Eugene f. megyesy-pressure_vessel_handbook_12th edition

PRESSURE VESSEL
HANDBOOK
Twelfth Edition
withforeword by
PaulButhod
Professor ofChemical Engineering
University ofTulsa
Tulsa, Oklahoma
Eugene F. Megyesy
PRESSURE VESSEL PUBLISIDNG, INC.
P.O. Box 35365 •Tulsa, Oklahoma74153

Copyright© by Eugene F. Megyesy
Copyright 1972, 1973 by Pressure Vessel Handbook Publishing, Inc.
All rights reserved. No part ofthis book may be reproduced in any
form or by any means including information storage and retrieval
systems without pennission ofthe publisher.
Library ofCongress 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 ofthe Pressure Vessel Handbook super-
sedes all previous editions, effective July l, 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 h~
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 formulas,
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 form.
The design procedures and formulas of the ASME 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, specialconstruction methodsor 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.
Alarge partofthis book was taken from the works ofothers, with some
of the material placed in different arrangement, and some unchanged.
The author wishes to acknowledge his indebtedness to Professor ·
SandorKalinszky, Janos Bodor, Laszl6 Felegyhazy and J6zsefG}'Urfi for
their material and valuable suggestions, to the American Society of
Mechanical Engineers and to the publishers, who generously permitted
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.
· SuggestioQs and criticism concerning some errors which may remain
in spite ofallprecautions 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
VESSELCODE-2001,Sect. VIII,Div.1
The American Society ofMechanical Engi-
neers set up a Committee in 1911 for the
purpose of formulating standard rules for
the construction ofsteam boilers and other
pressure vessels that will perform in a safe
and reliable manner.
The Code comprises these rules.
It's scope includes vessels:
I. made ofnonferrous materials, cast iron,
high alloy and carbon steel,
2. made by welding, forging, bracing, and
3. applying a wide variety ofconstruction
methods and details.
It includes all vessels where the question
of safety is concerned. ·
The Code - as it is stated in paragraph UG-
2 - "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 de-
tails of design and construction."
"The Code is not a handbook." "It is not
intended that this Section be used as a de-
sign handJ:>ook" as it is stated in the Fore-
word ofthe Code.
The updated and revised Code is published
in three years intervals. Addenda, which
also include revisionsto the Code, are pub-
lished annually. Revisions and additions
become mandatory six (6) months afterthe
date ofissuance, except for ,ioilers and pres-
sure vessels contracted for prior to the end
ofthe 6 month period. (Code Foreword)
PRESSURE VESSEL HANDBOOK -
2001, Twelfth Edition
The Handbook covers design and con-
struction methods of pressure vessels:
I. made ofcarbon 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 gener-
ally 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 ofthe Hand-
book, references are made to the applicable
Code paragraphs to avoid neglecting them.
Details of design and construction not
covered by the Code are offered by the
Handbook including: Design of tall tow-
ers, wind load, earthquake, vibration, ec-
centric load, elastic stability, deflection,
combination of stresses, nozzle loads, re-
action of supports, lugs, saddles, and rect-
angular tanks.
The aim of this Handbook is to be easily
handled and consulted. Tables, charts elimi-
nate the necessity of calculations, Geom-
etry, layout of vessels, piping codes, API
storage tanks, standard appurtenances,
painting of steel surfaces, weights, mea-
surements, conversion tables, literature,
definitions, specification for vessels, de-
sign of steel structures, center of gravity,
design of welded joints, bolted connec-
tions, boiler and pressure vessel laws,
chemical resistance ofmetals, volumes, and
surfaces ofvessels, provide good service-
ability.
The Handbook is updated and revised in
three years intervals, reflecting the changes
ofCode rules, new developments in the de-
sign and construction method, and in-
cludes the revisions of its SQUrces.

8
THE ASME CODE
ASME Boiler and Pressure Vessel Code, Section VIII, Division 1
An internationally recognized Code published by
The American Society ofMechanical Engineers.
PRESSURE VESSEL - is a containment ofsolid, liquid or gaseous material under
internal or external pressure, capable of withstanding also various other load-
ings.
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 con-
struction ofvessels. The first ASME Code was published in 1914.
ISSUE TIME - The updated and revised Code is published in three years intervals.
(200 l and so on). Addenda, which also include revisions to the Code, are pub-
lished 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 ofthe 6 month period. (Code Foreword)
SCOPE OF THE CODE- The rules ofthis Division have been formulated on the
basis of design principles and construction practices applicable to vessels de-
signed for pressures not exceeding 3000 psi. Code U-I(d)
Vessels, which are not included in the scope of this Division, may be stamped
with the Code U Symbol ifthey meet all the applicable requirements ofthis Divi-
sion. Code U-2(g)
THE DESIGN METHOD-The Code rules concerning design ofpressure 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 be-
cause 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 responsiple
for the application oft.00.Se programs to their design. (Code, Foreword)
DESIGN AND CONSTRUCTION NOT COVERED - This Division ofthe.Gode
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 ofthis Division.
Code U-2(g)
CONTENTS
PART I Design and ConstructionofPressure Vessels ............. 11
pART II Geometry and Layout ofPressure Vessels .............. 257
PART III Measures and Weights ............................................ 321
PART IV Design ofSteel Structures ........................................ 447
PART V Miscellaneous .......................................................... 465

PART I.
DESIGN AND CONSTRUCTIONS OF PRESSURE VESSEL
l. Vessels Under Internal Pressure ............................................ 15
Stresses in Cylindrical Shell, Definitions, Formulas, Pres-
sureofFluid, Pressure-Temperature Ratings ofAmerican
Standard Carbon Steel Pipe Flanges.
2. Vessels Under External Pressure............................................ 31
Definitions, Formulas, Minimum Required Thickness of
Cylindrical Shell, Chart for Determining Thickness of
Cylindricaland Spherical VesselsunderExternal Pressure
when Constructed ofCarbon Steel.
3. Design ofTall Towers ............................................................ 52
Wind Load, Weight ofVessel, 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 (ap-
proximatemethod), DesignofAnchorBoltandBase Ring,
Anchor BoIt Chair for Tall Towers.
4. Vessel Supports ..................................................................... 86
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.
5. Openings ."............................................................................... 122
Inspection Openings,Openings without Reinforcing Pad,
Opening with Reinforcing Pad, Extension ofOpenings,
Reinforcement of Openings, Strength of Attachments,
Joining Openings to Vessels, Length of Couplings and
Pipes for Openings.
6. Nozzle Loads .......................................................................... 153
7. Reinforcement at the Junction ofCone to Cylinder ............... 159
8. Welding of Pressure Vessels................................................. 170
Welded Joints, Butt Welded Joint of Plates of Unequal
Thicknesses, Application of Welding Symbols.
9..:Regulations; Specifications.................................................... 181
Code Rules Related to Various Services, Code Rules
Related to Various Plate Thicknesses of Vessel, Tanks
and Vessels ContainingFlammable andCombustible Liq-
uids, Properties of Materials, Description of Materials,
Specifiq~tion for the Design and Fabrication ofPressure
Vesels, Fabrication Tolerances.
11

12
10. Materials ofForeign Countries ..............................................
11. Welded Tanks .··········........········...........·~· ...............................
12. Piping Codes ..........................................................................
13. Rectangular Tanks ..................................................................
14. Corrosion
················································································
15. Miscellaneous .......................................................................
Fabricating Cap~citi~s, Pipe and Tube Bending, Pipe
Engagement, Dnll Sizes for Pipe Taps, Bend Allow-
ances, Length of Stud Bolts, Pressure Vessell Detail-
ing, PreferredLocations, Common Errors Transporta-
tion of Vessels. '
16. Painting of Steel Surfaces .....................................................
194
203
208
213
221
232
247
IN REFERENCES THROUGHOUT THIS BOOK "CODE" STANDS FOR ASME
BOILER AND PRESSURE VESSEL CODE SECTION VIII DIVISION 1 _ AN
AMERICAN STANDARD. '
2001 EDITION
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
ofstresses are the function ofthe nature ofloadings, the geometry and con-
struction 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
i. Abnormal pressures caused by deflagration.
13
STRESSES (Code UG-23) MAXIMUM ALLOWABLE STRESS
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 pro:vide4 in.d. pelow.
S = Maximum allowable stress in
a .
tens10n for carbon and low alloy steel
Code Table UCS-23; for high alloy
steel Code Table UHA-23., psi. (See
properties ofmaterials page 186-190.)
The smaller of S or the value of. a
factor B determined by the procedure
described in Code UG 23 (b) (2)
1.5 sa
S =(see above)a
d. General primary membrane stress -1.2 times the stress permitted in a., b.,
induced by combination of earth- or c. This rule applicable to stresses
quake or wind pressure with other exerted by internal or external pressure
loadings. Seismic force and wind or axial compressive load on a cylinder.
pressure need not be considered to
act simulta neously.

14
STRESSES IN CYLINDRICAL SHELL
Unifonn internal orexternal pressure induces in the longitudinal seam two times largerunit
stress than in the circumferential seam because of the geometry of the cylinder.
A vessel under external pressure, when other forces (wind, earthq11ake, 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 determined by the fonnulas:
l< i :ll
r-:-
1
S2 ... j -
'fll
. I
Si IlI I ""
...,
Given D =
p =
I =
96 inches
15 psi
0.25 inches
FORMULAS
CIRCUMFERENTIAL
JOINT
LONGITUDINAL
JOINT
D
p
S1
S2
I
=
=
=
=
=
NOTATION
PD
S2=-
2t
Mean diameter of vessel, inches
Internal or external pressure, psi
Longitudinil stress, psi
Circumferential (hoop) stress, psi
Thickness of shell, corrosion allowance
excluded, inches
EXAMPLE
15 x 96
4 x 0.25 = 1440 psi
15 x 96
2 x 0.25
= 2880 psi
For towers under internal pressure and wind load the critical height above which compres-
sive stress governs can be approximated by the formula:
H =PD
32!
where H = Critical height of tower, ft.
INTERNAL PRESSURE
I. OPERATING PRESSURE
The pressure which is required for the process, served by the vesseI, atwhich
the vessel is normally operated.
2. DESIGNPRESSURE
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 higherthan the operating pressure with 30 psi or 10 percent,.
whichever is the greater, will satisfy this requirement. The pressure ofthe
fluid and other contents ofthe 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) in corroded condition
(b) under the effect of a designated temperature
(c) in normal operating position at the top
(~under the effectofother loadings (wind load, external pressure, hydro-
static 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 (MAWP) code 3-2.
A common practice followed by many users and manufacturers ofpressure
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. HYDROSTATICTESTPRESSURE
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 allowableworking pressure.
Ifthe stress value ofthe vessel material atthe design temperature is less than
at the test temperature, the hydrostatic test pressure should be increased
proportionally.
Hydrostatic test shall
15

16
In this case, the test pressure shall be:
1.5 X Max. Allow. W. Press.
(Or Design Press.)
Stress Value S At Test Temperature
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 150 lb 300 lb 400lb 600lb 900lb 1500 lb 2500lb
Hydrostatic Shell Test
Pressure 425 1100 1450 2175 3250 5400 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-100
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-101.
S. MAXIMUM ALLOWABLE STRESS VALUES
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:
PR1
= 2SE + 0.4P
See notation on page 22.
p = 2SEt
R - 0.41
17
NOTES
I

