design for creep in pressure vessels
TRANSCRIPT
Lehigh UniversityLehigh Preserve
Theses and Dissertations
1-1-1976
Design for creep in pressure vessels.Antonio Serrano Perez
Follow this and additional works at: http://preserve.lehigh.edu/etd
Part of the Mechanical Engineering Commons
This Thesis is brought to you for free and open access by Lehigh Preserve. It has been accepted for inclusion in Theses and Dissertations by anauthorized administrator of Lehigh Preserve. For more information, please contact [email protected].
Recommended CitationPerez, Antonio Serrano, "Design for creep in pressure vessels." (1976). Theses and Dissertations. Paper 2027.
DESIGN FOR CREEP IN PRESSURE VESSELS
by
Antonio Serrano Perez
A Thesis
Presented to the Graduate Committee
of Lehigh University
in Candidacy for the Degree of
Master of Science
in
Mechanical Engineering
Lehigh University
1976
ProQuest Number: EP76300
All rights reserved
INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted.
In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed,
a note will indicate the deletion.
uest
ProQuest EP76300
Published by ProQuest LLC (2015). Copyright of the Dissertation is held by the Author.
All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code
Microform Edition © ProQuest LLC.
ProQuest LLC. 789 East Eisenhower Parkway
P.O. Box 1346 Ann Arbor, Ml 48106-1346
This Ther.is is accepted and approved in partial ful-
fillment of the requirements for the degree of Master of
Science in Mechanical Engineering.
(Date)
Professor in Charge
Chairman of Mechanical Engineering Department
11
ACKITCWLSGI.DINT ^
This work was conducted in the Department of Mechan-
ical Engineering and Mechanics of Lehigh University,
Bethlehem, Pennsylvania.
The author wishes to thank Dr.^Arturs Kalnins, Project
Director, for his patience, help, technical assistance,
and necessary guidance during the development of this proj-
ect, and for the permisson to use his computer program for
the stress analvsis of axisvmmetric shells.
111
T'ABIE OF CONTENTS
l TITLE PAGE
CERTIFICATE OF APPROVAL ii
ACKNOV/LEGFIENT ii5-'
TABLE OF CONTENTS iv
ABSTRACT 1
1. INTRODUCTION 2
1.1 Creer Behavior 2
1.2 Importance 3
1. 3 Applications 4
2. CREEP VARIABLES 6
2.1 Representation of Creep Data 6
3. CREEP STRESS ANALYSIS • 10.
3.1 Uniaxial Stress and General Conditions 10
3.2 Kultiaxial Stress 12
3.2.1 General Equations 13
3.2.2 Soderberg Approach 17
3.2.3 Bailey Approach 19
3.2.4 Maximun Shear Stress Approach 20
3.3 Creep Rates under Biaxial Stress ZZ
4. CREEP IN PRESSURE.VESSELS 24
4.1 General Considerations 24
4.2 Thin-walled Vessels under Internal Pressure 25
iv
.'.i-'.-inl 1 r^ "i ' ■ '" '"»
O 1 O - r-. ■ - ■
"* A"""." ^1!"
i,T-i rr\ i
? 1 •'.'. "■avarc■" a~o v,vnc;: 5 3";-.
no an
xi'3'' are .inn or-can't: an■• xnc
• vo ^- r' A '
'-. 9 ,"V,n"hlT,-'< ' a^ ^Vijj.cj.i v^irc
'Ov-crTicr: arc i":Oor':arn:
'o ,n i ii i o <■-• "] o*7") .''-' T 7~* >^~» ^" ^ .o o
■!■.?. 2 io-.l';:n Oontitionr'
;;-.2.2.1 Do-iren Gr
■'-.?.'?.? Qvor~^ Tn^o
h . 2 . ?..') A'^nroach
■;'-. "^ . 2 . ■'•:'' Gtrorr Stats
■• T n ,-i r : c< r> T A v;r r,'
p ,'-.; vi - T in - ■ r. -
)-->■- i - - -r ,-|i ,-1
'Q'^ !^~'" C\ '
1 -■
1 1
:s'.-.' o? ^A3Lt;::
v_ . ..' — u"'_ . L v..;
37
h. ->
k- 5
p p ~ 1 \ -~> '
(-• - ' ! O
111
'A 95
AT) i-<; 1 ^ i.',;
d'n'/• stuf-r o'ior^a'1 ar a result of './or1: ar
Art"ir"- lalr.ir.s, -ro:sf'"'or in the do""artneni cf
!iT"lnoerin;™ arf. ^ ochanlcs at ~:'eh;igh
1 p' ^ ^} ^~' ' ^ a 2
'i \rni ity, ir relation
• o T.ie ' er*;..~m or 3. 'orossurc vorrs.. uno'sr creep conriipions.
in the introduction, the croc:- phenomenon is explained,
bv:0 general behavior of the materials under croon conditions
is given, the view point is emphasised that a large number
of engineering applications require naieria" ancl design
that is based, wholly or martially, on creep conditions.
~i- i^ mi::;: erent tneo.nes are g:'.ven "ciiax have ooen pro po see.
:"or the representation of croe;;"1 data.
The rrocediure for creep stress analysis is given for
different stress states, which includes the fundamental as-
sumptions of the general eeiuations, the different ae'ToacIie.?
to calculate croon .-'train, and the effects of multiamial
"j^e' n—v/alie " Pressure vessels under crcs"; eondi—
fhen, the design for creep in thin-v/allcd pressure vec
sels ir discussed, v/here general conriderations, tempera-
tures and design stress and the specific design conditions,
such as- design criterion, creep type, approach, and stress
state are inc 1 ude .
7'inally, a specific design problem is considered in
detail v/ith ?."csPoct to a Pressure vessel that might be used
i n P e t r o c h o m i c a. 1 i n d u s t r y .
1. IKTRCDUCTIOI.
1.1 Creep Behavior
Creep is the name given to time dependent strain of
solid materials over long periods under load. V/hen a load
has "been applied (Fig. 1-1) the strain increases with time
to.the point where failure finally occurs.
After the initial instantaneous strain £© , materials
often undergo a period of transient response where the #
strain rate £ (d£ /dt) decreases with time to a minimum
steady-state value :v/hich persists for a substantial portion
of the material life. The final failure comes after the
creep rate increases during the final stage of creep.
For analytical convenience, researchers have separated
the creep curve into three stages "based upon the similar re
sponge- of many materials.
The creep strain occuring at a diminishing rate is
called primary creep; that occuring at a minimum and almost
constant rate, secondary creep; that occuring at an acceler
ating rate, tertiary creep (Fig. 1-1)(l) (2).
It is characteristic of creep that, if the specimen Is
unloaded during the test, some of the strain recovers, as
shown by the clashed line in Fig. 1-1. Thus, we find that
creep phenomena include both permanent and recoverable
strain. The permanent effects are analogous to the plastic
flow at high .-train rates which characterizes metal-working
processes.
Another test v/hich is characteristic of creep studies
is the "relaxation" test. A specimen is loaded rapidly to
a fiv:ed strain, and the load required to manintain that
strain is recorded. The result is shown in i'ig. 1-2. It
is natural that there snouxa be a close relation between
the earlier portion of the creep (primary creep) and the
relaxation curves.
Usually., creep is associated with high temperatures,
but whether the temperature required is high or not really
depends upon the application.
1.2 Importance
A large number of engineering applications require the
use of materials and design which must be based, wholly or
partially, on creep behavior.
It was believed for a long time that there e::ists a
limiting stress below v/hich creep and consequent dimensional
changes would not occur. But, with the improvement of the
accuracy of5 measurements, the undeniable fact has emerged
that such a limiting stress does not e::ist. Hence, it has
now become common practice to design for limited service
life at elevated temperatures.
The designers of power-plants are forced to consider
operations at higher temperatures in the interest of great-
er efficiency. This is seen most directly, of course, from
the formula for the efficiency 2 of conversion of heat into
work in ar ideal engine, operating between two absolute tern
;oeratures ?-, > '.?? (E = 1-Tp/T-, ). It is possible to raise T,
to make appreciable gains in efficiency, but this also
entails higher creep rates for given stresses.
Applying this argument, it is useful to realize that
the operr'jtiD>n, of steam turbines has steadily increased in
efficiency because it has been possible to increase the tern
peratures Mirough n:.v; heat-resistant materials. It is true
also of gas turbines, jet aircraft, and missiles that an
important limit on ^erfomance is set by the permissible
deformation of working ra.rts under high temperature and
stress.
Other basic reason why engineering design must allow
for stress analysis for creep at high temperatures is found
in the required strength of vessels, in which the high tem-
perature is^needed for chemical reactions. Quite often,
high presures are also required.
!•3 Applications
The fast growth of the automobile industry required
studies of mechanical behavior of steel in thermal cracking
equipment which is used for making gasoline, -and hence it
*r;nr a :ip.'c':r-:r O" -I-.TCT concern to on rc.j .merits xo '.-re
o c~* *; .'—- ^ ^ <~* *; *"•—; o <— p ~j — * o y» <~>. .o " ^
Alloys f'or the omhaust gar- turbines had to be produced.
: strength an ' ductility were required of those materi-
nl n
Higher operating temperatures of steam turbines have
forced metallurgists to look for new heat-resistant alloys.
duch problems also will become more urgent as nuclear power
plants gain greater importance. Additional problems arise
in such plants which are created by creep and consequent
distortion of uranium fuel elements and their cladding ma-
terial? . '
Jet aircraft and guided missiles have directed more
•attention to stress analysis for creep.
Aero 'dynamic heating at high speeds can lead to sus-
tained sd:in temperatures v/hich pose difficult problems for
the designer.
A vital problem of aircraft structural design is to
achieve optimun strength-to- v/eigth ratio while avoiding
the problems, of buckling in the skin supporting members,
iduch effort has been directed toward the development of
new ligth structural metals such as titanium and its alloys
in large part because of their creep strength.
The Pressure Vessel deseach Committee of the welding
Research Council has conduced investigations on the creep
rupture "^-o^ertier- of Pressure vessels for use in nuclear
and petrochemical industries (3).
2. c- ::LI VA^IABL^C
2 .1 Pe^rementation of Creep Jata
A number of different extxresions have been proposed for
the representation of creer> tensile curves.
The creep strain at constant stress in metals, at tem-
peratures far below the meJ.ting point, is written as:
Cc ~ £Q Lo3 Cai +-0 (2a)
in which a is a constant and 6e> is the initial creep strain,
some of which may be recoverable (•':•) (5)- Creep curves at
constant stress, at higher- temperatures, are written by ex-
pressions of the form: "^
. £c =, €a -i-JEZact"71' +■ JELkjt-'"./ (2b)
o < i^i < 1 nj > l
where y^'L/nj are constants. The coifficients 4-L , b> ^
contain the effects of temperature and stress (6) (7) {G).
_ one rcsearcr.crs nave trio:* TO ro^rorcnx tno creep rate
6 c ==• A 5/V7 A. /V_ "\ (2o;
v.'here A and ^ defend upon temperature (9)
Other v/orkei"\c' have been able to represent creep data of
almost all pure metals and many solid-solution alloys by
plotting:
• AH/RT €c versos iz e
(2") 4.H/KT
versus 6C £
v/here II may be interpreted as an activation energy, R is
the gas constant, and T the absolute temperature. The rep-
resentation is used above 0.6 the absolute melting temper-
ature (10).
Other researchers have found the stress depdr^.ence to
be given by a stress-dependant activation energy:
• UHtf U)1/*.T (2e) 6C = AC
7
where A i- a constant (11; (12).
i.anv worker1- have ~: is cussed the ^tress dependence of
creep, but the nort useful empirical generalization ir- that
minimum creeri rate-" (steady-°tate creep rater) are repre-
sented bv the expression:
where <£> Ir rtress and B and n are constants. The two con-
rtant depend upon temperature.
A useful approximation for .c'ome engineering purposes
is the representation of the entire creep by steady-state
flow:
£c = Bd ^ (2-2)
It is very important to indicate that small changes in
stress, temperature, composition, heat treatment, or method
of manufacture may greatly influence creep behavior, and
hence a simple empirical expression for the creep data may
be adequate for rational design.
The treatment of creep based on data obtained from
constant-stress creen test in uniaxial tension can be used
to 'oredict the creen strain in another tyne of loading.
Cn the _v -r hand, relaxation test data (Fig. 2-1)
(1") (14) and rupture stress data (Fig. 2-2) (15) (16) (17)
can correlate with constant-stress creep laws for the calcu
lation of creen strains and stresses for the general case
of steady-state and no:.isteady state multiaxial creep (13)
(19) (2").
o
ANALYSIS
°. 1 Uniaxial .gtrer-r an-' General Coniitionr
The treatment of creep, in general, har been bare:: on
data obtained from constant-stress test in uniaxial tension.
This is the most co'inon type of creep test and enables the
cree" properties of a naterial to be studied in the simplest
possible manner.
Practical design problems usually involve a more com-
plex stress state than constant-stress uniaxial tension,
and thus it is necessary to use the creep data in tension
for,the general case of steady-state and nonsteady-state
multiaxial creep.
It is assumed that tension tests are available for the
temperature at v/hich v/e wish to make the stress analysis
and that the data have been extrapolated, if necessary, to
the time duration of interest. Unless otherwise stated,
the temperature is taken as constant.
The procedure to be followed is basically that of fitt
ing an empirical expression to represent the experimental
constant-stress tension-creep data and v/ith certain as-
sumptions applying it to problems of varying combined
stresses. As a first step v/e must decide upon the accuracy
v/ith v/hich the exppression will represent the data.
As v/e indicated in the Section 2.1,small changes in
the variabler nay greatly influence creep behavior, and „
hence a ^im^lo empirical expression for "the creep data nay
be adequate for rational design.
