
Gas welding ....................................... 486
Gaskets, chemical resistance of ......... 224
Gate valve .......................................... 486
dimensions ................................... 365
General specifications ....................... 243
Geometrical constructions ................. 268
formulas ....................................... 258
problems ....................................... 268
Girth seam formula .............................. 16
Globe valve ........................................ 486
dimensions ................................... 366
Graphitization .................................... 486
Groove weld ....................................... 486
Heads ................................................. 334
definition ...................................... 486
volume of ..................................... 416
weight of ...................................... 375
Heat treatment .................................... 486
Hemispherical head, allowable
pressure .................................... 18, 22
area of surface .............................. 425
dimensions of ............................... 335
external pressure ............................ 34
wall thickness for
internal pressure .................. 18, 22
High-alloy steel .................................. 486
Hinge .................................................. 314
Hydrogen brittleness .......................... 486
Hydrostatic test .................................. 486
Hydrostatic test presssure .................... 15
Hydrostatic test pressure
for flanges ...................................... 28
Impact stress ...................................... 486
test ................................................ 486
Inches to millimeters,
conversion .................................... 431
Inspection opening ............................ 123
Inspector's checklist ........................... 255
Insulation, weight of.. ........................ 414
Intermittent weld ................................ 487
Internal pressure ............................ 15, 18
Intersection of cone
and cylinder .................................. 285
of cylinders ........................... 282-284
of cylinder and plane ................... 281
of cylinder and sphere ................. 286
of nozzle and shell, drop ............. 291
Isotropic ............................................ 487
Joint efficiencies ....................... 172, 174
definition ..................................... 487
Joint penetration ............................... 487
Junction of cone to cylinder ............. 159
Killed steel ........................................ 487
Kilogram to pounds, conversion ...... 438
Ladder ............................................... 315
Laminated vessel ............................... 487
Lap joint ............................................ 487
Laws, boiler and pressure vessel ...... 474
Layer or laminated vessel ................. 487
Leg support ..... ....... ................. ..... ..... 102
dimensions. ....... ......... ....... ........... 108
Length of arcs ................................... 297
Length of pipe and coupling
for openings ......................... 138, 139
of stud bolts ................................. 237
Lethal substances .............................. 487
Lifting attachments ........................... 119
Lifting lug ......................................... 118
Ligament ........................................... 487
Lined vessel ...................................... 487
Liquid penetrant examination ........... 487
Liquid petroleum piping ................... 210
Literature ........................................... 479
Liters to gallons, conversion ............ 439
-Loadings ...................................... 13,487
Locating points on
ellipsoidal heads .......................... 293
Locations of vessel components ....... 241
Long welding neck ............................ 341
Longitudinal stress .............................. 14
Low-alloy steel .................................. 487
properties of ................................ 187
Low temperature operations ............. 185
Lug, lifting ........................................ 118
Lug suppport ..................................... 109
Magnetic particle examination ......... 487
Malleable iron ................................... 487
Materials, description of ................... 192
properties of ................................ 186
test report ..................................... 487
of foreign countries ..................... 194
Maximum allowable pressure,
flanges ........................................... 28
for pipes ....................................... 142
stress .............................................. 13
stress values ........... 16, 189, 190,487
working pressure ................... 15,487
497
wall thickness for
internal pressure ...................... 148
weight of ...................................... 390
Pipe fitting symbols ........................... 369
Piping codes ....................................... 208
Plasticity ............................................ 489
Plate bending allowances .................. 237
Plate of unequal thickness,
welding of .................................... 178
Plate thickness, relation to
radiographic examination .............. 30
Plates, weight of ................................ 400
Platform ............................................. 318
Plug valve .......................................... 489
Plug weld ........................................... 489
Pneumatic test .................................... 489
Name plate ......................................... 317 Poisson's ratio .................................... 489
Needle valve ...................................... 488 Porosity .............................................. 489
Neutral axis ........................................ 488 Post weld heat treatment.. .................. 489
Surface ......................................... 488 Pounds per sq. inch to
Nipple ................................................ 488
kilogram per sq.