18
A
B
c
Il~J'ERNAL PRESSURE
FORMULAS IN TERMS OF INSJDE DIMENSIONS
NOTATION
P = Design pressure or max. allowable
working pressure psi
E = Joint efficiency, page 172
R = Inside radius. inches
D = Inside diameter, inches
t = Wall thickness. inchesS = Stress value of material psi. page
189 C.A. = Corrosion allowance. inches
f
h == D/4
CYLINDRICAL SHELL (LONG SEAM) i
PR
t SE-0.6P
P= SE_t_
R+0.6t
I. Usual!~ the stress in the long seam is governing. See
preceding page.
2. Wh;n 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.
SPHERE and HEMISPHERICAL HEAD
PR
t=2SE-0.2P
P= 2SEt
R+0.2t
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
l-3, shall be applied.
2:1 ELLIPSOIDAL HEAD
PD
2SE-0.2P
2SEt
P= D+0.2t
l. For el!ipsoid~l heads, where the ratio of the major
and minor axis is other than 2: I, see Code Appendix
1-4(c).
19..,...
EXAMPLES
IDESIGNDATA: E 1.00,jointefficiency ofseamless
! P 100 psi design pressure heads
I
S = 20,000 psi stress value of R 48 inches inside radius*
SA 515-70plate@500°F D = 96 inches inside diameter*
E = 0.85, efficiency ofspot-examined t = required wall thickness inches
joints of shell and hemis. head to C.A. = 0.125 inches corrosion ~llowance
l shell * in corroded condition greater
i with the corrosion allowance.
!
ISEEDESJGNDATAABOVE SEEDESIGNDATAABOVE
I
I
IDetermine the reguired thickness,
Determinethe maximum allowable
J tofashell
working pressure P for o.500 in. thick
shell when the vessel is in new condition.
<. 100x 48.125 .
t=2(f,'OOO X0.85-0.6XIOO =0.284 m. P=20,000X0.85X0.500 _
176
.
+CA. 0.125 in.
48 + 0.6 X 0.500 - psi
0.409in.
Use 0.500 in. plate
SEEDESIGNDATA ABOVE SEEDESIGNDATAABOVE
The head furnished without straight
flange.
Determine the required thickness Determine the maximum allowable
t ofa hemispherical head. ' working pressure, P for 0.3125 in. thick
head, when it is in new condition.
t
100X48.125 =O 142 .
2X20,000X0.85-0.2X fOO . m. p 2X20,000X0.85X0.3125 _
221
.
0.125in.
48+0.2X0.3125 - psi
+CA.
0.267in.
Use 0.3125 in. plate
SEEDESIGNDATA ABOVE SEEDESIGNDATA ABOVE
Determine the required thickness ofa
seamless ellipsoidal head.
Determine the maximum allowable
t
lOOX'9625 ' · working pressure, P for 0.250 in. thick
2X20,000X 1.0~0.2 XlOO =0.2
4
l in.
seamless head, when it is in corroded
condition.
+CA. 0.125 in. P= 2x202ooox 1.ox 0.250 _
103
.
0.366in. 96.25 + 0.2 X 0.250 - psi
Use 0.375 in. min. thk. head

20
D
E
INTERNAL PRESSURE
FORMULAS IN 1ERMS OF INSIDE DIMENSIONS
NOTATION
P = Design pressure or max. allowable
working pressure psi
S = Stress value of material psi, page
189
£' = Joint efficiency, page 172
R = Inside radius, inches
D = Inside diameter, inches
a = One half of the included (apex)
angle, degrees
L = Inside radius of dish, inches
r = Inside knuckle radius, inches
t = Wall thickness, inches
C.A. = Corrosion allowance, inches
CONE AND CONICAL SECTION
t- PD
2 cos a (SE-0.6P)
P= 2SEtcos a
D+l.2t cos a
I. The half apex angle, a not greater than 30°

2. Whent.tis greater than 30~ special analysis is required
(Code Appendix 1-5(g)) •
When the min. tensile strength
ofmaterial exceeds 70,000 psi.
see Code UG-32(e)
ASME FLANGED AND DISHED HEAD
(TORISPHERICAL HEAD)
t= 0.885PL
SE-0.1P
P= SEt
0.885L+O.Jt
When l/r less than 16 2/3
PLM
t 2SE-0.2P
P= 2SEt
LM+0.2t
1.10 I.IS 1.18 1.22 1.28 1.34 1 39
1.08 1.13 1.17 1.20 1.25 1.31 1.36 •
8.00 9.00 10.0 11.0 12.0 14.0 16.0 2_ •
.so 2.so 9.so 10.s 11.s 13.o 15.o 163"
.44 1.46 1.48 I.SO 1.52 1.54 1.56 1.58 I&!!_ 1.62 1.65 1,69 1.72 1.75
1.77
THE MAXIMUM ALLOWED RATIO : L = D + 21 (see note 2 on-facing page)
21
EXAMPLES
DESIGN DATA:
P I00 psi design pressure
S 20,000 psi stress value of
SA 515-70plate@500°F
E 0.85, efficiencyofspot-examined
joints
E = l.00, jointefficiencyofseamless
heads
SEE DESIGN DATA ABOVE
cos 30°= 0.866
Determine the required thickness,
1 of a cone
100 x96.25 .
2X0.866(20,000 X0.85- 0.6Xl00)=0.3
28
m.
L = 96 inches inside radius ofdish*
D 96 inches inside diameter*
required wall thickness, inches
a 30°onehalfofthe apex angle
CA. 0.125 inches corrosion allowance
* in corroded condition greater with
the corrosion allowance
working pressure, P for 0.500 in. thick
cone, when the vessel is in new
condition.
2X20,000X 0.85X 0.500X 0.866
OJ2iin.. P 96+ 1.2X0.500X0.866
152
psi+C.A.
Use0.500 in. plate
Ur= 16~
0.453 in.
Determine the required thickness, t of a
seamless ASME flanged and dished
head.
0.885xl00x96.125 .
1=20.000x1.0-0.1 x 100°.426m.
+C.A. 0.1
0.
Use0.5625 in. plate
: Knuckle radius r = 6 in. L!r ~ = 16
[i J:f= 1.75 from table.
I< Determine the required thickness t of a
~ seamless A·SME flange_d and dished
Ii head. .
1
i _ IOOX96,i2SXl.75 .
Ii t- 2 x20,000 -0.2 xi oo =0.
421
m.
I -
l +cA. 0.125in.
034b1n:
Use0.5625 in. min.thickhead
seamless head, when the vessel is in
new condition.
20,000 x1.0 x0.5625
P= 0.885 X 96 + 0.1 X 0..5625
132
psi
Knuckle radius r = 6 in. L/r
9
i = 16
M = I.75 from table
working pressure, P for a 0.5625 in.
thick seamless head when the vessel is
in corroded condition.
P=2 x 20,000 x 1.0 x0.5625 l04 .
96.125x1.75 +0.2 x0.4375 psi
NOTE: When the ratio ofLlr is greater than 16 i, !filln-Code construction) the values of

22
INTERNAL PRESSURE
· · FORMULAS IN TERMS OF OUTSIDE DIMENSIONS
NOTATION
E = Joint efficiency, page 172
P =Design pressure or max. allowable R = Outside radius, inches
working pressure psi D = Outside diameter, inches
S = Stress vaiue of material psi, page t = Wall thickness, inches
189 C.A. = Corrosion allowance, inches
A
CYLINDRICAL SHELL (LONG SEAMJ 1
~
PR SEJ
,_SE+ 0.4P p - R - 0.4t
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 0.38S SE, the formulas givenf.in
the Code Appendix 1-2 shall be applied.
B
~
PR p 2SEt
, _ 2SE + 0.8P - R - 0.81
I. For heads without a straight flange, use the efficiency
of the head to shell joint ifit is less than the efficiency
of the seams in the head.
2. When the wall thickness exceeds 0.3S6 Ror P exceeds
0.66S SE, the formulas given in the Code Appendix
1-3, shall be applied.
c 2: 1 ELLIPSOIDAL HEAD
PD p 2SEt
h~ t
2SE+ 1.8P D· -1.St
---·
I. D f I. For ellipsoidal heads, where the ratio of the major and
minor axis is other than 2:I, see Code Appendix l-4(c).
h = D/4
I
il
t
~
rt
EXAMPLES
DESIGN DATA:
P 100 psi design pressure
S 20,000 psi stress value of
SA 515-70plate@5000F
E = 0.85, efficiencyofspot-examined
joints ofshell and hemis. head to
shell
SEEDESIGN DATA ABOVE
Determine the required thickness, t
ofa shell
IOOX48 .
t 20,000X0.85-0.4X100-o.283 m
+CA.
0.125 in.
0.408 in.
Use: 0.4375 in. thick plate
Head furnished without straight flange.
Determine the required thickness, t ofa
hemispherical head.
100X48
t 2X20,000X0.85+0.8X100 O.l4l in.
+c.A.
Use: 0.3125 in. min. thickhead
0.125in.
0266in.
Determine the required thickness t ofa
seamless ellips()idal head.
100X96
t 2X20,000X1.0+1.8X100 °·239
in.
+c.A.
Use0.375 in.min. thickhead
0.125in.
0.364in.
E = 1.00, jointefficiency ofseamless
heads
R 48 inches outside radius
D = 96 inches outside diameter
t = Required wall thickness, inches
CA. 0.125 inches corrosion allowance
SEE DESIGNDATAABOVE
shell when the vessel is in new condi-
tion.
P=20,000 X 0.85 X 0.4375
155
psi
48-0.4 x 0.4375
head, when the vessel is in new
condition.
P=2X20,000X0.85X0.3125
222
.
48-0.8 X0.3125 psi
head, when it is in new condition.
P
2 x20,000 x 1.0 x0.375
96-1.8 X0.375 157psi
23

24 25
i
INTERNAL PRESSURE EXAMPLES
FORMULAS IN TERMS OF OUTSIDE DIMENSIONS
DESIGN DATA: heads
NOTATION
D =Outside diameter, inches
P=Design pressure or max. allowable a = One half of the included (apex)
working pressure psi angle, degrees
S = Stress value of material psi, page L = Outside radius of dish, inches
189 r = Inside knuckle radius, inches
E = Joint efficiency, page t72 t = Wall thickness, inches ·
R = Outside radius, inches C.A. =.corrosion allowance, inches
P = 100 psi design pressure R = 48 inches outside radius
S = 20,000 psi stress value of D 96 inches outside diameter
SA 515-70plate@50G°F a. = 30"one halfofthe apex angle
E = 0.85, efficiencyofspot-examined l 96 inches outside radius ofdish
l joints t Required wall thickness, inches
E 1.00, jointefficiency ofseamless C.A. = 0.125 inches corrosion allowance
SEE DESIGN DATA ABOVE SEE DESIGN DATA ABOVE
D
I
I !
_ t
PD P= 2SEtcosa
I 2 cos a (SE +0.4P) D -0.8tcos a
c -::I
A: I ~.J_
I
/) I. The half apex angle, a not greater than 30°
I·
cos 30° = 0.866
Determine the required thickness, t working pressure, P for 0.500 in. thick
of a cone
. IOOX 96 .
cone in new condition.
r-2X0.866X(20,000X0.85+-0.4Xl00)=0
326
m.
+C.A. 0.125 in.
p;2X20,000X0.85X0.500X0.866
153
.