If the creep curves show a well-defined region of
steady-state creep, as illustrated in Pig. 3-1, design nay
often be based on only steady-state creep and a relation-
ship can be written for the strain rate in terns only of
stress. In this case the strain rate is assuned to be a
function only of stress, and the creep curves are represent
ed by the lines A and £ shown in Fig. 3-1. Expressions for
the dependence of creep rate on stress have bee.r: indicated
in the Section 2.1 (Eqs: (2a), (2b), (2c), (2d), (2e),
(2-1) and (2-2) ). Attempts have been made to justify all
these equations on physical grounds, but 2q. (2-2) is usu-
ally the easiest to use and normally gives a satisfactory
fit to the data execpt Perhaps at low stresses.
The Fq. (2-2) has formed the basis for most creep cal-
culations in the literature. '.7hen creep data follow the
general shape of Fig. 3-1» and when steady-state creep
constributes most of the strain, this type of representation
should be quite adequate. An additional simplification is
made in many cases by neglecting elastic strain, but this
cannot be done im problesms involving the relaxation :of in-
itial strains by creep.
An upper limit for the creep strain at a given time
can be obtained by using the lines C and D in Fig. 3-1 as
approximation- to the ere or: curve. ?hi- approach er~on-
tially treat transient strain a*- an instantaneous effect
an"1 combine-' it with any initial plastic strain (Fig. ?-2).
Trie total initial '"train can then be represented in the
same manner ar creep rater, for example, as a power func-
tion of rtrers. </e can conclude that, this method will
improve the accuracy of Prediction at longer timer and
will Provide an upper limit for the displacement but will
not be '"•atirfactory for accurate predictions in the region
of TJrimary creep (Fig. 3-2).
If the steady-state type of representation is ina-
dequate, we murt lool.: for another relation (time hardening,
strain hardening, recoverable strain included)which will
predict the creep rate in terms of other variables in ad-
dition to the stress. This relation, which will be obtain-
ed from constant-stress tension tests, should also predict
the creep rate after a period of varying stress (18).
■liven for materials which do show a region of steady-
state creep, an accurate strain prediction may require
consideration of initial elastic and plastic strains as
well as transient creep (Fig. 3-2).
3 • 2 I.Iultiaxial Stress Analysis
In the stress analysis of elastic systems in equilib-
rium, the effects of separate stresses can be evaluated
12
separately and then added to find the effect combine''!
stress' system, (method of superposition), under creep con-
ditions, on the other hand, the relationship between
rtrerp and strain rate is generally nonlinear and the
method of supperposition cannot be used. The stresses
must be considered as a combined effect, rather than sepa-
rat ily, which greatly complicates the creep-stress analy-
sis. In this analysis we consider solutions for the case
of steady-state creep (strain rates depending only on the
stresses) and assume an isotropic material (the same mate-
rial properties in all directions). The method of calcu -
1ation is fairly well confirmed by experiment and is ade-
quate for a large number of engineering applications.
? • 2.1 General Equations \ I
In. calculations of elastic deformation the history
of loading is not important, and the strain at a given time
may be related to the stress at that time. however, in
nonelastic deformation the history of loading is important,
and it is preferable to relate stress to increments of
strain. It is convenient, therefore, in development a ■;
creep analysis, to work with the strain increments in u-
nits time or, in other words, in units; of strain rates.
During elastic deformation of most materials (the
outstanding exeoption being rubbery materials), the volume
is not maintained constant. The largely plastic deform-
ation, charasteristic of rteady creep is found in constrast
not to involve appreciable volume changes. If the princi-
pal axes of strain -"o not rotate during the creep, it is
possible to express the volume constancy by the relation:
-' plastic
Taich can be written B.V. , ( 6 , +■ e2 +■ €2~) u,f — ° » ^-
the strain are small compared with unity, which is usually
the case. Since we have assumed that the principal strain
a::es do not rotate during deformation, the preceding expres,
si on nay be differentiated directly with respect to time to
obtain:
£. +" €z +■ U = O (-2)
where., €,, £2 and £3 are the creep strain rates. Although
the equations in this 2J.ialysis apply strictly only to
cases in which the Principal strain directions do not ro-
tate, it seems likely that they will be good approximation;
even if this is not the case, e,g., in torsion.
Cti.er v;av" °- *. (^--; ?.:;•
.me
: 'ho rocoir a"r,irrH;jo
b^t'voon. "tro^.'"' art rtraiii .:• 10,^.1
p."!;70—'r iT'tG'" a'^G 'r''0"~ort"'.0]"";':'"^
'/;?. C'C'7 1'
^?:o'
■lovc-ho;: ro-La"Gior.r
lat tho ;^rinc:V':al -]
dt — d 2 <o2. — ^3 (» 3 - <^ / (3-;
-1 r = o /-• pi7*1 '—roriV Q *r n T'i ■fro""! "in "i "^7" l ^ T M ,......, .-*/■> <-- C' .-^, GO. Do::^r DV.Z
roi'i roruit to ;o~:!.nt :".?.! the bo-:]"/ and nay change
:o.r ~.:ir "G;ie ~G GG fho validity of *. (3-3), "GO
?.ir incro'Gentr ('elasticity) rather Li 1 ■• l/J. Ci-l-ii .:. Cl i
0^011 ': .".!"' Cl1 naii?r txnor in tho literature
:.r, a"G ~iiG "'.io'".ionx, r-uir. j.ciont.Ly accurate for a
C !'' ":■ O"" ,? An additional arrun-etion ronot. 1 vi,-, c. rear1 "i
that hohr'r circlor of ntrs.::.=: and strain rate are similar
o"" ~i ^ T"' "i t^i" (o_2^ an-! r-~) :
The problem is now one of identifying C, and this requires
rome knowledge of the creep behavior of the material.
One procedure is to follow the methods developed for
the plastic deformation of ductile metal? at temperature?
below the creep range and define the ouantity:
r -\'/2
(~-5)
It i? often assumed and fairly well confirmed by experiment
that d determine? the ability of a multiaxial stress state
to produce yielding and subsequent Plastic,flow (21).
Corresponding quantities in terms of strain rate? and
strains can "be ■■efinod af:
l* = fs./3 [_C £>-k2f+ C€z-€*)*+■ Ce3-€,^2J fc
(-',
**= /a/3 [ct,-€02+ C€z-€3/+<:t3-€j2J M Or;
and it has been shown by experiment (22) that in steady-
state multiaxial ereen:
6* = f C^J (3-;
This is the first nlace at which the analysis has been re-
stricted to steady-state cree^ (strain rate depending only
on stress)
3.2.2 Soderberg Approach
This approach is based on Liises invariant 3qs. (3-
5) and (3-6) according to the follov/ing considerations (23)
The numerical factors in 3qs. (3-5) and (3-6) are cho-
sen '"O that in a tension test with stress 4t and strain rate
£, ^ dt =. d and 6, ■=* £ , and thus the relation
sxrams can no ciinc; ar:
'/z £+ = /a/3 |_Ce,-eO2^C^-6 3;2-4-c<f3-€02J (■'■■-
<r* = /a/3 L^-^2+ C€z-£3y+C€3-€j2J (■•-'
and it hap been shown by experiment (22) that in steady-
state multiaxial creep:
; * r> , J *■ = f C<^J> (3-?
This is the first Place at which the analysis has been re-
stricted to steady-state creep (strain rate depending only
on stress)
"3.2.2 Soderberg Approach
This approach is based 021 I.iises invariant 2qs. (3-
5) and (3-6) according to the following considerations (23)
The numerical factors in 3qs. (3-5) and (3-6) are cho-
sen so that in a tension test with stress d, and strain rate
£, ^ 4i — d and £, « 6 » and thus the relation
17
of Lo. (°-7) can be obtaine'I directly fror: a tension tert.
Then, combining .2o_r. (?-''•) and (3-7), C = 36*/^^*
anr1 hence
^r* -"-— ■ -'V (?-) ^2 = _6^ /'^-//z <^3 W,J)
£ 3 _£_£ ^3- //2(^^))
Before Ear. (3-?) can be used to calculate cree'o
"train,?, a definite relationship has to be inserted in-
stead of i:q. (3-7). As a multiaxial counterpart of Eq. (2-
2) we take:
(3-9)
although an expression corresponding to either Eq. (2c) or
(2e) could be taken if it gave a better fit to the data.
i '••
r\ _,-,. \ ombining . Jqs. ('--'.'} an"! (~-9) load? to
6k =. St*11 ' ( d,- 1/2. C<**+ <0
6z =■ B^*" /^z- //2 (^3 -hd,)
6 3 = S^*" f^-//2(^W«J
where <^ is defined by 3q. (3~5)> a-ncl v/e &re finally in a
■position to calculate nultiaxial creep strain.0. The solu-
tions are limited in the same way as the constant-strain
rate uniaxial analysis indicated in Section 3«1- They are
accurate only when steady-state creep predominates. In
statically indeterminate Problems they will not give infor-
mation about the relaxation of initial elastic stresses
with time but will enable to carry out the calculation of
the steady-state stress distribution after relaxation has
occured.
3.2.3 Bailey Approach
This approach presents another method of obtaining
creep rates under multiaxial stress. Bailey's equation
(20) corresponding to ths fi-.^'t of "'ar. (3-1")
v/here m is determined from a creep tert in torsion.
The method,? of Soderberg and Bailav differ very little
and are in reasonable agreement with experiment. A compar-
ison of the predictions of Zqs. (3-10) and (3-11) has been
made by some authors (2l-r) who showed that the difference
between them is, snail and hence the simpler set of 3qs. (3-
10) is to be preferred.
3.2.••!- uaximun O'hear Stress Approach
This approach relates stresses and strain rates in
some other manner than by Eq. (3-5) sncL {3-6). It follows
the theory which states that only the ma::imun shear stress
determines the ability of a multiaxial stress system to
cause yielding and plastic deformation.
.'r i t t ' n '~r i
v/here d, > ^ > i*3 , we have, instead Zq (3-'-0» (1- ) :
3 d*' v 7
65 = 2 fc* 3 <^*
' ^3- /2 C*'+-*0)
In problems v/here the other d,)> dz J> <»3 does not
change during the test, -i)qs. (3-13) ^ay be easier to handle
The evidence indicates that the strain rates in steady-
state nultiaxial stress test correlate better on the basis
of the invariant (Soderberg Approach) than by using the
xtaxiinun shear stress condition.
A coriparision of experimental strain rates and predict!
ed strain rates by preceding approaches for biaxial stress
state can be seen in the Table 3-1 (2.5) •
21
3. 3 Groe") ?.ates under 3ia::ial .Ctress
The effcctr of combined stress can be reen more clear-
ly by considering bia::ial crecn v;ith £3 — o md— l^.t*/J/£. I
rather than the general care of tria::ial stress ds^da.^. <£/
Actually little loss of generality in involved, since a
hydrostatic component, which does not influence plastic
flow, can be .subtracted from a stress state to give
(_d,~ d3} , (.dz-dz} > an^ :-;» a- "t^e principal stresses used for
calculation of pl-.stic strains (13) .
?or d-3 =■ o in Eqs. (3-10) we obtain :
6 , = B (f d, Z- d, dz + d* J 2 ( d, -dz. )
6 * = & (TV,2- d, £2. ■+■ dz) ~^ [d2 -dj_ J
£3 = 3C4*-4S*+^^^(=&Zjt*.>)
(3-l;:0
writing the stress ratio 4>z/d/ •=■ <=< Cohere. —/^c< ^ /J)
and the strain rate produced by the stress di acting in
Tor.nor. as £ = Bi,n £..:c. (2.-2)), ;ar. (—!•''-) become :
k
<£
I _ =<
n- I s £ / - «KL +- -< 2^) 2 ( *i -_L
= £/-<< 4- °<2J) n- / 2 _/— °<r
C3-:
/h:aminlng -Jos. (3-15) v/e see that largest strain rats
(numerically) is £, -for —/ ^ °< -^ '/^ while £3 is
the largest for '/£^T<=>< ^. / . This latter strain rate is
negative i:f di is a. tensile stress. These results follow
directly from the assumption of constant volume that is
made in obtaining "~iq. (3-2).
The large changes in strain rate which may be produced
by changes in«<^shov; the importance of estimating correctly
the state of multiamial stress if strain "predictions are of
importance in the design.
91
^ 11'"' ~~ O" ° ' ,.. J. ^ .'. _1 abo—l; "th:
1 r^
ft.'. -. • -- tr
0 0-
■ » i,- - (rs.y
■■I p,_. i '1 * *n" ~ ■■ * ^ ~n -' ~ o
P ^' r; p ~ ^ "" "'~ P "*'" PO^*1^ ^ T: *;"-" P V'*"1 ' ^ -'-r ~i Q ->i -r^. '-' '-*
~] -n «."rp 1 "I o ' v^n , ! r' --■-,-*/~\ - ^ - p o " P~ r ""' "^ "1 * ^ "''' "
1 0"" 'r'O"0O OP"! rl "^ C G; ( O^VI ' ? tr.~: "' "
^ity, cr
p --i i-> ',--1 T - — ---, " p ~. ' "1 I-J -^ ^ -^ -^ o ' p -~*. ' , OT r •: p --»
^llO | (~« I •: ^i -- ^ --■—\ o ; ' p-» ^ -- r' - T ■•--> o ci ~" ". ." p I "-^ ^' ~ -'^ P < I P > r* . ">
''.ho outriic rail, .1' mall con""?.rs^. v.'lth tho cthor tv/o
P-I
o
orationr' c:il"r, an" h";ior arc tnio "or olar o._i
■ ~ --•> r c-ma " oo near.ecxor.