Non-pressure welding ....................... 488
centimeter, conversion ................. 440
Normalizing ....................................... 488 Pounds to kilogram, conversion ........ 438
strength ........................................ 488 Power piping code ............................. 208
test ................................................ 488 Preferred locations of vessel
Nozzle details .................................... 244
components .................................. 241
Nozzle loadings ................................. 153 Power piping code ............................. 208
Nozzle neck thickness ............... 122.140 Preferred locations of vessel
Nozzle weight of ............................... 413
components .................................. 241
Openings ............................................ 122 Preheating .......................................... 489
detailing of ................................... 244 _ Pressure of fluid .............. ..................... 29
extension of .................................. 128 Pressure-Temperature rating ............... 28
reinforcement of.. .................. 129-137 Pressure vessel ................................... 489
detailing ........................................ 238
weight of ...................................... 413
laws ............................................... 474
welding of .................................... 244
Operating pressure ....................... 15, 488 Pressure relief valve .......................... 489
temperature .................................. 488 Pressure welding ................................ 489
Optimum vessel size .......................... 272 Primary stress ..................................... 489
Organizations ..................................... 476 Properties of pipe ............ ................... 322
of sections .............................. ...... 450
Oxidation ........................................... 488
stainless stel ................................. 190
P-number ........................................... 489
of steel .......................................... 186
Packing, weight of ............................. 414
of tubes ......................................... 332
Painting of steel structures ................ 247
Partial volume of cylinders ....... 418,421 Quench annealing .............................. 490
heads ............................................ 422 Radians to degrees, conversion ......... 442
sphere ........................................... 422 Radiographing ................................... 490
Pass .................................................... 489 Radius of gyration ............................. 490
Petroleum refinery piping ................. 208 Radiographic examination ................. 174
Pipe bending .............................. 234, 280
relation to plate thickness .............. 30
dimensions of.. ............................. 330 Random length ................................... 490
engagement .................................. 235 Reaction of piping ............................. 153
length of for openings .......... 138, 139 Rectangular tanks .............................. 212
mitered ......................................... 280 Refractory .......................................... 490
properties of ................................. 322
Measures ............................................ 321
Measurement, metric system of.. ....... 427
Membrane stress ................................ 488
Metal arc welding .............................. 488
Metals, chemical resistance of .......... 224
Metric System of measurement ......... 427
Mist extractor .................................... 316
Mitered pipe ...................................... 280
Milimeters to inches,
conversion .................................... 433
Minimum thicknss of
shells and heads ........................... 182
Moduli of elasticity ................... 188, 478
Modulus of rigidity ........................... 488
Moment of inertia .............................. 488
498
Refrigeration piping .......................... 210
Reinforcement, Cone to cylinder ...... 159
Reinforcing of openings ........... 129, 137
Required wall thickness
for internal pressure ................. 18-27
Residual stress ................................... 490
Resistance welding ............................ 490
Right triangles, solution of ................ 270
Ring joint flanges .............................. 356
Rings made of sectors ........................ 274
Root of weld ...................................... 490
Saddle design ....................................... 98
dimension ..................................... 100
Scale ................................................... 490
Scarf ................................................... 490
Schedule of openings ........................ 245
Screwed couplings ............................. 368
Seal weld ............................................ 490
Seamless head joint efficiency .......... 176
vessel section ............................... 176
Secondary stress ................................ 490
Section modulus ................................ 490
Sections, properties of ....................... 450
Segments of circles ............................ 290
Seismic load ......................................... 61
map of seismic zones ..................... 64
Services, Code rules .......................... 181
Shape of openings ............................. 122
Shear stress ........................................ 490
Sheet steel, weight ............................. 399
Shell, definition ................................. 490
volume of ..................................... 416
weights of ..................................... 375
Shielded metal arc welding ............... 490
Single-welded butt joint .................... 490
lap joint ........................................ 490
Size of openings ................................ 122
vessel ............................................ 272
weld .............................................. 490
Shop welded tanks ............................. 203
Skirt design .......................................... 76
openings ....................................... 319
Slag .................................................... 491
Slenderness ratio ................................ 491
Slot weld ............................................ 491
Solution of right triangles ................. 270
Specific gravities ............................... 415
Specific gravity definition ................. 491
Specification for design
of vessels ...................................... 195