96 -(0.85X 0.500 X0.866) psi
0.451 in.
Use: 0.500 in. thick plate
;
2. When a is greater than 30°.. special analysis is
required. (Code Appendix 1-5(g)) ' SEEDESIGNDATAABOVE SEE DESIGN DATA ABOVE
llr 16~
E ASME FLANGED AND DISHED HEAD
(TORISPHERICAL HEAD)
WhenL/r= 162 /3
Determine the required thickness, t of a
Determine the maximum allowableseamless ASME flanged and dished
' head. seamless head, when the vessel is in
~ 0.88SPL SEt
I t
SE+0.8P P= 0.88SL-0.8tlllC:'" i .:::::::::11
f ~· LI
-- io When Ltr Less Than 16213
0.885X 100X96 . corroded condition.
t=20,ooox L0+0.8X l00=0.423 m.
t=0.5625-0.125 =0.4375
+C.A. 0.125 in. p 20,000X 1.0X0.4375
103psi
0.548in. 0.885 X96-0.8 X0.4375
Use: 0.5625 in. min. thick head
i

PLM 2SEt
When the min. tensile strength t= 2SE+P(M-0.2)t P= ML -t(M-0.2)ofmaterial exceeds 70,000 psi.
see Code UG-32(e)
VALUES OF FACTOR M
L/r
1.00 1.50 2.00 2.50 3.00 3.50 4.50 5.50 6.50
1.25 1.75 2.25 2.75 3.25 4.00 5.00 6.00
M 1.00 1.06 1.10 1.15 l.18 1.22 l.28 l.34 l.39
lt.03 1.08 1.13 1.17 1.20 1.25 1.31 1.36
L/r
7.00 8.00 9.00 10.0 11.0 12.0 14.0 16.0
16f
•1., <n 8.50 9.50 10.5 11.S 13.0 15.0
l SEE DESIGN DATA ABOVE SEE DESIGN DATA ABOVE
j Knuckle radius r = 6 in. l!r =
96 966=16 Knuckle radius r = 6 in. llr 6 =16
!M= 1.75 from table.
!Determine the required thickness t of a
M= l.75 from table.
i seamless ASME flanged and dished Determine the maximum allowable
~ head. •· , · - . working pressure, P for a 0.5625 in.
~ 100X96X l.75 . . thick seamless head when the vessel is
it=2X20,000X 1.0+fOO(l.75-02) 0.4I9m. in corroded condition.
' 2 X 20,000 X I.0 X 0.4375 .
i +C.A. 0.125 in. P 1.75 X96-0.4375(1.75-0.2)-J04psi
0.544in.
Use 0.5625 in. min. thickhead
M
l.41
t 44
1.46
It 48
1.50 1.54
t.56
1.58
1 "'n
t.62
t ..c
1.69
lt.7'2
t.75 It .,.,
t.52
• THE MAXIMUM ALLOWED RATIO : L • t = D (see note on facing page)
NOTE: When the ratio of Llr is greater than 16~ , (non-Code construction) the values of
M may be calculated by the formula: M= Y. (3 + ../Ur)

26
A
B
c
INTERNAL OR EXTERNAL PRESSURE
FORMULAS
NafATION
P =Internal or external design pressure psi E=joint efficiency
{J' =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.
CIRCULAR FLAT HEADS
t = d V0.13 PISE
This formula shall be applied:
I. 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 thi~kness, ts
t = d.../CPISE
C = 0.33tr/ ts
C min. 0.20
D 2 trmin. nor less than l.25ts
need not be greater than t
If a value of tr/ts less than 1 is used in
calculating t, the shell thickness ts shall be
maintained along a distance inwardly from
the inside face of the head equal to at least
2 ../dTs
Non-circular, bolted flat heads, covers,
blind flanges Code UG-34; other types
of closures Code UG-35
INTERNAL OR EXTERNAL PRESSURE
EXAMPLES
DESIGN DATA
p =300 psi design pressure £=joint efficiency
d =24 in. inside diameter of shell
s =17, l 00 psi maximum allowable stress value of SA-515-60 plate
~ t =0.243 in. required thickness of seamless shell for pressure.
r: =0.3125 in. actual thickness of shell.
!
DETERMINE THE MINIMUM REQUIRED THICKNESS, t
t = d ~ 0.13 PISE = 24 ..j 0.13 x 300/17,lOOx 1 = l.146in.
Use 1.25 in. head
, Checking the limitation of - =
d
1.25
24
= 0.052
The ratio of head thickness to the diameter of the shell is satisfactory
tr 0.243
c = 0.33 -,- = 0.33 - - - = 0.26
s 0.3125
r = d .,/ CPISE = 24 "0.26 x 300/17,lOOx. 1 = 1.620in.
Use 1.625 in. plate
Using thicker plate for shell, lesser thickness will be satisfactory for
the head.
t5
= 0.375 in.
t 0.243
c = 0.33 -f; = 0.33 0375 =0.214
t = d ..jCP/SE ·::o 24" 0.214 x 30C¥'17,IOO x 1 =1.471 in.
Use I.625 in. ptate
The shell thickness shall be maintained along a distance 2 .Jd'sfrom the
inside face of the head
2 J24 x 0.375 = 6 in.
27

28 -
PRESSURE -TEMPERATURE RATINGS
FOR STEEL PIPE FLANGES AND FLANGED FITTINGS
American National Standard ANSI B 16.5-1996/1998 ADDENDA
Class TSO lb. 300 lb. 400 lb. 600 lb. 900 lb. 1,500 lb. 2,500 lb
Hydrostatic
~": test . 450 1,125 1,500 2,225 3,350 5,575 9,275
pressure, psig
Temperature, F MAXIMUM ALLOWABLE NON-SHOCK PRE,SSURE 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
300 230 655 875 1,315 1,970 3,280 5,470
400 200 635 845 1,270 1,900 3,170 5,280
500 170 600 800 1,200 1,795 2,995 4,990
600 140 550 730 1,095 1,640 2,735 4,560
650 125 535 715 1,075 1,610 2,685 4,475
700 110 535 710 1,065 1,600 2,665 4,440
750 95 505 670 1,010 1,510 2,520 4,200
800 80 410 550 825 1,235 2,060 3,430
850 65 270 355 535 805 1,340 2,230
900 50 170 230 345 515 860 1,430
950 35 105 140 205 310 515 860
l,000 20 50 70 105 155 260 430
Ratings apply to NPS ~ 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)
A515Gr. 70(1)A516Gr. 70(1)(2)A537Cl. 1 (3)
NOTES:
(1) Permissible, but not recommended for prolonged use above 800 °F.
(2) Not to be used over 850 °F.
Flanges ofANSI 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 ofthe pressure-containing shell ofthe
flange. In general, it is the same as that of the contained material.
Flanged fittings shall be hydrostatically tested.
;

r
·.
'
'
~
!It
1·'I
,!
il'1
~,
@
[,
'.i:
~ i!f1
~
m
' ~~
u;
l~·
i
'
i
'
'
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 ofthe fluid in consideration.
Pressure in Pounds per Square Inch for Different Heads ofWater
ea
Feet 0 2 3 4 5 6 7 8 9
0 0.43 0.87 1.30 1.73 2.16 2.60 3.03 3.46 3.90
10 4.33 4.76 520 5.63 6.06 6.49 6.93 7.36 7.79 8.23
20 8.66 9.09 9.53 9.96 10.39 10.82 11.26 11.69 12.12 12.56
30 12.99 13.42 13.86 1429 14.72 15.15 15.59 16.02 16.45 16.89
40 17.32 17.75 18.19 18.62 19.05 19.48 19.92 20.35 20.78 2122
so 21.65 22.08 22.52 22.95 23.38 23.81 2425 24.68 25.11 25.55
00 25.98 26.41 26.85 2728 27.71 28.14 28.58 29.01 29.44 29.88
70 30.31 30.74 31.18 31.61 32.04 32.47 32.91 33.34 33.77. 34.21
80 34.64 35.07 35.51 35.94 36.37 36.80 37.24 37.67 38.10 38.54
SQ 38.97 39.40 39.84 4021 40.70 41.13 41.57 42.00 42.43 42.87
NOTE: One foot ofwater 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 ofWater in Feet Corresponding to
Certain Pressure in Pounds per Square Inch
Pres-
sure, 0 2 3 4 5 6 7 8 9
Lbs.
0 2.3 4.6 6.9 9.2 ll.5 13.9 16.2 18.5 20.8
10 23.l 25.4 27.7 30.0 32.3 34.6 36.9 39.3 41.6 43.9
20 46.2 48.5 50.8 53.l 55.4 57.7 60.0 62.4 64.7 67.0
30 69.3 71.6 73.9 76.2 78.5 80.8 83.l 85.4 87.8 90.l
40 92.4 . 94.7 .9't.o 99.3 101.6 103.9 106.2 108.5 110.8 113.2
50 115.5 117.8. 120.I . 122.4 124.7 127.0 129.3 131.6 133.9 136.3
00 138.6 140.9 143.2 145.5 147.8 150.l 152.4 154.7 157.0 159.3
70 161.7 164.0 f66.3 168.6 170.9 173.2 175.5 177.8 180.l 182.4
80 184.8 187.1 189.4 191.7 194.0 196.3 198.6 200.9 203.2 205.5
00 207.9 210.2 212.5 214.8 217.1 219.4 221.7 224.0 226.3 228.6
NOTE: nd ofpres~ure per square inch ofwater equals 2.309 feet ofwater
at 62° Fa t. 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.