.'■or'i'iblc to "cvolor local r'ir?j:: concontratiom- in tho momuro ver'c-2?r ao a r
tho cor.r"i;r?.i;'iJ; irmco'c". b;_ the clor,rro. i'o cloo~ a mo"-
r,,;"^r'. ~r ^ ^' r p ! ^ --, r ^ o "'" ^ '"> ^:* H*l -~\ "-* ri -i^ p —. r. p -p -"" ^ -'- ~ o~. n ^- "7 ^ c ^ ■"■ ■ - ~I
". 'oall'r, avoi"^. '-train concontration b;/ natcj^ina; tho croon
rato<" of -roll ana cloor.ro. At tho rare tioio, to avoi ' •;:•:
rai^ro ""'.""trro, tho na::i::rro tonrils 5'tror,o in tho olo'-irre
'"lo"1! " no-!"/ b" o"" o r'" o"" *' ■"■■
2'-:-
("-;■
* ; n r- -- ■ (-, . ^ • (21:
>~> 'i i"!""*"'1'^ ] p, ~I* O r ' '"O 1 '
, to;
;; TVO?."';:"r rtrp:nr ( '.Zn . (
t1:.^ "rr/i^'TG "nts. ror "rclrilo "lot,?.!"' ?."!; roo:'.i torroor3.trr'_
.L.., r.-J.,-, -'-,--< V,--- -■--;-"1 -. ■-, ^ !-o,--.-• n ^ - r O """ ~' O ' o - -> -
■Minf -f1-,^ -'o ] :^ 1 1
i Cl '-• <"• '1 -r r>" :cn\ .. _ . \, .-I..- . v_. -.<-., / ..... g. ........ u -. .J.... .
ir» i or . ,~V", -- -J ■ -> 0 -
;jroa"V/.ion*;j, anf *.*i
ith th;
TO'1.'
o p V "' O^"1'" '■ ^ ""1
,1...-.
.0";
^ O'' ° " '0 P "OT "■■ '■' ocrc^ro
.'3 '"Oo'1'' " rnvo r3r10"."V3"t' or
'11;::-p.::oo.;
0—*'.'a. ''* .'~\ ",^"l "> o "^
<"■■~: -••rn
>pl Hr rr'i.oora'ciLOii:'
-rr, ^ ->--. >?.r-t V
nr.cr p. ^* c* "■ ™ p ^1 p '"' o-p f "t ,!
? <
— _n steam turbines, ■"-' 'nil clearances must bs maJn-
taine " throughout a long operating life an-'! design, "-.v.rt
bo or the basis of very "■nail cree"> rater.
-'•or high tennerature Piping, 021 the other hand, di-
mensional tolerance if- relatively unimportat and the con-
dition to be avoided ir rupture within the design life.
-The efficient choice of high-temperature bolting
steels require,0 relaxation test data or their prediction
from constant-stress creep data.
-The design stress for slender members carrying a
coppressive load may have to be based on buckling consid-
eracions.
In all cases, except perhaps those in which rupture is
the basis of design, the alloawable stresses will have to
be based on creep data combined to some extent with stress
analysis.
"./hen rupture, rather than excessive strain, is the con
dition to be avoided, the design is faced with the predict-
ion of rupture life under multiaxial stress.
Ihe design stress chosen.for a part may depend greatly
on the opportunity for inspection and the convenience of
replacement or repair if required. The hazards and inconven
iences associated with failure must also be evaluated. For
example, we may compare the operation of power station with
that of an oil refinery or a chemical plant. Periodic
shutdowns in refineries and chemical plants usually Permit
2''
ir.r-~~Pction, ar;" p-irtr- r'howins G.".co."rivo crce"' car; be removed
or ro'"airoi. -ower-station shutdowns, on the other liar.;,
arc urually at less freauent interval.0. Furthermore, a:',
interrxPtlon of service by failures would be more critical
in a Public rov/er station ths.n in a private slant. As a
remit of there considerations, the oil industry uses les-
conservative stresses than power Plants. Potential hazard
is also of importance in this connection. it is clear that
failure in an oil cracking furnace or superheated steam tube
would be a great deal less dangerous than one in an external
oil transfer line or main steam ;oi_oe, and hence the allow-
able stresses should be modified accordingly.
The lifetime for which a unit is designed is of obvi-
ou- importance in choosing allowable "'tresses and materials.
?or units with a short design life, a considerable increase
in design stress can often be obtained by adequate heat
treatment. A similar increase for units with an expected
life of, say, 100,000 Hrs. is limited by the uncertainty
in predicting material behavior over an extended period.
The design life will also influence the extent to
which short-time properties, such as yield strength or ten-
sile strength, are important compared with long-time pron-
erties, such as creep or rupture life.
Fluctuating stress and temperature conditions are en-
countered in many applications (18) (26) (27). For example,
the pressure and temperature in a power Plant may fluctuate
27
to ~uit load rocjuiremonts or Mie rtrorr in a furnace tube
ur/.or constant 'rer-rure but will increase if the wall
thickness is reduced by corrosion.
There are many other factors to be considered in ma-
terial selection and choice of design stresses for ele-
vated temperature applications, which nay have possible
interrelation with creep.
In many cases elevated temperatures introduce the re-
lated problem of thermal stresses. In this case, thermal
conductivity, short-time tensile strength, termal-expansion
coefficient, surface heat-transfer coefficients, and elas-
tic constants may govern the choice of materials (15) (28)
(29) (30).
The resistance of a material to mechanical shock, or
impact, must be adequate at the operating temperatue and on
subsequent cooling (1G) (.31). This is important for metals
which may show embritlement after extended periods at high
temperature.
Three other factors, corrosion and oxidation (18) (32)
(33) (31'-) fatigue and damping capacity (13) (35) (36) (37)
(33) and irradation (18) (39) (/,IQ) (41), while important in
themselves, may also influence to some extent the creep
behavior of- a m a 13 r i a 1.
The availability of materials and their cost are impor
tant, and there may be cases where economic considerations
and availability of creep-resistant materials may dictate
2 8
t^o I'loicvO'1 ; patorial and design rtrsr^er ('.'-2) (';-"; (''-',)•
In addition "to meeting cost requirements and having
suitable high-temperature Properties, the choren material
must be possible to fabricate by the appropiate forming
operations » Including welding, if necessary. Generally,
the Problems of fabrication increase as the material be-
comes more creep-resistant.
U-. 2 .1.2 Temperatures and Design Stresses
In msst applications of steel, creep is not Important
in design at ambient temperatures, while at sufficiently
high temperatures the design may have to be based wholly on
creep considerations. For the intermediate range of tem-
peratures the designer must decide on the relative impor-
tance of short-time properties (yield point, ultimate
strength) and creep properties ( rupture life, creep rate).
An analysis of the temperatures and design stresses
can thus be based, rather arbitrarily, on three temperature
range in which:
-Short-time properties are important.
-Doth short-time and creep properties are important
-Creep Properties are important.
2.1." FomPeraturcs at which .Short-tine .ro ^r-
r>~ P ire J .mpor'carit ar.c, xneir Jeci~i'
."ij^sr'^^^
Xerhhcf ('.'5) -an analyzed the allowable membrane
stresses .for welded carbon-steel boilers and pressure ves-
rn.lr i^nd ha° given 575"'- a.i.- uhe upper temperature limit fo: i- -f-i
whicn snort-Time ^ro^orxiep are important,
this range ir often tahen a? 65r' ? rather t
ie limit o:
nan the value
o:° ^75"^ previously indicated, but Clark (^6) has stated
that for lo".'-alloy steels this is very conservative and
rihort~time properties Predominate in importance well above
650*.';'. A German Code for Creep Testing of Steel V-7)
states that the yield point determined in a short-time test
giver dependable information on the behavior under static
tensile loads only up to about 662°F for plain carbon steels
and possibly up to about C42 F for alloy steels.
The AFFFI "Unfired pressure Vessel Code" (Z!-F) and the
AFFF "Boiler Code" both specify that below the creep range
the allowable stresses are the lowest obtained from:
-25 "Jor cent of the specified minimum tensile
strength at room temperature
-25 ^er cent of the minimum expected tensile
s t r e ng t r i i t t e m P e r a t lire
-62 1/2 per cent of the minimum expected yield
strength for 0.2 per cent offset, at temperature
dhe r.bov^ value" a"Tl".'r to the range in v;
~hcrt-ti""e TO ""or*!;:.!, or nee'* bo considered. Oho tort results
for each specific material help to establish bottcr the up-
per limit of the temperature range in which only short-time
properties arc important. For enample, in the test realized
(<-!-6) on a carbon steel (0.15.'' C), on an 10-" stainless steel
("'.%'.' offset strain), and on a ho steel (50 Gr}, under the
following test conditions:
-Carbon Steel at 600°? and 00,000 psi
—10—C Stainless steel at 00 0°? stressed to the yield
point
-ho steel at 0-T° ? and at 1,0?" ? and 50,00 0 psi,
the following results were obtained :
fhe carbon rteel elongated to ''.39 par cent but showed,
no measurable creep rate at 1, .00 Hrs.
'["he 10-0 stainless steel gave a strain of 0.32<v per
cent after 5 Hrs and no appreciable elongation thereafter.
The ho steel (at 800 Paid 5°, 000 psi) gave a strain of
0.25 pel" cent, most of which had ocurred in the first few 0
hours and the creep rate was not measurable.
In the Ho steel (at l,000°Paid 50,000 psi), failure
occured in 1.10 hrs.
As the stresses for all three materials are well above
the values given by the "AS*-07, Unfired Z-ressure Vessel Code",
we would conclude that design could be based only on short-
tine "Torortios u"^ to at loss't 6r " ? for the Carbon Steel
air. at least ."■" f for tne other two materials.
fiisro short-tino properties, an for cxari-lc the ulti-
mate tensile strength, must bo determined at the design ten
feratu.ro. Che foregoing analysis applies to boilers and
■Torrurc vessels. In applications involving higher stress—
or. and shorter live:: than "orescure vessels, it nay not be
"^-e-ssiblc to neglect creep properties at the temperatures
•j.vor. aoovo 1 )
A'-.2.1.'.'- Temperatures at which Both Short-fine and
Croon Properties Are Important BJI'' Their
Design Stresses.
ferhhof (A'-5) has discussed the allowable membrane
stresses for welded carbon-steel boilers and pressure ves-
sels' and has. found that beyond 575°P to 750°?, the stress-
strain curve for carbon steel shows no real yield point,
and hence, both short-time and creep properties are impor-
tant.
The intermediate range in which both elastic and plas-
tic properties are important is more difficult to define.
The "ASI-IS Unfired Pressure Vessel Code", specifies that:
-In the transition range of temperatures, the stress
allowances were limited to values obtained from
a smooth curve, joining the values for the low and
high temperature ranges, the curve lying on or
°2
:lo'.v the curve- of 62 1/2 nor cent of
->---->(-! r>T ^ •,-•1 r, 1 cccc: y;1. e.'.-'.:. s"crong*cn ax oGn^cra^iirc.
'''!•• 2.1.5 -Oonneraturos at fhich 0roo'~ -rc'ertios
Are Ir.nortant and Their design Stresses
ferc^'of (•'.'• 0N| "'icT d.iscussod the allowable membrane
stresses for welded carbon steel boilers and pressure vos-
rc-j.r and rias noun.:, "ciax aoovo /5J ...■ complete rolanati-on o::
socondar?" stresses will 'ccur i:i a short-tino, and design
can be bared on ere on properties.
ddic "ACOOO dnflred drossurc Vessel Code" don the unncr
of tonneratr.ror, at whic!
bo considered, specifies that:
-At high temperatures, the stress valuer: are bared
on 100 per cent of tho "trees to produce a creep
rate of l/lOO nor 1,000 hours; the valuer so chosen
being based on a conservative average of many re-
ported tests as evaluated by the subcommittee; great-
ter weight being given to longer tine tests in eval
uating data. In addition to the above-stated creep
strength .requirements, stress values were also lim-
ited to 1000' of the stress to produce rupture at the
end of 100,000 hours; the values so chosen being
based on a conservative average as evaluated by the
subcommittee.
U ci Th 3 " AZ'.. .0 Boiler Go ~" e " a 12 o'.'.'r the . s an3 stror
on ere?'.' strain but only 60 per cent of the average, or 0 0
ner cent of the minimum -tress to caire nrotue in 100,000
hourr. As the creep-stress limit ir urually considerably
lower than for ru.Ptupe, the two code- often lead to the
-ame design valuer.
The choice of the above valuer doe? not neces ariiy
mean if •.-■-'-. the vessel will show 1 per cent of strain or rup-
ture in 100, OOC hourr. .Service temperature,0 and pressures
are urually .'< e-s than design valuer-; v/all t hie ■metres are
often increased by corrosion allowance, and material prop-
ertirs are usually above those specified, all of which re-
suits in an increased factor of steady,
To illustrate some of the preceding analysis, the
change in tensile strength, yiel strength, rupture strength
and creep strength with the Oemperature and the AS'i-jJl code
allowable stress for a 5 Cr-0.5f-- ^-o steel are drawn in Fig.
k--l (18) from the data g iven by Clark (^-6). It is interest
ing to note the decrease in the allowable stress given by
the code which take place above the temperature at which
long-time and short-time properties coincide.
The code requirements: apply to vessels and boilers with
an expected life of at least 100,000. hours. The general
method might also be applied to the design of a unit in-
tended for a shorter life of, say, 1,000 hours.
In the low-temperature range the elastic stresses are
I'he r,t1."'r,'~r"r in the u.P'"er temperature rango arj br.r"
en long-time "-ropcrtics (permissible strai/\or ruvtu:"~: :n
1 '"'', '\'.'" hourr ).