Specifications ..................................... 470
Sphere, allowable pressure ............ 18, 22
external pressure ............................ 34
partial volume of .......................... 412
wall thickness for internal
pressure .............................. 18, 22
Spot welding ..................................... 491
Square feet to square meters,
conversion ................................... 437
Square meters to square feet,
conversion ................................... 437
Stability of vessels ............................ 491
Staggered intermittent
fillet weld ..................................... 491
Stainless steel, properties of ............ 190
Stair ................................................... 313
Standards ........................................... 470
Static head ........................................... 29
definition ..................................... 491
Steel structures, design of.. ............... 447
Stiffening ring, external pressure ....... 40
construction ................................... 48
Strain .................................~ ............... 491
Stress and strain formulas ................. 448
Stress, definition ............................... 491
Stress values of materials.................. 189
Stresses, combination of ..................... 69
in cylindrical shell ......................... 14
in large horizontal vessels
supported by saddles ................ 86
in pressure vessels ................. 13,491
Structures, design of ......................... 447
Structural members, welding of.. ...... 458
Stud ................................................... 491
Stud bolts, length of.. ........................ 237
Studding outlets ................................ 357
Subjects covered by literature .......... 481
Submerged arc welding .................... 491
Support of vessels, leg ...................... 102
lug ................................................ 109
saddle ............................................. 86
Swing check valves ........................... 367
Symbols for pipe fittings .................. 369
Tack weld .......................................... 492
Tall towers, design .............................. 52
Tanks, rectangular ............................. 212
Tanks, shop welded ........................... 203
for oil storage .............................. 204
Tee joint ............................................ 492
Temperature, conversion
centigrade to Fahrenheit .............. 444
Tensile strength ................................. 492
stress ............................................ 492
Test .................................................... 492
Test pressure ..................................... 492
Test pressure, external ........................ 31
Thermal expansion of metals ............ 191
Thermal fatigue ................................. 492
Thermal stress ................................... 492
499
Thickness of vessel wall,
definition ...................................... 492
code rules related to ..................... 182
for full vacuum ............................... 49
charts ........................................ 49-51
for internal pressure ................. 18-27
for nozzle neck ............................. 140
of pipe wall .................................. 148
Threaded and welded fittings ............ 126
Throat ................................................. 492
Tolerances, definition ........................ 492
Tolerances of fabrication ................... 200
Topics covered by literature .............. 481
Transition pieces ........................ 287-288
Transportation of vessels ................... 246
Tube, bending of ................................ 234
properties of ................................. 332
Types of welded joints ....................... 173
U. M. plate ......................................... 492
Ultrasonic examination ...................... 492
Undercut ............................................ 492
Unequal plate thickness
welding of .................................... 178
Unit strain .......................................... 492
stress ............................................. 492
Valves ................................................ 365
Vessel, definition ............................... 492
Vessel, components,
preferred locations ....................... 241
Vibration .............................................. 60
Volume of cylinders,
partial ................................... 418, 421
of shells and heads ....................... 416
of solids ........................................ 264
Vortex breaker ................................... 320
Wall thickness for internal
pressure .................................... 18-27
for pipes ....................................... 148
Weaving ............................................. 482
Weights ..................................... 321,374
bolts .............................................. 412
circular plates ............................... 404
couplings ...................................... 413
flanges .......................................... 395
galvanized sheet ........................... 399
insulation ...................................... 414
nozzles .......................................... 413
openings ....................................... 413
packing ......................................... 414
pipes and fittings .......................... 390
plates ............................................ 400
sheet steel ..................................... 399
shells and heads ........................... 375
vessels ............................................ 59
Weld, definition ................................. 492
metal ............................................. 493
sizes for openings ................ 124, 125
Welded joint categories ..................... 174
design of ....................................... 174
examination .................................. 177
locations ....................................... 174
Welded steel tanks ............................. 204
Welding, definition ............................ 493
fittings .......................................... 361
of nozzles ..................................... 244
procedure ...................................... 493
of pressure vessels ...................... 170
rod ................................................ 493
symbols ........................................ 179
Wind load ............................................ 52
Wind speed map ............................ 54, 57
Working temperature ......................... 488
Wrought iron ...................................... 493
Yield point ......................................... 493