30
TABLES
For quick comparison ofrequired plate thickness and weight for various
materials and at a different degree ofradiographic examination.
.A .Stress.yalues at temperature -20° to 500 °F.
SA53 B
SA285.C SA 515-60 ·SA 515-70
SA 516-60 SA 516-70
85% J.E. 13,345 14,535 17,000
100% J.E.
=
15,700 17,100 20,000
B Ratios of Stress Values
13 345 14,535 15,700 17,000 17,100 JE13 345 - 1.09 1.18 1.27 1.28
14,535 0.92 - 1.08 1.17 1.18 1.37
15,700 0.85 0.92 1.08 1.09 1.27
17,000 0.79 0.86 0.93 - 1.01 1.18
17,100 0.78 0.85 0.92 0.99 - 1.17
20,000 0.67 0.73 0.79 0.85 0.86
Table A shows the stress value ofthe 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 ofthe vessel 12600 lbs.
2. What plate thickenss will be required, and what will the weight ofthe
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 ofthe two stress values from Table B=l.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.
[•
;: t!
'
L
".
!
i.____12_6_00~x-'-1._08_=_;;_13~6_08~l_b_.~~~~~~~~~~~~~---'f
'
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 Diyision are also satisfied. Code UG-28(f).
This shall not be applied ifthe vessel is operated at a temperature be-
low minus 20° F, and the design pressure is determined by the Code
UCS-66(c)(2) or Code UHA-5l(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-100.
The design method on the following pages conform to ASME Code for
Pressure Ves·sels Section VIII, Div. 1. The charts on pages 42-47 are
excerpted from this ~ode.
31

32
EXTERNAL PRESSURE
FORMULAS
NOTATION
P = External design pressure, psig.
P = Maximum allowable working pressure, psig.
·' if = Outside diameter, in.
L
0
= the length, in. ofvessel section between:
A.
1. circumferential line on a head at one-third the depth ofthe
head-tangent line,
2. stiffening rings
3. jacket closure
4. cone-to-cylinderjunction or knuckle-to-cylinderjunction of
a toriconical head or section, -
5. tube sheets (see page 39 )
t = Minimum required wall thickness, in.
t
.c
,...___w,--
D.
VESSEL
..,
--.c
CYLINDRICAL SHELL
Seamless or with Longitudinal Butt Joints
When D/t equal to or greater than 10
the maximum allowable pressure:
Pa= 4B
3(D0 lt)
The value of B shall be determined by the fol-
lowing procedure:
I. Assume a value for I; (See pages 49-51)
Determine LIDa and D0 It
2. Enter Fig. G (Page 42) at the value of LID0
•
Enter at 50 when LID0
is greater than 50, and
at 0.05 when LID0
is less than 0.05.
WITHOUT STIFFENING RING 3. Move horizontally to the line representing
D/t. From the point of intersection move ver-
tically to determine the value of factor A.B.
--M-----111--t-
VESSEL
WITH STIFFENING RING
4. Enter the applicable material chart (pages
43-47) at the value of A. Move vertically to the
applicable temperature line•.
5. From the intersection move horizontally and
read the value of B.
Compute the maximum allowable working pres-
sure, P0
•
If the maximum allowable working pressure is
smaller than the design pressure, the design
procedure must be repeated increasing the ves-
sel thickness or decreasing L by stiffening ring.
*For values of A falling to the left of the
applicable temperature line, the value of P0
can be calculated by the formula:
p = 2AE.
a 3(D0
li)
When the value of D0 1t is less than IO, the
formulas given in the Code UG-28(c)(2) shall
be applied.
EXAMPLES
DESIGN DATA
i P = I5 psig. external design pressure
•
1
• D = 96 in. outside diatmeter of the shell .0
Length of the vessel from tangent line to tangent line: 48 ft. 0 in. = 576 in.
'
i
.,
"
~
'
~
i
I)
ll
~
t,
I
'
I
J
i
'
~
'
Heads 2: I ellipsoidal
Material of shell SA - 285 C plate
Temperature 500° F . .
0
E = Modulus of elasticity of matenal, 27 ,000,000 ps1.@ 500 F (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.)
LID.=592/96=6.17 D/t=96/0.5=l92
A=0.00007 from chart (page 42) determined by the procedure described on
the facing page.
Since the value ofA is falling to the left ofthe applicable temperature-line in
Fig. CS-2 (pg. 43),
p - 2A £/3 (D/ t) = 2 x 0.00007 x 27,000,000/3 x 192 = 6.56 psi.a
Since the maximum allowable pressure P. is smaller than the design pressure
p stiffening rings shall be provided.
Using 2 stiffening rings equally spaced between the tangent l'.nes of the hea~s,
Length of one vessel section, L = 200 in.(length of shell 192 m. plus one third
of depth of head 8 in.)
i::
"'E-
I
i::
"'E-
"o
'
'oo
v
•_,____
"- ~
~
. v
N
• ~
00
'
o
-..0
'
'°-"oo
'
t' ~
.f•oo
.
L1D0
= 200/96 = 2.08 D0 /1=96/0.5=192
A = 0.00022 from chart (page 42)
B= 3000 from ch~rt (page 43)
determined by the procedure described on
facing page.
P0
= 4B/3(D.I1) = 4 x 3000/3 x 192 = 20.8 psi.
Since the maximum allowable pressure Pa 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.
33

34
EXTERNAL PRESSURE
FORMULAS
NOTATION
P External design pressure psig.
P0 Ma.ximum allowable working pressure psig.
D0 Outside diameter of the head, in.
R0 Outside radius of sphere or hemisphereical head, 0.900
for ellipsoidal
heads, inside crown radius of flanged and dished heads, in.
r = Minimum required wall thickness, inches.
E Modulus of elasticity of material, psi. (page 43)
+D,,
The maximum p = B
allowable pressure: 0
(R0
/t)
The value ofB shall be dete~mined by the following pro-
cedure:
1. Assume the value for t and calculate the value of
A using the formula: AF-0.125/( R0 Ir) (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 falling to the left of the appli-
cable temperature line, the value of P0
can be cal-
culated by the formula: Pn = 0.0625 E/(R0
It?
If the maximum allowable working pressure P0
com-
puted by the formula above, is smaller than the design
pressure, a greater value for r must be selected and
the design procedure repeated.
2:1 ELLIPSOIDAL HEAD
The required thickness shall be the greater or the
following thicknesses.
(1) The thickness as computed by the formulas
given for internal pressure using a design pres-
sure 1.67 times the external pressure and joint
efficiency £ =1.00.
(2) The thickness proofed by formula P0
= BIR0
/t
whereR.,=0.9 Du, and B to be determined as for
sphere.
ASME FLANGED AND DISHED JmAD
TORISPHERICAL HEAD
The required thickness and maximum allowable pres-
sure shall be computed by the procedures given for
ellipsoidal heads. (See above)R0 maximum=D"
EXAMPLES
DESIGN DATA:
P = 15 psig external design pressure
D0 = 96 inches outside diameter of head
Material of the head SA-285C plate
5000F design temperature
Determine the required head thickness.
Assume a head thickness: t. =0.25 in.
A = 0.125/(48.00/0.25)~.0.00065
R0
= 48.00 in.
From Fig. CS-2 (page 43) B = 8500 determined by the procedure described on the
facing page.
Pa = 8500/(48.00/0.25) = 44.27 psi.
Since the maximum allowable working pressure Pa is 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.
R0
= 48.00 in.
A = 0.125/(48.00/0.1875) = 0.0005
B = 6700, from chart (page 43 ), Pa = Bl(Rjt) = 6700/256 = 26.2 psi.
'Fhe assumed thickness: t = 0.1875 in. is satisfactory.
SEE DESIGN DATA ABOVE. Procedure (2.)
Assume a head thickness: t = 0.3125 in.. R. = 0.9 x 96 = 86.4 in.
A= 0.125/(86.4/0.3125) = 0.00045
B = 6100 from chart (page 43 ),P" - B/(R0 1t)I= 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., R0 =D0 = 96 in.
A = 0.125/(96/0.3125) = 0.0004
B =5200 from chart (page 43), P0 .. B/(R0 /t) = 5200/307 = 16.93 psi.
Since the maximum allowable pressure P" is greater than the design pressure
P the assumed thickness is satisfactory. ·
35

36
EXTERNAL PRESSURE
FORMULAS
Seamle$$ or with Bull Joints
WHEN a IS EQUAL TOORLESSTHANOO•
and Di/t¥ ~ JO
The maximum allowable 'pressure:
48
P,, = 3(D,!t!')
I. Assume a value for thickness, tr
The values of B shall be determined by the
following procedure:
2. Determine t,., L,., and the ratios L.ID1 and
D1/t,.
3. Enter chart G (page 42) at the value ofL/
DdUD,) (Enter at 50 when L/D1 is greater
than 50) Move horizontally to the line rep-
resenting D,/t. From the point 0f inter-
section move vertically and read the value
ofA.
NOTATION
4. Enter the applicable material chart at
the value of A• and move vertically to the
line of applicable temperature. From the
intersection move horizontally and read
the value of8.A =
B =
a =
D1=
D,=
E =
L =
Le=
p
=
Pa=
t =
te =
factor determined from
fig.UG0-28.0 (page 42
factor determined from
charts (pages 43-47)
one half of the included
(apex) angle, degrees
outside diameter at the
large end, in.
outside diameter at the
small end, in.
modulus ofelasticity of
material (page 43)
length ofcone, in. (see
page 39)
equivalent length of
conical section,
in.(L/2)(1 +Ds!Du
~ernal design pressure,
psL
Maximum allowable
working pressure, psi
minimum required
thickness, in.
effective thickness, in.
==tcosa
5. Compute the maximum allowable working
pressure, P".
If P" 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 appli-
cable line, the value of P can be calculated
by the fonnula:
P,, - 2AE/3(D1/t,.)
For cones having D It ratio smaller than IO,
see Code UG-33 (f)(b)
WHENa IS GREATER THAN 00°
The thickness of the cones shall be the same as
the required thickness for a flat hmd, the
diameter ·of which equals the largest outside
diameter of the cone.
Provide adequate reinforcing of the cone-to-
cylinder juncture. See page 1S9
"
EXAMPLES
DESIGN DATA
P = 15 psi external design pressure
Material of the cone SA 285-C plate
500 F design temperatur.e
CONICAL HEAD
D1 = 96 in. a =22.5 degrees
Determine the required thickness, t
D,=O
Length, L = (D,12)/tano:=48/.4142= 115.8, say 116 in
1. Assume a head thickness, t, 0.3125 in.
2. t,. =t cosa=0.3125 x .9239 = 0.288;
L, =L/2 (l+D ID1) = 116/2 x (I + 0/96) = 58
L~!D1=58196 =0.6 D1lte= 96/.288 = 333
3. A =0.00037 (from chart, page 42)
4. 8 = 5,200 (from chart, page 43)
4B 4 x 5,200
5• P,, = 3(D1
/1J 3(333) =20
'
8
psi.
SJI. D1 .I
Since the maximum allowable pressure is greater than the design pressure, the
a5sumed plate thickness is satisfactory.
CONICAL SECTION (See design data above)
D1 = 144 in. D, =96 in. a =30 deg.
Detennine the required thickness,
Length, L=[(DrD,)12]/tana =24/.5774=41.6 in.
24 144-96
144
1. Assume a head thickness, t, 0.375 in.
2. t,, =t cosa.=0.375 x0.866=0.324
L,,=(L/2)(1 + D/D1)=41.612 x
(l + 96/144) = 34.67
L,ID1 =34.67/144=0.241
D1lte = 144/0.324=444
3. A =0.00065 (from chart, page42J
4. B = 8,000 (from chart, page 43)
48 4 x 8000
S. po = 3(D1
/te> = 3 x (144/0.324)
=25.8 psi.
Since the maxi.mum allowable pressure Pa is greater than the design pressure
P, the assumed thickness is satisfactory.
EXAMPLES FOR CONICAL HEAD, WHEN 0: IS GREATER THAN 60°
ARE GIVEN AT FLAT HEADS
37

38
NOTES
EXTERNAL PRESSURE
~l
L
-L==="J
FORMULAS
Use L in calculation as shown when
the strength ofjoints ofcone to cylin-
der does not meet the requirements
descnbed on pages 163 - 169 It will
result the thickness for the cone not
less thanthe minimumrequired thick-
ness for the joining cylindrical shell.
Use L in calculation as shown when
the strength ofjoints of cone to cylin-
der meets the requirementsdescribed
on pages 163· l6.9
39