In the Iiiterme/:,.iatc-tempcrature range the stresses arc
obtained by drav/ing a smooth curve between the hi r;]i an:- lo".
temperature valuer.
The type of application '.'/ill, of course, infl'. ence th'
choice o:" a ~afoty factor in the lovz-tenpcrature range and
U.i':: 'a. . u cnt to v/hich croee strain or rupture is important
•'-'-.2.2 Dosi2ii ConcIitions
^.2.2.1 Deeign Oriterion
.1. i L
It is assumed that the operating temperatures are in
he upper range of tenperatures, at v/hich only creep prop-
eties need be considered, and hence, design ha'" to be bared
wholly on creep conriideratione.
Design nu^t be ba^ed on the naximun permissible creep
rate^, and thus the stresses are ba^ed on the permissible
^train or rupture life in 1-';^:,"?C hours.
It is considered that constant-stress tension-creep
data arc available for the temperature at which we v/irh to
mahe the stress analysis and that the data have been extra-
polated, if necc^'ar;, to the tine 'Miration of interest. Tn!e~s otherwise "tated, the temperature i" tahen a" con-
-*tant.
k. 2. 2 .2 Creep Type
It is assumed that the creep curves from test data
rhov/i well defined region of rteady-rtate creep, and that
thir latter contribute,0 most of the strain; hence, design
may ho based on only steady-state creep.
As we have seen, small changer1 in such variables as
stress, temperature, composition, heat treatment, or method
of manufacture may greatly influence creep behavior, and
hence a ^imP.le empirical - expression for creep data nay be
adenuate for rational design.
^•.2.2.3 Approach
":1s use the Soderberg Approach based on Ibises invariant
('ios. (3-5) and (3-6)) , which is accurate only when
steady-state creep predominate. The mothods of Soderberg
and Bailay differ very little and are in reasonable agree-
ment with experiment. However the Soderberg approach is to
be preferred because it lias simpler equations.
The evidence also indicates that the strain rates in
steady-state m.ultiaxial stress tests correlate better on the
""t"^o■■"'" a.p ~roach.
. • -~ • -^ • * : ,v l;J. Vi > • -^ wCi V w
In a thin-walled vsrrs.l trie radial stress ( »i },
which equals -P (internal pressure) at the inside v/all and
?,o:;o at the outride v/all, is snail compared with the other
two principal stresses and nay usually be neglected. Hence,
we have the care of n thin-walled vessel under a biaxial
stress state.
Under creep conditions, the relationship -"between stres;
and strain rate is generally nonlinear, and hence the
stresses must be considered as a combined effect, rather
than separately, which greatly complicates a creep analy-
sis. In some cases the stress analysis is simple while in
other cases it may "Tor:.I the main problem of creep analysis.
The effect of biaxial stresses can be seen more clear-
ly by considering biaxial creep with ^j ^ o and | ^r ^z/di^s I
rather than the general case of triaxial stress £3^ ^z~^/
hence, the creep rates under biaxial stress states may be
governed ^j 3qs. (.3-15) •
7
Table 5-1 cho':;c the rocultr obtained of the analyr.i r
realized in the ^receding rectior.r;.
The curvec of :'J3- 5-1 v/ere slotted fir on the da"' ■
rhov/n in the table 5-1 • Thene curves may be u.red for the
design of thin-v/alled verselr under internal prerrure and
v.'itii the conrideration of rteadv-.^tate creer).
(:-
n
d2/d, = «=<
"> '"O i - n
■ r\ - --i T>
■-----»*-] •>--«, ? r-| ~- ~ "' n T ;~>
ZJL. /O.
Ac cor
** - "i .-•: ■ ■
; r>. T;ln ' :.r- of rer-ult'' (la-
"oroco iM'"r *~'octtori, v*o rose1'! the
ri - _ co
V 1 H PV;
C O V (" 1 - i <- • OH'
— The lare'e chan^ee j.n rtrain rate ",'h.ich
r*ia'* ha ^iro',i.icn^ h'r ^'"iisl]. ohar|':*'ar' jn the
r,i;rc!rr ratio C <^»/^/ =• c><0
i'l^ortance of correct."!.'* catiriat:' n
•~ r^--r ■.- n rv
r■ + ,1t o o "^ '".i ■" ~! t i n'. *'' a 3.
oar o '. oil rxram
" T"» ,c -; /-i <~t -. "~<--^-i
icxion::
"be cone iiicroaatnf If iar'crtant, a a ti
incroaaer v/liica. ahov/a the irirortance of
c*"'tl:aatina; correct!'* the valuer' of n fro:
cree^ -ata or fro:a the extrapolate '; crec
nate .
h.e curve*"' o~r "ti,a;. 5-1 na." he or
p. p' "I p*"!-"! ■"")' !*>■*» "Pp
m
-!-Vi i p„-'-n 1 1 r"..~! -r.^ rr-^ I c
"L,^ao.*---"-uaT0 cre(
.c'.'A
P
6
■fc
r, T, , r2
6C
6c
&o
^ »
AH
R
<^ / ^ ^2 , ^3
6/ , €2. , 63
• • •
^*
k* 6*
.0 3.
Instantaneous Strain ( or initial
c^eon st'^a^ 21
6 or </£/</*• Strain -late
-£ r Susture .life or :iunture 1'
p Sufficiency
Absolute Ser.rserautre
Cree'o Strain
Green Hats
Constant Initial Stress
Stress
Activation Snor^y
Gar: Constant
Principal Stresse-
Croon Strains
Creep Strain rates
Stress in uuitianial Stress state
Strain rates in terms of d *
. Strain in terms of <£ *
L...' '._'A;.
:"-,-!'•> ~.-l •on o.\ rinci^al Or'
or a.:. Tor-it A ■■■"> r~> o ^ - "> O '
:La:::i.a.L v» r* f r~* i ]-^iTi r\". r* ~ ' ";"s;~i "^.-
.'able -_i
Oort Oat a o .Va'"roll anO J'ohnron
(25/ for 0.17 r>or cent carbon
■op"! p t ° ^ o
'■'train nation a" a function of
Otrecr Oatior for thin-Y/alleO.
/orro 1 r"< unfor -in.xori"al Orsr.FU"^^
ana uonai.tionr of
'ee"o,
"coao^r-oxaxo
ho
<D a>
+> 1 CO p, < c
v-r-
-p ,0 c Si a L, o o
<M -p CH c •H <u n o
>> ^ X 0) - - p.
cd
CO
n
o
CD o
O
a
o
o o M o
o»o CH rH
CM I *— M
CO
c o -H CO -C< CO
CC Cd
5, o
<M
o
CO
co a .M-H
o ox
-p •H
o -p
rH a a M C. &C CJ •H E^ Cti
u CM -P O to
<H Cd • i K -p r-< ^ O Cd
X-dC (DO VPN
>H cd -p cc r£ o co cd r. o -P
E-1 P.E-t cd
r-t O r*"\ J*
CO -^ o <—•
; i cv • • • • • • ,| A r^ r^\ ■■ c c ■;_
?~~ v~_* C C- a •^ .-.- « 1 1 1 1 1 1 u. •
■-*-'
+■> r— 1 CN CN CN rH r> r~« c. 0". O
03
i VTN.
-V CN- -^ -*■ CO -*• CN-
t_ O *\ r^ o /- c ?"■■ »—^ o c. a) u , « -■> • 1 1 1 T i 1 1 1
a 'Ml • c .c . i. i C; CC NO -4. CN Cv. r*\ CO CO < i CO CVJ NO -S" ^J" o -^» CN-
. C O rH N.' ' c^ c c c.
s •>• c •
o ON vn NO o CN- r^> r-i CJ l-\ rH c_ r-i *—
<\J O r^ o c o f—N c- O O c_. m - - • 1 1 1 1 1 1 .^, • o
i i cc C\! -♦• c NO fN CN- CO i -V cv. cf r-. r^ CN- r~\ NO'
i. . d NO • • • • • • m • rJ cd
•4
*>•
_ C-N. o o o c> o c c o r~ •r-
o vr\ • c
1 i 1 I I 1 i 1
r ft '"""""» I c^- CN- r> c r-% NO CN- cc c p, i
CD c^ rH NO -*.
■^ CO CN. NO
NO NO o r-^ c ;j ^ c c o ^ ON • *H) • c rH O r- r-i t>- ^3-
X 3 C"\. _^- rH rH c rH G c~\ a NO r-\ o o C c - c- o o c o n —u m 1 1 1 1 1 1 u •v» • ' '" Cl i VA r-N. CM cc u^ C NO NC p. 1 -i- cv. ^J- rv r~, CV r> NC < vn
as r^ o c C '~ . r~* c c o N —*i • 1 l 1 I T 1 i 1
fclfl 9 ■—-\ "i NO cv ON ON OJ -V NO NO
co 1 c^ CNJ *n C-N. —c CC' C~i NO
XI CO u '^ NO o rH o C c o !~' C" o *\J <"N •
TT • o rH Cvi -X. cv CNi ^J-
o o —* VPv viS NO CM c CO ON vn
« rH rH rH rH o e c o £~- c •\u • • 1 1 1 i 1 r- C' o c 1 1 CN- .cj- rH v,-> c c-, ^J- cc
-H O^ CV CM rH r~, rH ?S VA f * o c^- c O VA O C C^ C o rH c o I * M) • • 1 1 1 1 1 1
• r -N O
&- 1 | —j NO VTN CN>- CM ON -k. cc c o IV CN. -V VP\ C rS NO c ON <v r •vu
ON • •
rH rH O c c rH c c> ~N. o e o o c- ^ O c r^
co CO cv r c- _^- c CM -1 o o *n CN- rH ~^- CM CN f>
•(—. «« NO U-N. ' B • « «k ^» «k •. » c \» vo c^. cv C\J r^ r, ^- NO vn CN- f 1 1 1 1 I I 1 1 i 1
• .-. o c- o o o o o <^> C c. NO vn CO CO CM o C^ -*. c CM c *% VO o o ON CN- rH VPV CM CN CN-
M • -*-
CNJ CVi _-J. ON CC CN- C VA CN-
+- iH rH rH M rH CO
*o
CO Oi
•H -P T3
K) © ra U o 3 U w -P W CO <D
u <Hft o
rH C nt O C
•H JH -P Q O-P • *5 G PH 3}=^ (1)
Pt, 0) fc fc C o o
•Hfl
CO 3 ■p o at
•H ra -p -P.H CO 0t CD i K ra t» ra T) C o nt
•H > ft) cd -p fc-ct ro -P 0) CO H «H
rH o ctf
• £-"■• W H '. n I G n
WH •H .G -p
<D EH •H H . TJ ja:U n at O n EH^: o-
•4»<«B«T<tf\f»9fvi^^sfrorriro(\j'r^^ • I f I | • I f »+ • »' » » » un» i *4» ill ii
"paropoooeeBaoeeooeoDaoeepesRcseeooi peeoeeo«oooDBccioeoef)ecpoeeaoeoo|De
loooBooceesoPOooooocBCocooecaoocooo
• •*••••••••••••••••••••••••••••••!
«^«4eCMocsteirin<HliMn^cviroooaff>ocncjtv'ff><rf^<vi(rp<roaa
«) M t I • l • I M • • I I M M M I | I | l I M M > • I - «9C90*4(T(NJrO<-(flSJir)^«-l<VJ«H | »-4 f f t I I • I I «"•' '~-
|W» - f»» f <rt» f I I f f I t eoBBoeooooocooooPDOooeaoeoeoeeooei * -IpeeaBeceeBcieiBBeioBOBesBoPicjoeoBefsoeo "^9 ZBeBOOBPPDgOODPODCPOODOODOfJOnoOBPB M <pB0Boeo0BBBePBaBecBaeeoBeeBo6BBBD< ^ „••■#•••••••••••••••••••• •! ||
; 0ap^e«cDapecDaoaoaoaD«p«Q<Bap«o«oao«D<B«oaD«3<e«o«>«O«>oo«>e 0
<MCUoe«p«-ico>4'apV4«oirto««oroooocr>c30>oroeo«oroo<ro<roc9e3 vu ^_ ,«C^^p«^^K«pcOeOPr)^«0\0(Vje3«Po(sj^4«-t«9iOroro\De9«^<-«(siC9aioi vr. Ofoto«ipf^m«O(O<>-i^rotrt«ov4tx)mataecrf*?vor^vDtOiD«r>nt0'O9>e3C9e ,■ >-KKo«erwu>ou>wN1u>UNCT»irif2»u\ina)(vjrfinc=|^^ouN-»"<vi^in»fke9i _^ ^ ,
twfwot^.tf' | row | <v/,-» MIMH |i i| | i ~* u °i ^ vi : • i r •■ o cl> eroBooooooooooooeaooooesooooeooaooi ^j.