40
EXTERNAL PRESSURE
DESIGN OF STIFFENING RINGS
NOTATION
A := Factor detennined from the chart (page 42) for the material used in the
stiffening ring.
As = Cross sectional area ofthe stiffening ring, sq. in.
D0
= Outside Diameter ofshell, in.
E = Modulus of elasticity ofmaterial (see chart on page 43)
Is = Required moment of inertia ofthe stiffening ring about its neutral axis parallel
to the axis of the shell, in.4.
I's = Required moment of inertia ofthe 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 ...fi5t in.4.0
Ls = The sum of one-halfofthe distances on both sides ofthe stiffening ring from
the center line ofthe ring to the (1) next stiffening ring, (2) to the head line at
11.i 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 ofstiffening ring and detennine 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 11.i of its depth and
detennine dimension, Ls.
III. Calculate the moment ofinertia 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 ofa circumferential stiffening ring shall not be
less than detennined by one ofthe following fonnulas:
I' - D.2
Ls (t+A/L)A I - D.
2
Ls (t+A/L)A
s - 10.9 ·' - 14
The value ofA shall be detennined by the following procedure:
1. Calculate factor B using the fonnula:
B=%[ PD0 ]
t+A/Ls
2. Enter the applicable material chart (pages43 -A7) at the value of Band move
horizontally to the curve ofdesign temperature. When the value ofB is less than
2500, A can be calculated by the fonnula: A = 2B/E.
3. From the intersection point move vertically to the bottom ofthe chart and read the
value of A.
4. Calculate the required moment of inertia using the fonnulas above.
Ifthe moment of inertia ofthe ring or the ring combined with the shell section is greater
than the required moment ofinertia, the stiffening ofthe shell is satisfactory. Otherwise
stiffening ring with larger moment of inertia must be selected, or the number ofrings
shall be increased.
Stiffening ring for jacketed vessel: Code UG-29 (f)
I
~
i
i:
: l
EXAMPLES
DESIGN DATA:
p = 15 psi, external design pressure.
D = 96 in., outside diameter ofthe shell.0
Length ofthe 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 500°F
E Modulus ofelasticity ofmaterial, 27,000,000 psi, @500°F (see chart on
page 43)
0.500 in. thickness ofshell
Oo
v.,
s::
~
s:: ~
~
'°00
t-
'<!'
00
v.,
I. An angle of 6 x 4 5
/16 selected.
As =3.03 sq. in.
II. Using 2 stiffening rings equally
spaced between one-third the
depths of heads (see figure),
Ls= 196in.
III. The moment ofintertia ofthe
selected angle: 11.4 in.
1. The value of Factor B:
B = % [PD0
/(t +A/Ls)]=
%[15x96/(0.5 + 3.03/196)]
=2095
2. Since the value of B is less
than2500,
A =2B/E=
2 x 2095/27,000,000=0.00015
rv. The required moment ofinertia:
_ [Da2Ls(t+As!L) A] =962
x 196x(0.5+3.03I196)X 0.00015 = 9.97 in.4
Is - . 14 . . 14 - -
Since the requlred m~ment ofinertia (9,97 in.4) is smaller than the moment of
inertia ofthe 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.
41

I
'
~
2
d
!~>=00~
~~
~~
~~
~o
c: i'J;l
~~
:=~
~~
~>
~!'.""
;3
~
~
~ §§~§~~i;;~i;;i;;~ ill E!l~8 i!l i13?J!!l8:;
"'
"'.p.
~ ~
"' ."'.~~ ., C"l
""1
q
~8
>~
"'
.p.
"'
"'..,Cl)
:... "'
2
J
E • 29.0 x 10 6
E =27.0 K 106
E = 24.5 x 106
E • 22.8 x 106
E • 20.8 x 10E
I 1111
r---... ...._
...........
-
r- CZ
~
2
:,.,,,,,,,.
/
I ,.,,.... ...,,...
... ~-') ,,,,...., ~
""""-
0 ....... / ~"""' -'Fl 'J' '~ /
r1, '/
"/, IJ ,,
111, (,,
'I/J.
() fl
Fil'
rt i
2
UDO
- ....... --"I)
ju h. Q.. ():) b
"""
----..........
---
--'-
-
....,.,. _..,,..; N
~ b.~b g; 9'- :"'-!~;OP tu F-9> f"''P
0 0000 0 OOt.'.:?O
I I I I
25,000
,up to 30,0 ~- 20.000
18,000
16.000
14.000
12,000
_,,,
--- v
/_..
--i...--""'
i,..- _,~~
-
FIG.CS-2
I I I I
2 3
500 F _
I I
700 F-
I I
800 F _
I I
900 F
10,000
9,000
8,000
7,000
6.000
5,000
4,000
3,500
3,000
4 5 6 7 8 9 2.500
.1
.00001
3 4 56789
.0001
3 4 5 6 7 89
.001
3 456789
.01
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:
!il ~ l!l ~ ~
b b 0 b. b
(!) i:: (!)
..c: ttl .s...... (!)
B 8 'O
"' ~ i::
=: "' 0
~ ~-~
• 0
...... II) II)
...... i:: ....
•. ·- 0
- - k
0 ~ Q. •
= gBt;~
Cde~=_, > II) 0 <l.l
lo"4 Q. N ,_,
o ..2 e ·c .a<..... ..... (!) 0 ttl
r lll +.-1 .....r:: i-
U b (!) <l.l g_
< ..c: .s ..c: s~ ~<+-""'11>
0 ..c: .....
"' .... II)
~] -~ -5
ttl <l.l .....
0 II) i:: 0
B ..c: .S? -o.......... ~ .... ~
....... ~ II)
~ 0"' k
E-..; k <l.l
0 B 8:z .s :::I
t'3
SA - 283 C SA - 515 } ll G d SA - 53 - B Type 405 } St · l . St I
I SA-285C SA-516 A ra es SA-106-B Type4IO amess ee I&

I
2
.00001
I I I I
25,000
vup to 3~ ~-
500 F _
20.000
18,000
16,090
14,000
E = 29.0 x 10 6
E = 27.0 x 10 6
E= 24:5 x 10 6
E • 22.8 x 10 6
E = 20.8 • 10 6
I II 11
3 4 5 6789
.0001
__.,'-""'
v
/ l...--'"
...-
_,.,.,.
j ......
_......
ri I /
_......
VI ...,,. ./ 1.--'
'i' ; ~
/J IJ I/
r1...... t..
/, '/; J
I// rJJ
--......~ f//j
!"-... {j VII
-J) YI r
/.~
2 3 456789
.001
FACTOR A
2
-......
,~Ir""
i.-- - vLo-- .....
vt...-i- ~
--_.....
- .,...v~
- i.--
--- ~
--
FIG.HA-1
3 456789
.01
I I I I
2 3
. THE VALUES OF FACTOR B
I I
700 F -
I I
800 F _
I I
900 F
12,000
10.000
9,000
8.000
7,000
6,000
5,000
4,000
3,500
3,000
4 5 6 1 8 9 2.500
.1
*The values ofthe chart are applicable when the vessel is constructed of austenitic steel (18Cr-8Ni, Type 304)
(Table 1on page 190)
.00001
2 3456789
.0001
2 3 456789
.001
FACTOR A
2 3 456789
.01
2
25.000
:?0.000
18.000
16.000
14,000
12.000
10,000
9,000
8.000
7.000
6,000
5.000
4,000
J.500
3.000
2.500
.1
*The values ofthe chart are applicable when the vessel is constructed of austenitic steel (18CR-8Ni-Mo, Type
3l6)(Table 3 on page 190)
=~
0
~
u
<~
<!) i::: <I)
-5 «:! -5<I)
.s e 't>
Cll f;; i:::
~ en o
«:! «:! ·-...... ...." <..>...... <!) <I)
-.... i::: ....
,, - ...... 0
~ - ...... 0 <I) 0.
..... .
= gE<d ~
~ e c:.:::,..,,, > <!) 0 <!)
""" 0. N ._.
o ] e ·;:::.ar..... .... <!) 0 cc
<""" <I) .... ..c::: ::;
u ::; <!) <!) 0.
< ..c::: 5 ..c::: e~ ~<;.... .... <I)
0 ..c::: ....
~ j -~ ~
~ ~ ~.::::
<..> i::: 0
<!) 0
.E-5·.;::-g
•• <;.... g <!)
~ 0 ell .....
E-< .... .... <!)
0 ..c::: <!) 0.
M .._. 0.
z ·;::: .s ;:j
<!) i::: Q)
..c::: cc ..c:::.... .....
0 <!) <;....
..... e o
~ ~ s::
- ell 0
~ ci;j ·.;:::
...... oi 0
-.... i::: 2
<;.... :..= 0
0 ....
<I) e °' .;:j ::3- <!)
- ....... c:s c:
ce ttt +..1 · -
;;.. .... i::: -<!) 0 <!)
<ll 0. N ._.
..c::: e ·- ;:j
+-' Q,) 6 ~
Q) ..... ..i::: ....
..... <I) <I)
<I) ..i::: <I) 0.
..i::: ..... ..c::: e~ <+-< ..... <!)
ell 0 ..c::: .....
<!) "O .'t:: ]
~ i::: ~ -0 <I) <+-<
i::: <!) § 0
"""'"I -:S ·- "'d
•• <;.... t) [i
~ 0 Q)
[_, ell ....
[""' .... <!)
0 <!) 0.
..... 0.
z .s ;::!
t
'--~~~~~~~~~~~~~~~-'-~~~~~~~~~~~~~~~~-'~

IM#lli);lif,.i$1WJ.Jti!Z1''i$"""'TT'' I----
14.000
12.000
10.000
9.000
8,00(
BOO FI I I I I I J.OOC
6.00(
5,000
4,000
3.500
FIG.HA-3 Httffl3,000
2.500
I I I I l I I I I I I I #W I I I I i I I I I I t I I I I I I I I I J I I J I I I I I t I I 2 OQQ
3 456789'2
.00001
3 4 56789
.0001
2 3 456789
.001
FACTOR A
2 3 456789
.01
2
.1
*The values of the chart are applicable when the vessel is constructed of custenitic steel (I 8CR-8NI-O, 03 max.
carbon, Type 304L) (Table 2 on page 190)
~
·~
0
~
u
<i;r..
<U s:: <U
..i:::: <tS ..i::::
- <U ....
Be~
"'~ s::
::::: "' 0
<tS <tS ·-
~ ... t)
...,. <U <U
"""i:: .....
.. ·- 0
-- .....0 <U 0..
..... .<U;j-<U
;j ...... <tS s::
c; rs?E~
;>l!)O.u
0.. N ,_,
] El ·;::: .s...... <!) 0 o:l
<U - ..i:::: ~
..... <!) <!) 0..
] .s ..i:::: 8
,,. """ .... <U
;>- 0 ..i:::: .....
"' ..... <!)
<U -0 ·- ..i::::
"'s:: ~ -o:l <!) """
0 <U s:: 0
s:: ..i:::: .9 -0
......i ~......, ~
•• """' ~ <U
""1 0 "' .....
E-< ...... ..... <!)
ofiiES:z ·;::: .5 ::I
~
. !liZU!S!i:l!i .··~- --~~iidhA!J.111!!!! L!f.llilf.l ..L ·- [_ ; m *!!!!!!iii pr r· - b k! __il!r!!L1U!!!!! ' - ' ... ,
2
.00001
I I I
up to 100 F
....._.i..--
I I-........ f I I
- - -300 F
:.,... ..... I..-- .....- I I
J.•.• .__ .. - 400 F'
I I I........ ...""' i---
,001 Fl-i... .. c.,...~
1.......... i -&--
--
7 I,.....-""" L..-.... .... ... i..- '-800 F
1..... ..... -~
- .-
,__
~~ ...
'I -- ~-
_......
J -II _i...- ~ ....
'II '--""
w~·-
E = 28.0 x 106-:-
"" t'&E : 26.4 x 106-
FIG.HA-4E 24.5 • 106-
~E 23.1 x 106-
I3 456789
.0001
-:---;
&
2 3 4 56789
.001
FACTOR A
2 3456789
.01
I I I2
3 4 56789
.1
20,000
18,000
16,000
14,000
12.000
10,000
9.000
B,000
7.000
6.000
5,000
4,000
3,500
3,000
2,500
2.000
*The values of the chart are applicable when the vessel is constructed of austenitic steel (I 8CR-8Ni-Mo-0.03
max. carbon, Types 316L and 317L)(Table 4 on page 190)
]§].... ....
0 """'.... 0
~
~
<
"""0 <U
~ g:;-::d)- .w o< c
~ ~ .w --
~ ;>~§~
0 .uO..Ni-.
.r:! 8 ·- ::I
~ ':;;l <!) 5 d
U <!) ""'...C:: ...
... <U <U
<]£<DO..
i;r.. :::: """£ ~
"' 0 ..i:::: ......
<!) -0 ,-;: ]
~ i:: ~ ......
0 <!) """
i:: <!) § 0
..... £ ·- -0
•• """ t) ~
""1 0 0
E-<-~~
OfiiES:z ·;::: .s ::I
...__~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-l~

48
EXTERNAL PRESSURE
CONSTRUCTION OF STIFFENING RINGS
LOCATION
Stiffening rings may be placed on the inside or outside of a vessel.
SHA.PE 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 neces-
sity 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 1!h 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 b1i 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 circum-
ference 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 '°'<xt•m'1 ring l
1:Figure A Figure B
EXAMPLE: RINGS OUTSIDE W' x 3" lg. fillet weld on 6" ctrs.
RINGS INSIDE '4" x 2" lg. fillet weld on 6" ctrs.
The fillet weld leg-size shall be not less than the smallest ofthe following: 1/4 in,
~ ""' ...... • ''· !_!-A.
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
49
20 30 40 so 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
SPHERICAL, ELLIPSOIDAL, FLANGED AND DISHED HEADS
(Specified yield strength 30,000 to 38,000 psi, inclusive)
To find ~e required l!ead thickness: 1. Determine R, 2. Enter the chart at the value
of R, 3. Move vertically to temperature line, 4. Move horizontally and read t.
t = Required head thickness, in.
R = For hemispherical heads, the inside radius, in.
For 2:1 ellipsoidal heads 0.9x00
For flangeq and dished heads, the inside crown radius, in. Rmax=Do
D0 = Outside diameter of. the head, in.

50
CHARTS FOR DETERMINING 'IHE WALL THICKNESS FOR
VESSELS SUBJECTED TO FULL VACUUM
I ...
110.
100.
•00.
10.
....
.....
....
+--l--l--++-+~i-'"""'~-+-+---+.....~...,1oo1--i--i-~.~ ~
-11--1.........,,__lt'--+-+--+-+--4<-~-+~-+-~bl--1--1-+.:1 o:i"<),
i::
~'-;;;j'---f-t-f-~tf---+-f-+-~-t,1~+-,t.+--l~--l-=!100. ~
r/l
~'1'--"1'~-f--t----,f--+-~-f-1f---l---l--+--+-+..;;;ioo. ~
~-..;a<-+-¥--+->"--1f---l--l---f-l--+--l--l--+--I-~ ... j
w
Ti), lt7".ff:;'lf7-;1'17''7't-/'-i;'--17'-+tl-+--7ll--~--+-..,4---A--+--l--l--l-+..::I Ti), Bi
""... t"7'"T.>V'-:r-:il'-:~'l'-7"-1"'-+-of--,.<---+-;.;<---+-~--1--,,L......-1----+----l--1--l--l-.::ioo. 0
... 1::""7'7lr:;~r<-;;f-7'f--i;>"'-t--.P.'---7"-l~--[;1Fo':.._+,.,.<:+~-l----l-+--+-+-+-=i ~
... ".... "'7'-7''"1>"'"7'T":;"'"t7"t--,,....+-f-7'"---+-7"'---+-¥:...+-+---1----+----l--1--l--l-.::i ~... ..... ...)
10.
CYLINDRICAL SHELL
(See facing page for explanation)
"'
II
....i
.....
0
Q
CHARTS FOR DETERMINING 'IHE WALL 'IHICKNESS FOR
VESSELS SUBJECTED TO FULL VACUUM
.10 .is .ao .z .:ao .35 .C> •.as .so .ss .ec .es .TO • TS .eo .as .80 ~1ill&
....
500.
...,..
---315.
-305.
"""215.
...,.
.....
"°"',.,..
ISO.
,,.,
•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 D0
3. Move vertically to temperature line
4. Move horizontally and read D0 /t
S. Enter chart above at the value of D0 /t
6. Move horizontally to curve D
7. Move vertically down and read the value of t
NOTATION
Required shell thickness, in.
D0 Outside diameter of shell, in.
L Length of the vessel or vessel section, taken as the largest of the following:
l. Distance between the tangent lines of the heads plus one third of the depth of
the hea.ds· 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 plu's one third of the head depth, in.
The charts are from:'
Logan, P. J., "Based on New ASME Code Addenda •.. Chart Finds Vessel Thickness,"
HYDROj::ARBON PROC,.ESSING, 55 No. 5, May 1976 p. 217.
Logan, P. J., "A Simplified Approach to •.. Pressure Vessel Head Design," HYDROCAR-
BON PROCESSING, 55 No. 11, November 1976 p. 265.
Copyrighted Gulf Publishing Co. Houston. Used with permission.
51

52
DESIGN OF TALL TOWERS
WIND LOAD
The computation ofwind load is based on Standard ANSI/ASCE 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./sq. ft.
When records and experience indicates that the wind speeds are higher than
those reflected in the map, the higher values ofwind speed shall be applied.
The wind pressure on the projected area ofa cylindrical tower shall be calculated
by the following formula. ·
F qz G CtAt Table6-1ANSIJASCE7-95STANDARD
L
(Numbers of tables and paragraphs are references to this
Standard.)
(D x H) Projected area oftower, sq. ft.
I I height of tower considered, ft.
outside diameter oftower, ft.
Shape factor= 0.8 for cylindrical tower (Table 6-7)
~--Gust response factor (Gh & G,)* (Para. 6.6)
When the tower is located:
in urban, suburban areas, Exposure B 0.8;
in open terrain with scattered obstruction, Exposure C 0.85;
in flat, unobstructed areas, Exposure D 0.85.
'-----Velocity pressure at height z above ground, lb./sq. in.
0.00256 KzKz1 V2 I, lb./sq. ft. (Table 6-1)
Design Wind Force, lb. l11 lmportoncefuctor 1.0 fu"tructum that
on projected area of present low hazard to human life in event
tower. (Para. 6.2) 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, C & D (Table 6-3)
* See tables below for values of q and for combined values
of Gh, Gz, and Kz in Exposures B, C, and D.
VEWCITYPRESSURE,
Basic wind speed, mph, V 70 80 ~ 100
Velocity Pressure psf0.00256 V2, q 13 17 21 26
110 120 130
31 37 44
•'I ;
53
WIND LOAD
(Continued)
COEFFICIENT G (Gustresponse fact~edwith Exposure Coefficient)
HEIGHT
EXPOS~Above Ground, ft. EXPOSUREC EXPOSURED
0-15 0.6 1.1 1.4
20 0.7 1.2 1.5
40 0.8 1.3 1.6
60 0.9 1.4 1.7
80 LO 1.5 1.8
100 1.1 1.6 1.9
140 12 1.7 2.0
200 1.4 1.9 2.1
300 1.6 2.0 2.2
500 1.9 2.3 2.4
The area ofcaged ladder may be approximated as 1sq. ft. per lineal ft. Projecte(rarea
ofplatform 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 pres-
sure 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 ofthe tower. With good arrangement ofthe equipment, the exposed area ofthe
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 = J<()Om.p.h
diameter oftower, D = 6 ft.
height oftower, H = 80 ft.
the tower located in flat,
unobstructed area, exposure: D..
The wind load, F=qz xG x Ct At
· q from table = 26 psf
G frorµ table = 1.8
Shape factor = 0.8
Area,Aj';'DH=6 x 80 480 sq. ft.
F""' 26 x 1.8 x 0.8 x 480 17,971 lbs.

54
Alaska Note:
MAP OF WIND SPEED, V
(miles per hour)
For coastal areas and islands,
use nearest contour.
ANSllAASCE STANDARD 7-95
Courtesy of American Society of Civil Engineers
. I
Notes:
MAP OF WIND SPEED, V
(miles per hour)
~ Special Wind Region
• Population Center
Location V, mph
Hawaii 105
Puerto Rico 125
Guam 170
Virgin Islands 125
American Samoa 125
1. Values are 3-second gust speeds in miles per hour ilt 33 ft.
above ground for Expo'Sure C category and are associated with
an annual probability of 0.02.
2. Linear interpolation between wind speed contours is permit-
ted.
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.
55

56
WIND LOAD
Computation of wind load as alternate method based on standard ASA A58.l-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.
20 30
25 40
25 30 40 45 50
30 40 45 55 60
EXAMPLE:
Find the wind pressure Pw from map.
35
45
55
70
50
60
75
*Multiply values ofPw with 0.80
when the horizontal cross sec-
tion is hexagonal or octagonal
and with 0.60 when the horizon-
tal cross section is circular or el-
liptical.
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 shall be multiplied by shape factor 0.6, then the
wind pressure in different zones will be 15 and 18 lb. per sq. ft. respectively
If many pieces of equipment are attachfd to the tower it is advisable to increase the
shape factor (according to Brownell) up to 0.85 for a cylindrical vessel.
Users of vessels usually specify the wind pressure for manufacturers without refer-
ence 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:
Pw 0.0025 X Vw 2 where Pw =wind pressure lb. per sq. ft.
Vw wind velocity mph
EXAMPLE:
Wind of 100 mph velocity exerts a pressure:
Pw 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 ofthe tower. With a good arrangement ofequipment the exposed area ofthe wind
can be reduced considerably. For example, by locating the ladder 90 degrees from the
vapor line.
57
MAP OF WIND PRESSURE
; '