„ BBeeaBBBBBBBBBeBBBBBBepfiBBBrBDaBa || * ZBeBPBeBPaPBBOBOCOOBOOBBBBOBBaoaeO . ' ^peepeoeBooeproaeBceBpocorpBBeteoocsi -\J c" -5
<«o«oepDCT»<proc3fNJirnccruDiAooi5ouMrve3^«ovD»Doo-*c3UMno«=es p >-:
COtt0t*t««**t»t««tt«ttt0*«*«ttt»«»« ^ p- 1 lA^CO^ J- | W«Si | CM*-I |<H| |rlt | «| |f | | «4 9 9 ! I » i I 11 T! « T-
•O«O«o«o«o«o<Dao«O«e><oe*oao€O<Bao«Daoac>co«o«o«o«Daots«oao*oao«O0i TL •0«a0eoae*s«oao<eco*D«9co(oee«B«o«o«D«oa(>e(ME>«D*E«o«D«9«oan«o«o«c> i2 ,. j5
ITppooooopoooooooooopooooGOooDooooo' ^ q £ <B|iopaooBi90BBPBBaoBOBBBQBBeBeBBeoe -p b -p OfOOOOOpopOOOPBOOBBOOCOBPPOOBeoOOOD C <• o cr HU\i^o^fr>^M^Hfvjrjw,fo^fs.gr-oif\^cr'WvDao»4N.N,^«Diowcr»inif>o
WHBrlH I *-»i-l |r)| |H| |rl| I I | If I | . V* Iff I
JL poOoooeeeooooooooooBOBBOOBOBOoeea ■< PBBBBBBBDBBBBIpBOBBBBBeBBBeBBBeBBB ^ <
ZBBeBOeBOBBBDOOBBBBBOOOBBOOBBBOBBS Q_ ffl «ooooBBf:BBBf36PBeeBoeBPeBBOBOBBeBee «_ ^ ^
• •••••••••••••••••••• •••••t*«t*t* < < or.
* - - - : * «ceooaoea«o«o«o«x>^^<4'fvjcvjvoeeefvjt\fCvjwr<#-4,«oa>^««o«Beoe
C«H«S«4 " t* i * * i i " i » * »V«3e5 *' ** "' *" 'w*Jt<X
*'"- _ ; ' : -i^ I
.1?
Fig. 1-2 :
?i-°". 2-1:
norna"^ c ;urv
Fi/r
2-2:
'ig. ?-2
• chenatic Relaxation Curve
Re 1 ax at i on c urve - : (a) C arb on
' teel (at c5"°?, initial -tre-r
lr',0^° nsi); (b) "read rubber
(at 1?/)*C_, initial elcngation
5n' 'ler cent)
Tyoical tensile stress-rupture
data: (a) Arnhalt (pitch-tyrje
bitumen); (b) Killed carbon
steel (Timlten /'.oiler Bearing Co) ;
(c) Reinforced rlartic (polyester
fiberglarr laminate)
•Schematic ere en curver two
stresses:(A) and (B), method of
idealising a" steady-state creer;
only. (G) and (.3), a" steady
state plur lumped transient cree'o,
Creep curve showing initial elas-
tic and plastic strains as well at
transient ereen.
^
'3 0~ Z:
"cr, ■ " .o -~ an:
i_^ov;ao±e c- *-• ^ c* '
;rain /.atio? as a .unction cf
'ijc- £atio^ :°or •nr.ir.-'.'alle'1
- T" : :-i T; ~ r"-~ a
-on::ix:.cn'~ - u d o —
VD
M < K CO
Tertiary
?, Fracture
^Initial Plastic Strain , Initial Elastic Strain >
J Elastic recovery-
Permanent Plastic Strain
TIME (t)
Figure 1-1. Schematic creep curve. Dashed line shows behavior on unloading.
47
p*
< o
TIME (t)
Figure 1-2. Schematic relaxation curve.
48
tn *—V
a •<-1
to o a o a ^ * rH
i-i ' u
rH Q) <D .C a) &
■p 3 to cc
12
10
CO
0} OQ
K EH to
24 _
20
16
12
8
(b) Rubber
(a) Steel
.001 0.01 0.1 1.0 10 100 Rubber
0.1 1.0 10.0 100
TIME,
1000
HOURS
10,000 Steel
f igure 2—1. Relaxation curves: (a) Carbon Steel at 850 F, initial stress 10,000 psi); (b) Tread
rubber (at 130 C, initial elongation 5° per cent)
^9
+3 n tfl r-\ a, T3 o o U o
«H C
•H a
cr:
.«a += r-l i—; O Co CO x: -P P CO c. < >—<.
•H CQ ft
CS- — s C o o \ > Cr •-t bd *~*
» m
a ra CQ a © CD k ^
-p -P co CO
50.
10
l 10 ioo i,oc)o 10,000
10 100 1,000 10,000 100,000
TIME, HOURS
Plastic
Asia halt
Figure 2-2. Typical tensile ntress-rupture data: (a) Asphalt (pitch-type bitumen); ("b) killed carbon steel (Timken Roller Bearing Co); (c) Reinforced plastic (polyester fiberglass laminate)
50
(-1
EH W
w g O
TIME
Figure 3—1. Schematic creep curves for two stresses: (A) and (B), method of idealizin as steady—state. - - ■_ - (G) and (D), as steady state plus lunroed Tcansient creep.
51
Primary Tertiary
S3 M <
EH CO
Fracture
Steady State (Minimum Rate)
Initial Elastic Strain
TIME
Figure 3-2. Creep curve showing initial elastic and plastic strains as well as transient creep.
52
M CO P-t
c o c
CO CO
EH CO
T S: Tensile Strength Y S: Yiel Stress (0.2% off set) R S: Rupture Stress (100,000 hrs) C 3:: Creet> Stress ( '1$ in
100,000 hrs)
ASKE Code 5/8 Y.S. 1/4 T.S.
60
50 - ^"^^V. T S
40
30
Y S \
20
10 s- "iT" "X" "a -^
c s \V<^ ^^ 0 I i- i ii ^*i*-
200 400 600 800 1,000 1,200
TEMPERATURE
Figure 4-1. Change of the different stress values with temperature and the ASME code allowable stresses for 5 Cr-0.5 M steel
53
\ N \ - N m
?*2
2 &" .
2.4 .
'? . 0
1.6 .
1.2 -
;.8
.4 -
l\ A'A\
i\ r 1 i\« i
• \ 11 1
\\ i l\
Vr \ \\\
,^ III! _. .., i II i
-1.0 -"'•.6 -0.2 0 0.2 0.6 1.
STRESS RATIOS: dz /<i, = c<
Figure 5-1* Strain Ratios in Function of Strees Ratios for Thin-Walled Vessels under Internal Pressure and Conditions of Steady-State Creep.
54
', -1
r. II »
].o--^", Cha'^t. •',', 9uttc>rv.'oth .3 CO. It."., Icn'on, 1 ■?"'■'/•
I-"AJ'TrJ ..■:.-": ,d. J. , "Interpretation and 'dr. o of Croo"~ .on;
T A'-.i C',-,/-. " P. 4-nl^, 9.'''.. : 7 ': lO-'-'
'?.,?,, C . J. i-'. , de BLiK 3A.;II1JC , J.J., TfTGd, A../.-, an:
, .{.0., "The Green du'^ture I'rcnertJ er. of .'-recrure
Verrelr", Telling Journal derearch ounnlement, Anril
•''■. 'TAd'Tf, 0.";., "Transient Greco in iure . etair~", .'roc.
Thys. Goc, London, 366: 53-9, 1953.
£r. CCfTTdl.J., A.::., "The fine Lav/s of Croon", J. .och. and
i'hyr. Soli'lr, 1:5."-', 1952.
6. JOIIfCOi;, A.f. , ?>nI Fl'iOST, N.J., "The Temperature de-
pendence of Transient and Secondary Green of an. alumi-
num Alloy to British Standard 2142 at temperatures
between 20°and 250°C and Constant Stress", J. Iinst.
Petals, 91: 93, I952-I953.
7. HAZL3TIT, T.H., and PA7J33, '.3.3. "nature of the Green
Curve", J. ^etal^, °i : 0^. IQC?_IO<":
ASC > <- • » -Hr-
L • ,
<-} T* ^» ^
17 ,
ture~-;~h
rre?
.etal^ at .Jlevatei to::"ora-
rbolic Sine Pe lax ion between. St re""- an"!
Mo", 'Pran^. ASPP, 6;: 761, ISP-.
■n ■ :',-^-i.
:p:, Pationad. -'■lyrical laboratory PJ yr.'i" or: i-
u;n on Green and fracture of Petals at Pi^di fenncraturo,
Teddinccton, Pine land, II. ;•.. Stationary Office, Lorrlcn,
7. ",9, 1956.
11. PPiPTPAP, J. , and SPAGPPPAP ..-. , "Green of Poly
ryrtalline PicPel", JP Petals, " :122s, 1956.
, ai i GPAPP, P.J., "Creep and Stre< Tl;
:urs of Aluninun as a function., of Purity", J. ..etalr,
1°. PCOPPf, 1., "Prediction of Relaxation of Petals fror.i
"data", ..roc. ASPP, 51, Sn, 1951. 'y»no ~",
1<!-. P0:30LSJCY, A.V., and AfiPPPS, P.J., "Systems ^anifesd:-
iny Sunernose■"■ Slastic and Viscous Behavior", J.. Chen,
j. ii.: , . , J- _.. . _.' , .;'■/■ .■ j .
t -* • »
o ! ' n"
-C-
o^n ~ ^ '
, v-, p. I CS ■" -» ~ . O O "'»
■ o -"->"■> .o -. ■:.c:
:.:i: „..,-_CJ. ;air -o,
-/. ■-.':-;.:c-_3"r"9ra"ciir" .leJ-axj-ons/ii^r: lor
T-i.^> r- c- o < Aeiniorced .-ia"xic , :TCC. AS:
— ..■' ■ • » — y -
—■~t
o .:.■:•_air" ", -C Grav-j-ill s --> -' ^ 1 ~ « ■J- -- » -^ >■ ^ J '
Iran?. A3.3, 61: 239, 1939-
21,
3A±L_L'Y, M.-'J., HiK:] Utilisation of Creep Test Data in
iDnsineerin^ design", Yroc. Inst. i^ech. Sngrs. , 131:
PAYAI, A., "Theory of Flow and Fracture of Solid?",
::cGrav/-Hill,Nev/ York, 195:.
22. JYC^C:;, A.3., "Creep under Conple:: Stress Systens at
Elevator] Temperatures", Proc. inst. keen. E'ngrs.,
16';-: ^°2, 1951.
£"7
9" 'C"j :~3.':?fJr, C.'.'l. , "Intor-Tntat: or. of Croo- _o::tr for
,0^;,.,^(, -u. _ Art- -? ^ - . n-^: loV - ■- -- ^- » ^_CJ.. i . 21...- -J , _, . / _. _, » — , _ - ■ p r» •■>": r"!
-A-""!:'! , <J. , "focharioal - ro'^art.ior of .Material rro-
•^rti?~ of .^atorlalc and Joripn'V Char. '5, . .acGrav-
1 T '^T-r " '^-.V.- ~] O '.9
?orrior
, . . . O • I , A.G., "Croe^ under Combined
--i^. - r,--^ ?■''. TO/V"
:03I:.GGI-, f orroeraturo Variation on the
o -.: -^ — , ?u i^' • i-i..-.-... j i O n; o 1 o
£ ! ::oc" O::' i9:.i">3ra"curs variation on "cno
;ranc. Avh-d, r- «
(■■■■ •■ { ( ( i •"• < o
• p ■ <~-' TI '
n j.i'riCT C' 0'"c.-.*i.c .^99Tin~
,J °: V -° 10 d r"g''T~r; ]_°p T;'I'T^ c- AC''~r
^o.cc mr 01
:.v3Ch. ..'Ub]
.-.-< ) -/ • - . J .0 ^' '1 r-
-lochs t doc. , 21: I'd?, 1 C: C. -
. -i - ,. 1 • » "hhomal datigro and dhomal GhocX",
_.er oar en mil. dor. 10, April, 1952.
., G.v., "froportiac of Letalsr at Elevated hornror
■.?", ..cGrav'-Hill, hew Yorh, 1950.
urn
■ ^ >
i. s - - f/ -"•!-•»
. ft 1 »
) -- _ ' — >
,
,n ^' c- a
<
::A:
5""-c> '■ ~ n" '-3 : , T
o *: o ''"^ o o " ", A: A?:..,
ocii."ica"".LOiir an:: ..■or'::.:'.
'According to the ".lev ;lia"ra;~i o:;' the irirtallatior.,
e working conditions of the nrerrure vo^rol an t'hi fol-
io-vinT :
-"dluid : runerheat vancr
_,r~n-i-|'-.r>ci+lT!''n • 7^? ' [.'-'."' '' ':
.- j_ ., . i ..- . . - - \ . ./ U. : /
-fubjeciod to abnormal te-yr-ioratu.rs o'lcur^ionr of in
.o 1,112°? (6'"0*G). -I'otal duration of the oncurrion- Inn
n.r" lifeiinc, about l'-0 hourc.
'Jnscificationc; of the vem-Mlr ("if;. 12-1 and 12.-2]
are tho f ollov/inr::
■'hd i
C;*,r 11 n 1 r*j.ca 1 purfacg :
-Innide dianeter '-J c
-j.enT'cn
(—- c:i)
■J- •■•. yo j.ii
C'CO en)
-fhic::nem of internal refractory <'Mn (10.6 c:
-:o
\
-,:a::.vr (h; "f."7 in
(1 c -.;
-An-le ( <f> ) '-5'-°
-';h?.c1'nor'"1 or" material refractor^ '.'■ in (1 . ■'. en,1
•rP Q -i p -j ,'lp 1 r> T ] -ii ^ q ^ ^ •
-/hahiu- ( dN 27^-59 in
(7 ■ cm)
- An°;lo ( "jk *! V °
-Phicd-mor- o? internal refractory •''- in (l'.d cm)
>rir:i Criterion
In the dOvi.^n the v/or-: conditions are considered dur-
ing the abnormal operation of the installation.
Accor "in^ to Section '''-.2.1.5 the ves.sel temperature T
(1,112 '?) iri in the irener ranp;e of temperature ( T> ?so0f)
at "/hich only crso'" rro^ertics nee"', be considered, and.
h once, the r"le",imn har to he based ".7holl"r on ere en condi-
t i onri.
jimonslonal tolerance is relatively unimportant and
the condition to he avoided is, rupture v/ithin the design
"I i'^o: four f">e dor'Asm rtrncp^r' avp hnppri nn Th-^ y;■■■•-'.-!-n-^.^ ■-, -■-'-'- -•'- ■--■=. --c^- -Tresses are oases on xae runtur
i n ■■• n, o:~ the vsrrel (.Sections h.2.1.1 and h.2.2.1).
Ac cor' _;:''" to ; r". 7 2- , tno crco"1 c.'.rvo ~ro:n tort ac-
tive valerial shova a 'vcll-dof ino H reader of stoad"r-
o""^, and d":ir roller; cov'tributer" ::icr't o? the strain.
. , ..orio;n ray bo based on only steady-state croon.
According to vectlon ''1.2.2.4, tho measure vessel is
under a biarial stress state, ana crcen rater are governed
:vr T.D.0 ,0~. (°-15.;, ..GC'GlOn _'.'> 3 •
'; a
a 11 c -
12. " .""J t r e a s 0 a 1 c ul a t i o n
Accord ins; to Section 7 v.-hcre the importance of esti-
railny correctly the state of nultiarial stress ia aht¥v/n,
v:o are tho Computer Iro^ran Dr. Art urn Kalnina (fable 12-
l ) or ~no nenorano sxrer calculation for the shell cvlin-
'■rical surface! and for the cloaure (srherical and toroidal v
surface) of vessel (Pis. (12-1) and fig. (12-2) j ('j-9).
12--'- fatcrial
i,Te chooro a material for the vessel with the
lov/iny specifications ( ^ 11) :
Chemical Composition (.')
C: 0.10
Kn: o.k-5
<? -i • r~ i o
f ol-
.<>.'
.0 :
' 1^
'17
ec
Heat Treatment Annealed 1,551 R
Grain Size 7
3rine.ll Hardness 126
Type of Furnace electrical Furnace
Physical Properties at 1,1.12 F
T e n r i 1 e S t r e ng t h ^ k-, 0 0 0 p s i
Yield Stress (0.2;.:: ~et) 15,000 psi
Proportional Limit 5t5":0 P" i
dlons-ation in 2 inches 0.85'"!'
Reduction of Area G3f
Oharpy Impact Resistance
1 hour at temperature 5l\- Ft-lb
1,000 hour at temperature 55 Ft-lb
Young's modulus 2^.5 x 10
Creep Properties (^6)
Rupture Strength at 1,112*F:
Fracture at 1,000 hours 11,250 pci
Rupture at 10,0 00 hours 8,750 psi
Rupture at 100,000 hours 6,250 psi
Creep Strength at 1,112°F:
10' at 10,000 hours 5,500 psi
If' at 100,000 hours 3,000 Psi t
' f~% p r' r* ~* y.- c> :.es.i.s:n x,m.r, xi p "r T ,~, r\ ■" p *7*,p *-° " EL— J 13.T i -' / ° p
inches (° en) of
rcsion allov/ance
.c.:norr, ,/°2 inch: ( '. 2 c:.">; of cor-
i p £ dcsuits
dhe output of tho Cor.nutGr frogran (Table 12-1) shows
the n nribraiie stress values for the. Shell and closure of tho
vessel.
In the calculatioii of stresses 6/ and »2 tho nem-
^.0. paid 6<£ , respectively, are only orane sxre^'se^
included. dho stresses ""'roducod b~r the "bending sionent
( e,rAo-/hZ and 6 ** / W C\ ^~> pi "I included in design rules, ac-
w- ..j no: and .rressure Vessels Cole, Section
curves Pi^s. (12-d), 12-5) and 12-6) v/ere dot
tsd dro:a the data shov/n in dable 1^-1 and the critical val-
11 pi rj -f 'or tho stress ratio of the vessel- are the follov/ing:
Cylindrical surface er 77
.-6d> '(-rhX)
7,7:7
Toroidal surface cr •12. 67j =
-"'.o2c0
Snherical Surface cr dz -
d, 6,56?, =r O.O96S o
~ O O "
4. \ Z.C~C'-l"'', 1
c
€ ^ Bd, n
{12 ■
n arc ccrr'TanTf-; oo\" 'Oi. L iT-
"^'i*-)^r Q^on-";, "T^O"" "^"^"i^ *"' ^ r~ 0'' "C : 'ial (.3 octi or. 12-'':\
ra:m rax; nouiT ^o-
o" a rzrsr.r- o: £ C'
•A-i i "'train irate in 1' D.oi-rr ir nro-
:.ucea ay a rxref?" of i ,'V-'
_■' t -■■ -'
l'\
= (i^
n =. <?»% sC<n \ D t _' . i •-> ■■■' ■-• /
. CK. o± . o
.79-79:
7
( .' <
91
.V
'-I <■'
'_! .o r*" -t rv-~v
n-T-t ■:, -,, rical 'jurlacs
K7 9' 62 =
cr
Ji.rr-':.'!-91? (
r>''0 j?0 "^ *"■ P "^ ^II^'^PQr-
1L 9r-7
V* ..T7n'
( -<„.-=-:-. 72 7
£* = -■ .557? ( '-lb
■^■ip^i r*p 1 ;.;nvivnn.n <^..u . C„l,
:'.'" 1 --
( o<r — 0. o-.o' > cr ~ ' - ■■' - ■■' ■
£3 = - ■".?/.'? ( 12-lc
-acin.r tha .Jq. (12-1) into lqc. (12-la), (12-lb),
su~7 (l2-lc;, '/9 can c.e- ne 0 rxrain rax80 0: n v^.o.
rlinIr i cal 7Jur :7ace ;ensicn
c __ •" c 19 .1-721 ;: 1: -91
(</, = 7,707 psi i; o 9 o P 9 O 9 _9
9 7'"> 7 ' ' ^-'' ;^_ 11 . A'-7''''"rl" nr
£z - n '7 '7 i i i
79 7
19" 7 -, 7 -. ->
--- 1 7 1 'Is!-- _ i - - / » f ' — __ -. ■J2-
■ 7
' r~, 1 ':ace (4=12,67-'
6, = -I < i "on - - -i . P1 _ . " 7070
■ n;^ <~ , pf
07 r;---]
£2 = .2,67-9 P--1
£3 = -0-557' .?-
1 O <7I;
--<■- J ■- / ■
•7?:?? O ''' •' rr--"l
'-..'—-_. - - ^~* C-'- -—
6, =
€3 =
6.1521 :■: 1
6.i:'21 ::
-< 1
( ^,= 6,55 ;ii .■jjjj
_P1
_7"l
.21
^ r- /' ^■5 3.79:7? O .-''. O ■■ - "
70'"'7i*l^ _7
79:79: I— -16. 2'1::1 ,-7
:otal rtrainr of the o. Trpcco ; pf-v,-^ cLx. "J o: follov/iii;.?
Cylindrical Curxacc
" 1 ^'9
/? — ■-" 7-"'.' irT? ,. T,.
.'-■-:-:75^! 1 ■-)• :.r
.0
, -, n no rf !--■]-
.or
-■". .01772.' in l"o
Toroi lal Surface:
£, - - '■6.'27- : T '">'
Ji6~2^ in. 1
<f 2 -
.-1 OOTO .' 97 ' :.i ±0;;
>? "i ^ / ? :\-''.C
. l~2 0d :ln V"0
6/
T-y.3rical .Ourfaco : _9
O ,'',9 1
. ^o!\.£-; in i~.~. :■:
-7 62 = 6.779 :i 10 ' :: 1?" Oir
£3 = z
. r':'~:6'77^' ' in 100 Hrf*
t -7
162"! " in 1*0
o:0
0Te can cor.'oars critical "trecr: and critical strain:
:3 verr:?A ">/ith the AS;-!! codo allo'/abla valuer:
7'
— > -■■--•'- - >
1 'I,.-, (^,
7,7 7
U 1,11?/.?, ( £> 1
-i /"•..-; * i /■* -
0"r a r: '"• i O -"■ '"' o *
■"O-. ' 'PA. '.V-"~'ci.CP:
/> "1 1
At 1,11.? ~, ■-.°27'\' rtrair. ( £2 )
in .1 ' "' Ilr-"' i," nroluc-3'1 ~"r s-
\ r> - - ~~ -: ^ ■■
At 1,112 1', (6 > :.l
"U'TTCUI"?: li;io in 10 '.
.n ■-.r- >
'- "i^n"! ;ir>0'' ce
T' or: 1 ~: ft:'-'-. — - > ...'
-L,
7:
11„-
■ ^ ■)"--•*-' r-, f» -!
<-.-L-.-.o ; ( e, :■
- '")j70'"uc; : or
^ + :
^..-. .. ,■ , At 1,112°?, ( £ > -.1 ' in 1
runturo I!;"? i"i 110 Hrr ir nroducod.
b""r a ''''cr-sr.r of .13 •'r."'1 "~ni
JO Allov/abl-
At 752°? (:•" ^ > -u i i "~\ r; "» c- ^n of tlo vo-r,r:el could DQ
baro^ onlv on rhont-tinp. nro^jro P "'"■ rl "I '-"> c' (4-6) ('iff. In thi
c ?. .'■••• can a3.ro cormaro critica2. rtrerrcc of the varrel in
normal operation (752. •-*■'; v/ith the AClIf code allo'.vablo val-
•.'-Linp.rical iur;: acs
7,7'7 fri at 752' 12,9Z*-0 "OSi at 752
Jo'1^ A'':
°^
^
72
^ ''^S> " ' ■ C3 PC
7-'-
,""-' "'")"-i o"" i C 3 "^ -5-11 ^" "^ £1 c ^
at 75-5
lor-
1 9 O - • - > ,- t 752
, A-'-Aov;aoi
onclu
i 'O T, i« .in' "i-ho .t^, '.:o can uro 'd\
,'~J "^ P) c "L" ? C 8 \' 2 o IT. r ..o Steel (Sectio n
j' i ■* c' ~i -° ■ 1 £ / ' 9 .r.caer (3 c:-i)
)cioii A11O".'<'-CL .c( 3/32 incher (0.2 c;^}
I Figure 12.1. Dimension of Pressure Vessel
/ 74
Part No 2
Figure 12-2. Cylindrical Surface (Part No l) Toroidal Surface (Part No 2), and Spherical Surface (Part No 3)
75
u-<
.30 _
• c
-3- I c! 20
En
10
0 200 40- o pn §00 1,000
TTr.I3, HOURS.
Figure 15—3- Creep curve from test data of 4-Cr M Steel (Testing conditions: 1,100 F, 8,000 psi)
76
-C X \ N>
^ *
* "?
II II ■a. 4>
>• \9
II II •y *«*
M >3
c o
cv
2U0/^i ooi 'SSSH;
77
vo
o rH
c -Cv}
c rH
CO "-1
,-••■1
3
E-i
s O o o
o M Q M « S
CD O
k > CtJ <H \ JU
\ 3 \ CO
\ rH ) cd
t2 I •H
! O u
1 *' ° 1 -- *'EH
1 C 1 •H
/ CO 1 CO
CD t U
1 ■H CO
1 1 CD
i § ^ ,Q
CD
i 1 C\2 rH
* v«
•z ■*
CD u
•H
n n Cr-'
-a. 4> •\a ^
tl 11 •»
>* >»
/ /
/ J 1 1 L
vc rH cv -=;• VO CO ' C:
' • I I rH rH rH I I
,tuo /2}i GOL 'sSEilOlS
78
CM
o
EH CO
14 _
12
10
8
6
4
2
0
'"»*.
2
4
6
8
10
12
14
+ + + + , 155 160 165 170 175 -180
' Meridional Coordinate, Degrees / I /
L ./ t i u i i i
r
^2 = <^=r A/^ /h
Figure 12-6. Membrane Stress in Spherical Surface
79
(d.dd:CIATid?d C? CC.-P-vT.JR rdCGdAI
K
x'ART do 2
'FAR™ No .?
^
N
11 =. U<j>
npyo. ~ h4cf>
UTHJ'JJA = ^-9-
•=s M <*
Cylindrical Surface
Toroidal Surface
.Spherical Surface
deri 'ional Coordinate, dirtance
d along generator in Cylindrical
Surfaces.
deriiicnal coordinate in "• career
in toroidal and rnherical rurface^
An°:lo between normal and a"i^ of
":imetr~r foi 01 volution;
c.i rcurnfcrencial angle for tonu:.
,.'irr'lace:'cnt in normal direction
Tr an *~'ve r r* ° ^d ^^^ --T^'im "^^yg" ~~crc,'~i
in normal ..direction
dinPlacement in ^pyi ■. j Q Y\ ci J ; ■ i i y1 ^ Q —
tion.
the norm? 1 -in
der'ultant force in meridional
direction
Angle of rotation of
me ri d i onal ai re c t i on
.-irnlacenent in circumferential
di re of i on.
C'ir&nnf^ential .rhear force
I-'sri'icnal bendin" mc
■I =\/vJ &-
\ = M-&-
6$ _ov-. ,yr: 11 "1 /"% -.'■>
' ( = /^ /h ±6M<^/^J
-, -,i o "."i .<•"> r- T "> "» ,"\ *""* f" (".'*' C ' "''"* f1 ^ * ' , -, -,.-, J- ^ -, i
1 -->.-! Q-- ~ Q--1 ( = N-e-/h±: ZM-o-Zh'
\r T! "° r~' '"' "' ":" ^i "
0T.3V-'
\
o
u o -p
P- E o o
o w
+> ©
U
i
•H
62
1 Jt •; ^ : c*
a.
it
UJ 00
UJ
o 1-1 ttf Ui X Q. co
»-»
O
X
X a. x
»- Of
CD
CO
X C/>
o a? t- Ui X X >- CO M X «t
u. o CO M GO >■
-J «z z <l
or o u.