I
58
,..
H
1£1
I
....._
-+---1-
b 3'-6"
7 [£Z1)Platform
r-Il..._L
~ --"O
"O
"'...l
...0
Q,
~
WIND LOAD
(Continuation)
FORMULAS
SHEAR MOMENT . REQUIRED
STRESS THICKNESS
NOTATION
= Width of the vessel with insulation etc., ft.
= Efficiency of the welded joints.
= Lever arm, ft.
= Distance from base to section under consideration, ft.
= Length of vessel or vessel section, ft.
= Maximum moment (at the base) ft. lb.
= Moment at height hT, ft. lb.
= Wind pressure, lb. per sq. ft.
= Mean radius of vessel, in.
= Stress value of material or actual stress psi.
= Total shear, lb.
= Required thickness, corrosion excluded, in.
EXAMPLE:
Given: D, = 4'-0" D2 = 3'-0" H1 = 56'-0" H2 = 44'-0"
hT = 4'-0" Pw = 30 psf
Determine the wind moment
Lower
h, = H,12 = 28'-0" hi = H1 + (H212) = 78'-0"
Pw x D x H = V x h = M
Section 30 x 4 x 56 = 6720 x 28 = 188,160
Upper
Section 30 x 3 x 44 = 3,960 x 78 = 308,880
Total V = 10,680 M 497 ,040 ft. lb.
Moment at the bottom tangent line
MT= M - hT(V - 0.5PwD1 hT) =
497,040 - 4 (10,680 - 0.5 x 30 x 4 x 4) = 455,280 ft. lb.
EXAMPLE:
Given: D1 = 3 ft. 6 in. H = 100 ft. 0 in. hT = 4 ft. O in.
Pw = 30 psf
Determine the wind moment
h, = H/2 = 50 ft. 0 in.
PwxD1 xH= Vxh,= M
Vessel 30 x 3.5 x 100 = 10,500 x 50 = 525,000
Ladder 30 x 98 Jin. ft. = 2,940 = 49 = 144,060
Platfonn 30 x 8 !in. ft. = 240 x 96 = 23,040
Total V = 13,680 M = 692,100
Moment at the bottom tangent line ft. lb
MT= M - hT(V - 0.5 PwD/ hT) =
692,100 - 4 (13,680 - 0.5 x 30 x 3.5 x 4) = 638,220
ft. lb.
SEE EXAMPLES FOR COMBINED LOADS ON PAGE: 69
i I
'
,I
59
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:
I. shell
2. heads
3. internal plate work
4. tray supports
5. insulation rings
6. openings
7. skirt
8. base ring
9. anchor ring
I0. anchor lugs
11. miscellaneous
12. + 6% of the weight of items I through 11 for
overweight of the plates and weight added by
the weldings
Equipments:
13. insulation
14. fireproofing
15. platform
16. ladder
17. piping
18. miscellaneous
Erection weight: the sum of items I through 18.
B. Operating weight, which includes the weight of the:
I. vessel in erection condition
2. · trays
3. operating l1quid
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
ct
where S = unit stress, psi
W = weight of vessel above the section under consideration, lb.
c = circumference of shell or skirt on the mean diameter, in.
t = thickness of the shell or skirt, in.
The weight cif different vessel elements are given in tables beginning on page 374

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 ofVibration: Tsec. T= 0.0000265 (-jf)2
...jifII
Maximum Allowable Period
KofVibration, Ta sec. ~=0.80 g
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 oftower, lb.
w = Weight oftower per foot ofheight, lb.
EXAMPLE
Given: Determine the actual and maximum allowable
period ofvibration
D = 3.125 ft. 0 in.
H = 100 ft. 0 in.
g = 32.2 ft/sec2
t = 0.75 in. T=o.000026s(100~ "36ox3.12s = 1.05 sec.
v = 1440 lb. 3.125 0.75
W= 36,000lb.
in operating condition .Y36000 x 100
w = 360
Ta= O.so
1440
X
32
.
2
=7.05 sec.
'
The actual vibration does not exceed the allow-
able vibration.
Reference: Freese, C. E.: Vibration ofVertical Pressure Vessel ASME Paper 1959.
:i,.
DESIGNOFTALLTOWERS
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).
F,- t vH/3
V-F, I YH
-L_l
(a) Seismic Loading Diagram
w(b) Seismic Shear Diagram
Base Shear
SHEAR
Base Shear
FORMULAS
MOMENT
M= {F1
XH+ (V-F1
) X (2H!3)]
Mx=fF1
XX} for X:::; H;
3
Mx=fF,XH+ (V-F1
) X (X-H/3)]
for X> H;
3
The base shear is the total horizontal seismic shear at
the base ofa tower. The triangular loading pattern and
the shape ofthe tower shear diagram due to that load-
ing are shown in Fig. (a) and (b). A portion ofF1
oftotal
horizontal seismic force Vis assumed to be applied at
the top ofthe tower. The remainder ofthe base shear is
distributed throughout the length ofthe tower, includ-
ing the top.
Overturning Moment
The overturning moment at any level is the algebraic
sum ofthe moments of all the forces above that level.
NOTATION
C N . l ffi . 2.3SS= umenca coe 1c1ent~
(need not exceed 2.75)
C =Numerical coefficient= 0.035
D =Outside diameter ofvessel, ft.
E =Efficiency ofweldedjoints
. F1
= Total horizontal seismic force at top ofthe vessel,
lb. determined from the following formula:
F,=0.07 TV (F, need not exceed 0.25 V)
=O, for Tso. 7
H =Length ofvessel including skirt, ft.
61

62
J~ '
xH
- D
·-
DESIGN OFTALL TOWERS
--1
(Continuation)
NOTATION
I = Occupancy importance coefficient (use 1.0 for
vessels)
M =Maximum moment (at the base), ft-lb.
Mx =Moment at distanceX, ft-lb.
R = Mean radius of vessel, in.
Rw =Numerical coefficient (use 2.9 for vessels)
S = 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
b)Stiff or dense soil condition where the depth is
less than 200 ft. S = 1. A soil profile with dense or
stiffsoil conditions, where the soil depth exceeds
200 feet. S = 1.2.
A soil profile of40 feet or more in depth and con-
taining 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 ofsoft
clay. S =2.0.
St = Allowable tensile stress ofvessel plate material,
psi.
T = FundamV,1tal period of vibration, seconds
=Ct x H •
t = Required corroded vessel thickness, in.
I2M or I2Mx
nR2
StE nR2
StE
V = Total seismic shear at base, lb.
W = Total weight oftower, lb.
X =Distance from top tangent line to the level un-
der 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).
,t
I
I~··
i~:
l
!i
.
'
'
~
DESIGN OFTALL TOWERS
EXAMPLE
Given:
Seismic zone: 2B
D= 37.5 in.= 3.125 ft.
H= 100 ft., 0 in.
Z=0.2
X= 96 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= Ct x H% = 0.035 x 100% = 1.1 sec.
and
I= I, S= 1.5, Rw=2.9,
C= l.25S = 1.25 x 1.5 = 1.76<2.75
r2
13 1.1 2
13
V= ZIC x W= 0.2x 1x1.76 x35,400=4,296lb.
Rw 2.9
Ft= 0.07 TV = 0.07 x1.1 x 4,296 = 330 lb.
M= [FtH + (V- Ft) (2Hl3)] =
[330x100+(4,296-330)(2x100/3)] =294,756ft. - lb.
X > H thus
3
Mx = [Ft X + (V-Ft) (X - H/3)] =
[330 x 96 + (4,296 - 330)(100-33)] = 281,138 ft. - lb.
63

For areas outside of the United States, see Appendix Chapter 23 of UBC :1991
·-- - - --·~ - ·-··- -- ·------· --~ - --··-· ·.~-=- ···--"-"'-'····-·
Cf.I
tT:1
-r:,r.,
s:::
-C":l
N
~tT:1
s:::
?;
0
"Tj
~
tT:1
e
~
~
0
Cf.I
""'
~7Jl
---~-....-==.-..,;;;;;..-:::.,,..- - -·-···="-,,,..,.,..,._.•_.. -.-·--·-===-~-· tat ..~ £ .. ____ -=-- ·-~ ---·· w s *
(
z
Q
~
DESIGN
°'.!>-

66
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 arrange-
ment 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.
£IFt-.
. I
l i
I w
•t: ...
Given: e = 4 ft 0 in.
R = 15 in.
t = 0.25 in.
w = 1000 lb.
FORMULAS
MOMENT STRESS
REQUIRED
THICKNESS
e
E
M
R
s
t
w
M= We S- 12We
- 7!R2t
NOTATION
12We
t = R 27!SE
= &x:entricity, 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.
&x:entric load, lb.
EXAMPLE
Determine moment, M, and stress, S.
Moment, M = We = 1000 x 4 = 4000 ft. lb.
= 12 We = 12 x 1000 x 4 = 272 si
S 'IT R2t 3.14 x 152 x 0.25 p
When there is more than one eccentt<ic load, the moments shall be summarized,
taking the resultant of all eccentric loads.
1.·
67
Design of Tall Towers
ELASTIC STABILITY
A tower under axial compression may fail in two ways because of instability:
1. 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 With Stiffener
s= 1,500,000~(<}yield point) s~ 1
•50
~·000
jt;t; (< j yield P.)
NOTATIONS:
Ax = Cross sectional area of one logitudinal stiffener, sq. in.
Ay = Cross sectional area of one circumferential stiffener, sq. in.
a. = Distance between logitudinal stiffeners, in.
{;, = Distance between circumferential stiffeners, in.
K Mean radius of the vessel, in.
S = Allowable compressive stress, psi
= Thickness of shell, in.
t + ~ The equivalent thickness of the shell when longitudinally
1
x dx stiffened, in.
~ The equivalent thickness of the shell when circumferentially1
Y =
1
+ dy stiffened, in.
EXAMPLE
Given: · R = 18 in.
= 0.25 in.
Determine the allowable compressive stress (S)
1,500,000 x t 1,500,000 x 0.25 - 20 833 .
Given: A,. = 1 sq. in.
dy = 24 in.
Longitudinal stiffener
is n.ot used, ·then: '
tx = t = 0.25 in.
1
t =t+-=
y 24
=0.25 + 0.04 = 0.29
S= - , psi
R 18
Determine the allowable compressive stress (S) using
stiffener rings
S
1,500,000 • r:-:-
= R V'fx =
1
•5
~~ooo V0.25 x 0.29 = 22.438 PSI
Reference: Wilson, W. M., and Newmark N. M.: The Strength of Thin Cylindrical
Shells as Columns, Eng. Ex . Sta. Univ. UL bull. 255 1933.