X 0. CD
\:
X CO
— ", V-?' I
CVJ
o
Ui to
u CO => CO
a o u.
CO I- z
00 U-' u
-co Ui a" i- 00
V) z o
u Ui -I u. UJ o
X ft- z
X a
CM CM H O O C • • I
UJ Ui Ui o «VJ CP o a» CM CP o K .4- CVJ «o
fO CO CVJ I I I
^ CD © a l i
Ui UJ vD in .* <T> P«- «o in o cr> cvj
• • • O U> CM
I I CM CVJ CVJ o o o * + + UJ U. U CP CP CP CM CVJ CVJ
H H H cr> CP cr> (T> U> O*
vO uO vO
ro ro
I UJ <J0 o tr in H ro
UJ H O CO
fO CM O ts I I
UJ lu CP to CM CP CVJ e= e? cj
I«H o a> H
L O O C3
UJ T-t VD
I2 • »
ix -» ^r
13. oo on no ro ro ro
H * ' • U-' ' X o r*. J- co e» in in
a «c K 2 p W U\
X. M
- ■ ■ ■■ X a <t to
1*0 CVJ wt
I I I UUlu
N. 00 O
.♦ CM H D OO
I I I UJ UJ UJ oo es CM D (C O' vO flo in IftffK <OtOO
o I
ro CM CD a I I
UJ Ui r«- ^» K. OO1 <C CM CP in OWN
H WM»<
I I I Ui U. Ui eo e CP J- 0D i-l rIOOM vO HN (O S O
OOB
M M *H O O O
i i t UJ Ui Ui in cr> o
CP -* CM CM O IN. •JJP OO O
CM CM CM
CP CP CP CP CP CP
or> CP CP CP CP CP
UI U- U- CP CP CP CM CM CM H ■•-( H CP CP CP CP CP O*
ro N. CM I I t
CO P. vO o oa I I I
UJ UI Ui o ro H in «o vO rlvO 0D ro in ro r>» m CP • • •
-» ro «H l I
CM CVJ CM o o c + + ■+■ Ui UiUJ CP cP CP CM CVJ CM
•H »-t ^H CP CP CP CP CP CP
ro rs. CM I I I « N- \D C3 O O I I t
Ui UJ UJ in a in in ^ in CP N- «c OUJfO ^ in i* • ■ •
J- ro -^ I
CM CM o o <*. * UJ U- <r <r CM CM
i CM
+ u~ CP CM
CP CP CP CP CP CP
(JO vD vJ3 I
ro ro ro POO
III U- UI u. iD vO en P- N vc r- »D in •-• p- ro ro ^ vO
KD «JD VD
ro ro ro o oe
I I I UJ UJ U' -* CM j- j- -* ro in ^ ro ro CP in vO K cr<
vO O vJT" vOvO^O ^OvO\J3
ro ro o o l I U UJ o ec
ro CM in ■"* CP «-I
ro C5 I
li- es a
r>- CM
r^ CM CM C3 o o I I I
Ui UJ UJ vo r- r*- r>^ CP eo O CM CO r^ * in cv er «-•
CM CM CM C3
I UJ
CO OO in r- «H CM
O
I u. ro vw cr CP r^
cv rr j-
ro P-
I I UJ UJ ♦ J- * in
OO T4
OO S- P- vO
CM o I
U- o-
vC
~± IT »JD
ro rr< ro OOB
I I I Ui UJ UJ p- oc CP es in oo ro r in <or- N *-4 in CP>
UD 0P CP
ro ro ro o o I I
UJ U in ro »-t er VJD v£>
I UJ CD P~
CP
ro ro o IP I l I
U- UJ UJ o in CP N, CP TH
J- ro
CM I
P» I
CP I
ro r«- l I I
(TMI
CP
CP
ro ro o «p
i' • U- U-1 UJ
►* CO in ro CP -J-
ro a I
CP
CP
I CM I
P- CP I I
C2 I
UJ I
UJ I
U- in eo ro j- ^- lO ro ro ro oo on en ro rn r"
C3 I
U> P-
I UJ
I u; Cf ro -T vO
m ro ro OP on oo K5 PH fO
I UJ N- J-
I UJ
o I
U-' eo ro
rrs ro ro oo OP a1
ro ro ro
<rr p o I I I
UJ U. UJ r» ro ro j- J- VO ro ro rr< or eo eo ro m ro
o o I I
UJ UJ oo rr -I i£)
ro r> c BO or> ft)
I UJ
* ^ CP
r«» in J- Ifi « n
0s »f> ro CM eo -J" 4 M>H •-• ^ K
J- «=> in HO 00 SON
K »* ^H in ■*-• r«- et p- in CM„m oo
P- n- oo in j CM CO HJ>
*-■ —
OONN CM 3" tr>
i
p» »-• in m r«- eo
u\ o J- eo er «H
^ CO CM ^4 CM J-
CM P» •-•
ro CM •■< o o o l I I
UJ U. Ui p. ea CP HO1* a> ro CM p» o P- ro oo «E>
ro P* CM I i I
OO N. a a I l
UJ UJ UI o P. CM in oo J"
vO
I
vO fO in CP
ro H l i
CM CM CM O C5 O
+ ♦ ♦ UJ Uv UJ cr cr cr CM CM CM H H H CP CP CP CP CP CP
vD vO \£>
CM CM CM o e> o I I I
Ui U. UJ i-t H o
er *o CM cr o CM ro in vo
I u. vO op or. in a
C3 O
I I U-1 UJ •H CP ^O oo
J- -r-i J- CP
CM I
CP I
I I I UJ UJ UJ
J- J" OH ro ro p-- or oo ep ro m ro
eo J- eo MHO .*• r- c
•-< IT. o Kef p -H H CM
83
c*
Ul
UJ X
NNN C9 e o I I t
UJ UJ UJ O «D K. N. CM co ■# \0 ~4 tr> CM \D OlftN • ft
*-• CM *D I • I
to w w
UJ UJ Ul •-I .# O CO CO p
<J» o» o a* o> es w w •* t • •
K» CM CM o ea o I I I
UJ UJ UJ •■4 *-» CM
PWT4
<r •* to CM *-i «-i • • •
«-l CM 10 I •
W W fO O O o + ♦ * UJ UJ UJ in CO *4 » coo CJ* 0"» O cr> o> o ro to •* • t •
i in CM CM o e o I l I
UJ UJ UJ J" ^ N.
«o a> is. (COM
t • • CO CM \D
» I
es o o + * + UJ UJ UJ is. a> T* co <D o 0T» <X> O o^ (T» ea PJ to J- • • •
l*> CM CM
I I UJ UJ (V CO vO <T> 0 «-< CM tn
• • T4 CM
1 I to to
UJ UJ IS. CO CO CO
CT> CT> *? ro • •
I UJ CD vO N. CM CM •
vO I
to
LU
W CM CM to o e i I I
UJ UJ UJ J- is. to tn in <r>
HO-CM • •
CM vO I I
rr> to o o o ♦ 4. + UJ UJ UJ N. CO T>I CD CO O O^ O^ ?3 cr> o* e>
• • •
tn -* co
I
TO CM CM m CM CM
I t • UJ UJ UJ CM in <r> *. to N. co ^ is, *M J- ~i 0 to rj • t •
«4 CM <0 1 • I
W fO WJ
UJ UJ UJ IS. GO «H ceo CJ> CT» O &> a* eo n ro .* • • t
pi> * .*■«-• cr :OB\rt «4 IS. CM |P«ON N U\ J
CM m • • •
e ^ co •-I CM
in co H • i ■
CM J- in
tp a o
©* *P t* CM co ■» J- CM —I
f • • is. mi U\ ITKCO
I » I UJ UJ UJ m*. r*. CO *H O CM *H CO •H .* *H O tO CM • • •
«-» CM vO I I I
to to to ooo ♦ 4- + UJ UJ UJ is. «9 «4 CO «o €3 CJ» <T> €3
to to ^t • • •
I j 1.
1 i
1
!
» a o
*■» r> is. •» 0 m *-" e» co •> e CM
in •* is. co is. m CM m co
«-* cr *p is. CM eo in j^ CM CO«i4
»D »»» O CO J- 0 CM ^ tp •* Is. C3
• • •
CD O H
• • • ^ CO fvj •* CM J-
t • • MIS H ^t in is.
• C • Hmo N. 00 O
84
UJ, ooo
a. CD
X a.
x a. =3
W (\J rl o o o
I U-
CM fs»
i i UJ UJ cn r^ K- eo in -* ao o ff> «o • ■
• I CO N.
CM I
I UJ in o CM ro ,4
CM
UJ cr CM vi CT> cn
CM O I
U. N. TO CM CM
•
I t UJ UJ
ro <M ro tC
• •
CM CM *= O .+ 4. U- UJ or> rr> cv' CM
o> cn cn cn
t i CM E3 I
UJ I*-
I u. CM eo 4- ro in h- an
I LU w evj
t cn in cn •
CM l
■ ^
e I
! U> i f*.
: J- ■ ro
I UJ o> in cn
cn
!i u.
O
I? S cn
P O I
UJ ro
ro ro eo ao
iL
in «-i SO N- CM in ' t a
co »H CM «VI fVJ CVJ
ea P o o t
ro CM ** O CD O I t •
UJ UJ UJ in in in «-i o r«- *-• in CVJ <T> O N. fO 00 O • •
ro r- i i
ao K- O » I .
UJ UJ UJ >o cr o» \C tn CM in i»3 «3 ro »JD PO ■d- in cn ■ • •
.*■ *0 «H I I
CM CM CM o ep o *• * ■*•
UJ UJ U-; CX1 CT> <T> CM CM CM
CM
O »
cn or. cn cn : • t 10 vO i CM CM o o i» ' U~ UJ
•r • » «4 JH *H |>H
p I
ro o l
UJ UJ rr cn en >H CO CD in J-
i • •
CM N. I I
cn Cn •
vO
CM a I
UJ ro CP in 00 o •
r* 0 I
UJ CM in <y>
<T 9
<r i
o p e= I • I
U U,' UJ N. «P K. J- J- vu WWW er eo «c
0 o e= i I I
UJ UJ UJ n *-4 ^ (VJ O N «-t tn CM cnoK CO 8} o • t •
ty> N. CM • i i
oco 1 I I
UJ UJ UJ CM CT <T> J" J- CM -*■ tr> eo ro *f> ro j- in tr» • • •
•3" PO T* I I
CM CM CM ooo + + • UJ UJ UJ <T> <T> CT> CM CM <V r4 -r* T* <T> (T> CT> (T> <T> CT» • • •
kC vO «D
CM CM CM
I I UJ UJ
I u. o
<j> a. in ^
0 CM r* • • I •
CV CM j(V)
ro rr> rr> poo
1 l I U- UJ UJ iD ec ro or, w-{ in co Q (T
0> J- (J1 • • t
K av I i
CM I
o o I I
UJ u. i>» «o
^ ro r^ or er cr
P
Ui
to
Nl CM »-t OOO I I I
UJ UJ UJ GT> CT> J- (OtTN O ^ CM CP o (J> tr> ao o • • •
f"3 l>>- CM I I I
eo N- vD OOO I • I
UJ UJ UJ 0 w-t CT1
(^ in CM eo ro oo
■J- in <r> • • •
■jt rr> wt
• I CM CM CM OOO «f + ■♦• lb UJ UJ CT1 CT" CT1
CM CM CM »-l i-l TH 0> Cjv O1
o> <y> <T» • • •
»X) >X> >£)
CM CM CM Ooo
1 I I LU UJ UJ r- r» vO UJ u\ j- r» ro o> «r4 ro -* fr. j- in • , • t
CM CM CM
. I UJ fs.
co in
. • CM
a c I I
u; UJ
•H m C3 CT>
^- CT> ■ • •
• I
fn in f) fi « ! M p>! r i>)i»)R n i*1
er (E. o » I I
UJ UJ u N. oo tr> j- j- vD rr tn re or on eo
w CM -H ooo I l •
UJ UJ LU ONM
,.,oo CJ> n. O J- CM o> O f^ W«Oo • • •
fO l>» CM I I I
00 N- <D ooo I I I
UJ UJ UJ N- '-t <T« N. in CM t^> tO CO fO ^O M -*■ in cr» • • •
-* fO w4 I I
CM CM CM POO •♦> * + UJ UJ UJ <T> CT> CT1
CVJ CM CM o-l »-t W-4 <T» CT> <T> <T> a> o>
a • t UD \C) vD
CM CM CM OOO
1 I I Ui UJ LU -* ^t ro •J fO CM <j> in «H ■J" <D ec
• • • , CM CM CM |
K) !«•> fc ; o I
LL r» ac CD IT cr
a CM O- I I
o l
UJ cr
• o~> i
c »
LU
f or>
P o I I
U-' Lk. oo rr
a ao
^ -r-t rr\
N in j- in oo <H • a a
on CM r- fM J- in CM CM CM
cr KO ro CM CO •* J- CM «-< "H J" K
m 9 t t*. r-t u\ in N. ao CM CM CM
I
I*-. «r> K -* o m «-4 O 00 r* er CM
a • • in o J- BOH CM ro t»
K- ^ •rH in »HK oo K m CM in co • • .
J" "O CM •H CVJ ^ ro ir> fo,
.i... _..
I o I
UJ CM f» CM N.