68
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.
Given:
DJ = 2 ft., 6 in.
E = 30,000,000
H = 48 ft., 0 in.
I = R3 -rr 0.3125
Pw =30psf
R = 12 in.
t = 0.3125 in.
FORMULA
NITTATIONS
llM = Maximum deflection (at the top), in.
DJ = Width of the tower with insulation, etc. ft.
E = Modulus of elasticity, psi
H = Length of vessel, included skirt, ft.
I = R3-rr t, moment of inertia for thin cylindrical shell
(when R> IOt)
R = Mean radius of the tower, in.
t = Thickness of skirt, in.
Pw = Wind pressure, psf
EXAMPLE
Determine the maximum deflection: llM
30 x 2.5 x 48 (12 x 48)3
/lM = 8 X 30,000,000 X 123 X 3.14 X 0.3125 = J.
69
in.
The maximum allowable deflection 6 inches per 100 ft. of height:
48 x 6
for 48'-0" =JOO = 2.88 in.
Since the actual deflection does not exceed this limit, the designed thickness of the skirt is
satisfac..tory.
A method for calculating deflection, when the thickness of the tower is not con-
stant, given by S. S. Tang: "Short Cut Method for Calculating Tower Deflection".
Hydrocarbon Processing November 1968.
,(
·1~..'
I•
!
69
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 windward side
+ Stress due to wind
+ Stress due to int. press•.
- Stress due to weight
At leeward side
Stress due to wind
+ Stress due to int. press.
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 side
- Stress due to wind
Stress due to ext. press.
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. At the bottom of the tower
2. At the joint of the skirt to the head
3. At the bottom head to the shell joint
4. At changes of diameter or thickness of the vessel
The stresses furthermore shall be examined in the following conditions:
1. During erection or dismantling
·2. During test. ·
3. 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 d.ue 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..tbe,tower (or which a certain thickness is adequate.
tjtp 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7
m l.O 0.91 0.84 0.79 0.74 0.71 0.67 0.64 0.62 0.60 0.58 0.56 0.54
tjtp 1.8 1.9 2.0 2.2 2.4 2.6 2.8 3.0 3.3
m 0.53 0.51 0.50 0.48 0.46 0.44 0.42 0.41 0.39
3.6 4.0 4.5 5.0
0.37 0.35 0.33 0.32
x
t
TABLE 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 calcu-
lated for internal pressure satisfactory also to resist the wind
pressure.
X = H x m
IP = The required thickness for internal pressure
(Hoop Tension) in.
t,. = The required thickness for wind pressure at the bottom head
joint to shell, in.
EXAMPLE: 'P. = 0.233 in., tw = 0.644 in. tjt = 0.644/0.233 = 2.7
o.o
0.1
0.3
::i::
i:i 0.4i.i
~
~ o.s
"'0
... 0.6
::i::
Cl
iii 0.7
::i::
0.8
0.9
ff = 100 ft. p
From Thble m = 0.43 and X = mH = 0.43 x 100 = 43 ft.
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.
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:
for internal pressure, tP = 0.250 in.
for wind load, t.., 0.625 in.
at the bottom required
f/2 + fw = 0.750 in.
at height 0.71 H;
0.5 x 0.750 = 0.375 in.
thickness for internal
pressure t/2 = 0.125 in.
required thickness at 0.71 H = 0.500 in.
0.1 0.2 o.3 o.4 o.s o.6 0.1 o.a 0.9 1.0 Fig. B
Ratio of plate thickness required at the bottom
(t 12 + t) to thickness required at the consid-
eted height.
I,,
I
1:
I
..•
',,,••.
·'
,"
,'
EXAMPLE - A
Required thickness of cylindrical shell under internal pressure and wind load.
2'M 6n
~
DESIGN CONDffiONS
D = 2 ft. 0 in. inside diameter of vessel
D1 = 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
c hr = 4 ft. Oin. distance from the base to the bottom
. head to shell joint
... ~- p = 250 psi internal pressure
"" 0II PW = 30 psf wind pressure
:c .. R = 12 in. inside radius of vessel.,.
s = l5700psi stress value of SA 285 C
~r ... II
... material at 200°F temperature
~ ..:: ~
..:: v = Total shear lb.
No allowance for corrosion.
Minimum required thickness for internal pressure considering the strength of the long seams:
l'R 250 x 12 - 3,000 = o228 .
1
=SE - 0.6P = 15700x 0.85 0.6 x 250 - 13,195 · m.
Minimum required thickness for internal pressure considering the strength of the girth seams:
PR _ 250 x 12 = 3,000=O
112
.
t = 2SE + 0.4P - 2 x 15,700 x 0.85 + 0.4 x 250 26,790 . m.
Required thickness for longitudinal bending due to wind pressure. Moment at the base (M):
P.., x D1 x H = V X h1 = 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.., D1 hr) = 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:
- -11:.x_ - 871,200
t - R2 'IT SE - 122 x 3.14 x 15,700 x 0.85
871,200 0 145 .
6,037,135= · m.
The required thickness calculated with the strength of the bottom girth seam:
For wind pressure 0.145 in-
For int. pressure 0.112 in.
TarAL 0.254
This is greater than the thickness calculated with
the strength ofthe longitudinal seamtherefore, this
minimum thickness 0.257 in. shall be used.
71
For simple vessels where the moment due to wind is small, th~ abov~ c~lculat!on is satisfactory.
Vessels which are subject to larger loadings may need closer mvest1gatton with respect also to
economical viewpoints. See pages 76-84 for skirt, base and anchor bolt design.

72
•
EXAMPLE B
Re~uired thickness ofcylindrical shell under combined loadings ofinternal pressure, wind and
weight of tower.
DESIGN DATA
D 3 ft. 0 in. inside diameter
D, 3 ft. 6 in. width of vessel with insulation, allowance for
piping, etc.
E 0.85 efficiency of welded seams
hr = 4 ft. 0 in. distance from the base to the bottom head to shell
joint.
H I00 ft. 0 in. length of tower
P = 150 psi internal pressure
Pw 30 psf wind pressure
R = 18 in. inside radius of vessel
S = 15700psi stress value of SA-28SC material at 200°F
temperature
V Total shear, lb.
Head: 2: 1seamless elliptical
C,,. = 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.
1 = PR = 150 x 18 _ . .
SE - 0.6P 15700 x 0.85 - 0.6 x 150 - 0.204 tn. Use 0.25 tn. plate
Minimum required thickness for internal pressure considering the strength of the circumferen-
tial seam of shell.
PR 150 x 18
2SE + OAP= 2 x 15700 x 0.85 + 0.4 x 150 = O.IOI in.
Minimum required thickness for head
t = __P_D__ 150 x 36
2SE - 0.2P = 2 x 15700 x 0.85 - 0.2 x 150 = o.2o3 in.
Wind Load PW x DI x H = v x h1 = M
Vessel 30 x 3.5 x 100 = 10,500 x 50 = 525,040
Platfonn 30 x 8 !in. ft. = 240 x 96 = 23,040
Ladder 30 x 98 Jin. ft. = 2,940 X49 = 144,060
Total shear V: 13,680 M = 692, IOO ft. lb. moment at
Moment at the bottom head seam (Mr)
MT= M - hr<V - 0.5 PwD,hrJ =
base
692,100 - 4 (13680 - 0.5 x 30 x 3.5 x 4) = 638,220 ft. lb.
I = 1l_&_ = 12 X 638,220 7,658,640
R2 ,,. SE 182 x 3.14 x 15700 x 0.85 = 13,583,556 =o.564
Try 0.750 in. plate for the lower courses For int. pressure 0.101
0.665 in.
JI;
........
-0
v. -'
0 "!
-.... c
----0 -0 ~' ' -... "'
~ c::i....
-
0
"' -... .,..
... c::)
-0 ,.....:.. ,__
Shell 40 x 97
32 x 195
24 x 294
Head top 0.3125 nom.
bot. 0.8125 nom.
Int. plate work
11'ay supports
Insulation rings
Opening
+ 6%
Say
73
EXAMPLE B (CONT.)
The preliminary calculation of the required wall thick-
ness 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.
From diagram B, Page 70 can be found the required
thickness and length of the intennediate shell sections.
Using 8 ft. wide plates, the vessel shall be constructed
from:
(5) 0.25 thick 8 ft. wide courses
40 ft.
32 ft.
24 ft.
Total 96'ft:"
WEIGHT OF THE TOWER
(See tables beginning on page 374 )
3880 Skirt 4 x 195 780
6240 Base ring 720
7056 Anchor ring 260
160 Anchor lugs 120
393 --1880
800 + 6% 113
110
1993220
Say 2000 lb.900
-- Insulation 460019759
Platfonri 11601184
Ladder 2800
20943 lb. Piping 1400
21,000
9960
Say 10,000 lb.
TOfAL ERECTION WEIGHT: 33,000 lb.
Trays 600
Operating liquid 2400
3000 lb.
+ Er~ction Wt. ·
33,000 lb.
TOTAL OPERATING WEIGHT: 36.000 lb.
Test water 42,000 lb.
+ Erection Wt. 33,000 lb.
.
TOTAL TEST WEIGHT: 75,000 lb.
For weight of water content, see Page 416
--··

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.
.. $1r!':ss due_.to internal pressure
S _ PD _ 150 x 36.75 .
- 4t - 4 x 0.75 1837 psi
Stress due to wind
s - .!l.Mr_ - 12 x 638,220 - .
- R2 ir t - 18.3752 x 3.14 x 0.75 - 9•
632
psi
Stress due to weight,
in erection condition
in operating condition
s - __!!'.__ - 31,000 - .
- Cmt - 115.5 X 0.75 - 358 psi
S = __!!'.__ = 34
•
000
392 psi
Cmt 115.5 x 0.75
COMBINATION OF STRESSES
WINDWARD SIDE LEEWARD SIDE
IN EMPTY (ERECTION) CONDITION
Stress due to wind + 9,640 Stress due to wind - 9,640
Stress due to weight - 358 Stress due to weight - 358
---+ 9,282 psi - 9,998 psi
(No int. pressure during erection)
IN OPERATING CONDITION
Stress due to int. press. + 1,837 Stress due to wind 9,640
Stress due to wind + 9,640 Stress due to weight - 392
+ 11,477 -10,032
Stress due to weight - 392 Stress due to int. press. + 1,837
+ 11,085 psi - 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 bot.tom of the vessel is satisfactory.
Stress in the shell at 72 ft. down from the top of tower. Plate thickness 0.50 in.
Stress due to wind.
Shell
Platfonn
Ladder
xP XD XX=VX-=Mw I 2 x
30 x 3.5 x 72 = 7,560 x 36 =
30 x 8 lin.-ft. = 240 x 68
30 x 70 lin.-ft. = 2,100 x 35
Total Moment M,.
s =
12 M 12 x 361,980
R2 ir t 18.252 x 3.14 x 0.50
Stress due to internal pressure
(As calculated previously)
272,160
16,320
73,500
36T,980 ft.-lb.
8,303 psi
1,837
Total 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 insig-
nificant. 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. ' ·
[.
i
i
0
0
v
II
x
75
EXAMPLE B (CONT.)
Stress in the shell at 40 ft. down from the top of the tower. Plate thickness 0.25 in.
,....,.
-~ [LJ_
0 --
·=I:
Stress due to wind.
PW x D, xx
xV x - = M
2 x
Shell
Platfonn
Ladder
30 x 3.5 x 40 = 4,200 x 20 = 84,000
'.lO x 8 lin. ft. = 240 x 36 = 8,640
30 x 38 lin. ft.= 1,140 x 19 = 21,660
Total Moment M"
12 Mr = 12 x 114,300
S= R2 ir t 18.1252 x 3.14 x 0.25
Stress due to internal pressure
(As calculated previously)
Total
= 5,316 psi
1,837 psi
7,153 psi
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.

Eugene f. megyesy-pressure_vessel_handbook_12th edition

Eugene f. megyesy-pressure_vessel_handbook_12th edition

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Viewers also liked

Viewers also liked (16)

Similar to Eugene f. megyesy-pressure_vessel_handbook_12th edition

Similar to Eugene f. megyesy-pressure_vessel_handbook_12th edition (20)

Recently uploaded

Recently uploaded (20)

Eugene f. megyesy-pressure_vessel_handbook_12th edition