I
o I
UJ
W CM O I
UJ vO J* O CO O J*
po ao o a • •
ro i>» CM I (
ao S. 0 o I I
UJ UJ co W (O K) K> CM J'WCO n "•o w J* in <y>
a • • Jj- W "H
I I CM CM CM OCO ♦ +. * UJ U- UJ cr <T o*> CM CM CM
cr <j> cr> ci> o> cr
a • • vO vO lO
CM CM CM O O CJ
1 I u, u. CM T-I
«p-t N- (T oo
a CM
ao
CM
I li- es o IT!
ro
oco I I I
UJ UJ la- in er oo in cr
a CM I
J- a
I •Jl—
in cr ■»-(
o-> . •
I
I o I
UJ UJ u. h» co rr> j- J- K; fr. OO CO
U3
on ro rt) ro
rtJTiO rw CM oo in .* CM
a • •
^IflS ro K. to
ro CM o o I l
UJ UJ IOKO
o I
UJ
en <r> oo -r ao o ro
a ro i
eo
eo CM rs.
a CM I
vO
ro
eo a
N. I
r>- ooo I I »
UJ UJ UJ o CKK \D <T> CV. r>* CM co
vO ro in cr>
• • a j- ro «-•
I l CM CM CM 0 o o
UJ UJ UJ cr <T> cr> CM CM CM r< »-l TH cr> cr> CP en en en
a • a vD \0 vO
CM CM CM OOO
1 I I UJ UJ UJ f»- rs. v£> cr> ou r^ CM eo J" y-t CM -J" O T-t CV.'
a • • ro ro ro
ro r^- ro ooo I l i
UJ UJ UJ en «* ,-! ee ,f CM (Pec in -* CM en -*■ en
CM I
en I
ooc
I I I U' UJ UJ N. eo ro -T -T \D ro ro ro eo eo eo 1*1 ro fi • • •
io r^ c cr J- as
J" N- p a • a
»-» m O
ro ro J-
l I
O O O o o o
ro CM o o I I
UJ UJ in ro en en v£> \D en o ro oo
a a ro N. I I
OO K eo o I •
UJ U. in vo CM vO
ro vo
a •4-
in
ro •
CM CM O o * +
UJ u. en en CM CM
** ro o o
• I UJ LU -*r^ ■»-• u^ rorw r^ CM ■= J*
a a CMro • t
iO oo «= o • t
UJ LU •"> * n- 4- eo eo ro en (T« ro • •
I CM CM O O * + LULU en en CM CM
CM —4 o O I I
UJ LU ro ro O v£) en CM o N. co o
a a CM I
<X> o I
UJ UJ o -*• in j- CM en n» ro in en • •
ro -H l I
CM CM O O 4. 4> Lv U- en en CM CM
en cr> en en en en en en en en en en
vO vD vO vO vO vO
CM CM O O I I
UJ Lu 4" 4-
4- c
CM ro • •
ro ro
ro o i
Ui in \o TH in en in en
CM I
I LU IS.
a
r»- I
y-t o •
LU no
CV CM o o I I
U- LU ro ^ in in <JD yC
n- r-
• • ro ro
ro tyj o o • I
LU LU in
>£ en 0 en CM un en cr- • •
en CM 1 •
CM CM O O • I
LU Lu CO ro
o
CM cn in
•
oo p
ro ro
C3 CO • I
LU LU •eo »». y~* in en CM ro *H 4- cn • •
I
f> ro ro f»- • • a
Ooo I I I
UJ U, UI lu ^••N. co \C JJ- j- **'■ ro ro ro °n oo or or
ro
P
v£>
•o a
° N- -* j- T-I en
«= CM u. m oc ^i
f= J" 0C oo CM •>- O ^ fM CM j- m
85
WNN [ 1 PO (VI C\J 1*5 f\J
f CVI to CVI CM PO CM CM po CM CM PO CM CM W CM CM W CM CM
<p o e o a o o o «3 o o co <s o o o o o o o © o o o O O o I I I 1 1 1 1 1 1 • 1 • 1 • 1 1 1 1 1 1 i 1 1 1 1 1 1
«' UJ UJ UJ UJ UJ u; UJ UJ UJ UJ Ul UJ UJ UJ UJ Ul UJ UJ Ul UJ UJ UJ UJ UJ UJ Ul UJ t— ^ton <» CM -*• N. O PO p^ e «\J ,* o* cs CM in i<- a> a> ^ on CO fO fv- ^ O UJ N. 3- CM PO in CM to in CVJ CM in CM CM J- CVJ O j- «-l \D j- J- o a r»> CM N. (P X U\ ~* «0 N- »-< co rw *■« CO N. wi CO P*. «-t CO K «-i eo vD »H «0 cr» CM <y> CO CM N- »-1 H^r4 *H .* «■« *-i .* ■»-« «-t .*• «H «-l J* «-» «H J- <r4 «-l ^r ^ »-• ■* »-• CM ^ »-4 ar O M CM OMN (9 M CM O to CM o to CM O PO CM es M CM o fr> CM O W CM
HNiO *4NvO vH t\J vO «-l CM vO •H CM tO *-« CM 03 «-l CM vO <-< CM vO ■H CM v/J) 1 1 1 1 1 1 1 • 1 1 1 1 1 1 1 I 1 1 1 • 1 1 1 1 1 1 •
*» r*> w> PO to PO to to to i*> PO PO PO PO PO PO ro po PO w ro M W PO to PO PO O CD o o o o a a a CS o o 000 C9 a C9 C3 o"o ODD QOO
• ♦ * ♦ * * * * + •*• * * * * * + + * + ♦ + 4- * * * * * ♦ «« UJ UJ UJ UJ UJ Ul Ul UJ UJ UJ UJ UJ UJ Ul UJ Ul Ul Ul Ul UJ UJ UJ UJ UJ UJ UJ UJ K» N. CO wA N. co -* N. CO «-t h. CO v4 is. to *-i N. CO «-l N. CO -4 N. CO *4 h. co «-• bJ co«oo CO CO O CO <0 o CO co O CO CO 03 CO CO o CO CO O CO CO O CO CO O
X (T o> e> cy <y< es a* a» O a> <T> CD a> o> o a> a> e> o> 0> O CT1 CT* 63 CT< 0" C3 tm <y> o» e> a* <T> o cr> cr> a 0*< *5 cs o* c* o cr <T> «=> cr> or» o <T> o*» e> O*1 <T> O z W W «* fo ro J- M K3 J- PQ /* •* WWJ; PO w jr to w J- fO PO ^ PO W -4-
er j-cceoi\j K er w-t CMCM j- in
86
2.
•*•
1 e e e
[
m eo a o e C9 e CD cs e CD a O CD O O o e O a CD O
lu t*> CM 4-4 PO CM «-4 fO CV.' *•* ro cvi w* CVJ CVJ ~-4 CAJ CM ■-• 4-1 ■M «4 4^ 4-1 es a C3 4-4 X o o o CD CD o CD a c CD CD O CD CD e» CD CD CD CD O o CD O CD CD CD O t— 1 • 1 t 1 1 1 1 1 • t 1 1 • I 1 1 t 1 1 1 1 1 * * • -> 3 LU UJ UJ LU LU Lu LU LU LU LU LU LU LU UJ LU UJ Lu Lu LU LU LU LU Lu LU LU Lu U
CM in CP «o ro tn in «-• *o cr *4 in •*■* ro ro cr V0 cr in ro CM CM cr eo N- ro o *«4)
X a X
i0 no in cr J- o <y> ■* s a «-» CD CM a> j- Cu r> V0 4H —i -J- 4-1 UN ro «A> in cr es 10 N. %£} f" ^ ■* co j- ro in CVJ j- in *•* cr cr CD cr sD J- in ic «0 es CM CM CO GO \0 h- «-• vD »-t vO CVJ vD j- cr ro co *-* N. cr cr CM «0 ro r>~ 4-1 o CD CM in ro h- o CO h>- CD in CO ^4 in «-! CM in in CO CM <0 ro j- J- CM CM cr CM O cr CM
WKN CSJ N. CM cvj r* CJ oo <r CVJ rvi cr wi CM V0 «H ro ««• 4-« TO cr J1 J" eo 4-1 t 1 1 1 » 1 i 1 1 i i i i l 1 i 1 1 1 1 • K »0 CO N. «o CO r«- <x> 0O K V0 N. I*- V0 N. eo \D iO v0 in in in in in in .*■ o es o CD CD C3 CD CD CD CD o CD CD CD CD CD IS a a cs es CD CD CD CD CD CD
1 i 1 1 1 1 1 1 1 • 1 1 1 • 1 1 1 I 1 1 I t 1 • I i l LU UJ UJ LU LU LU LU UJ UJ LU UJ UJ LU LU LU LU LU LU LU LU LU LU Lu LU LU LU Lu4
«-4 m 4-t 4-1 CM «r \C VJO ^ oo CVJ K ro o ro ro CM ro \0 CM *0 r^ CD CO i0 CM in
z a M v0 N- 4-t CT> N- M C2 N. CD -» CD cvj in J- ro 4-1 10 V0 i0 in in OO in r*. O UA
«D in J- 4-1 in in «-l ro -H CO CD N, in ao ro CO J" o CM •«H J- cv 4-( 4-1 4-t -* CM 4-4 10 ro cr j- »H <T> C3 J^ 00 CVJ «f in ro CD cr -r »-t cr 10 V0 10 ro TH 4-1 ro CM
0 ro in <T> K .* O^ vC ro cr o V0 CVJ vO «-i in m-t -* *-• c? K »4 ro 4-» V0 J" V0 4-1
j- ro 4-4 .*• ro «-• v£> fO ^| -J- ■S CM CM cr CM in ro ^-i ro fx» -w* 4-1 4-t 4-1 4-1 CO CM i • i 1 i I 1 1 l I i i • 1 • 1 1
CM N CM CVJ CM tNJ nj CVJ CVJ CVJ rvi cvj CM CM rvj C\J CM CM CM CM CM CM CM CM CM CM CM i a es o e=> o o o CD »C e= en CD O CD es CD es CD CD CD O CD CD er CD C3 O
+ •> + ■+• *■ *v • * + + ■f •+ •4- * + + + *■ -> 4> •*- + * •> * •V * LU LU LU LU LU LU U- LU LU Lu Lu LU LU U- UJ LU Lu LU Lu Lu LU LU Lu LU Lu LU LU CT> (T <x> cr cr CT^ a« cr cr cr cr cr cr cr cr cr cr cr cr cr cr cr cr cr cr cr cr
1-4 x
CM CM CM CM CM csj CVJ CVJ CVJ CVJ CVJ CVJ CM CM CM CVJ CM CM CM CVI CM CM cv CM CM CM CM
a. a% o> cr (T> CT <r> cr cr cr cr cr cr cr cr cr cr cr cr cr cr cr cr cr cr cr cr cr z cr cr cr cr cr a> a> cr cr cr cr cr cr cr a» cr cr cr cr cr cr cr cr cr cr cr cr
%o iO 10 tC t0 vD a} vT> <J9 vO V0 vO 10 V0 V0 V0 vO i0 10 i0 i0 LO V0 V0 (0 iO «0
fvl CM fvi CM cv CVJ r\i CVJ f\j PVJ CVJ CVJ CM CM nj CVJ CM CM CM CM CM CM CM CM CM CM CM C3 O o CD <=> c= CD C CD CD CD a CD CD o CD CO CD O CD CD CS es CD CD es c:
1 1 1 1 i 1 1 1 1 t I t 1 1 1 t l » 1 1 1 » f 1 1 1 1 LU LU UJ Lu- Lu LU Lu a. Lu LU Lu Lu Lu u. LU LU U.' Lu Lu Lu LU Lu Lu LU Lu LU LU r^ N iO -»■ J- ro »i es ep to- N- UD j- ro -«-» cr 10 «* CM in o ao J- -f 4-1 .* eo
»-« CVj «H o D O" CD cu N- U) rn •*• ro ro CM ^-^ CJ C' ou CO r- ao N- CD J- J" in cv. X CO J- o es IT> w* TH N. W n cr in m v< r«- t~ CM or 00 J- CD CD r- ro ro cr jf a CP PO J- j in N- S- 00 CD CD »-t ro ro in V0 <X> <o cr cr «- ro r- j- V0 i0 s. cr =» N- «c cr D"* e» >-« TH CM .d- 4 in V0 iO r»- 0O CC cr CD CD CM ro ro ^• in in 10 h-
rO fo ro P •* -* J1 ^ ^ -r ^> j- J- J- J- ^t j- in in in in m in in in in in
fO fo ro fo in 1
m i ro ro CVJ ro ro CM fo ro r^ ro ro ro CM ro CM CV. 4-< 4-» •H 4-1 CM o to o CP e=> a ts o es a a «=> » CD CD CD CJ o CD CD CD c. CD 6= es CD CD
• J» 1 1 l 1 I 1 1 1 I 1 1 1 • f i I 1 1 1 1 1 1 l 1 1 Lu Lu LU LU LU LU U-i Lu LU U Lu LU LU LU U, LU LU LU LU LU LU Lu LU LU Lu LU U- w <T 4-t vO >JD in cr a- ^D eC IT CM N. ix-i «0 r^ op eo in 4-1 4-1 OP CM 4-t <0 cr CM cr tn -* ►- CV in f- J- i-t cr CD »-l r*. cr J- ro •-< N • O in r\j ro V0 cr -* in cr 4-4 CM 4-t C3 ao N vO ro r^ p ec cr CD in »-t ao r- V0 -* CO SO cr CM in in 10 -*
o in fv (T> t*5 r. ir> cr ro ro ^-t cr- ro J- in O ! in vO CO •0 4-1 in in 4- cr CM ro eo <F |* GC (T J- CT^ cr 03 CS j- «H CD K «-" V0 ro er 10 CM CD CD ro in cr cr vo J-
CM K. a> <\i r^ <r> CVJ rs- »H re a ^H tf. \£> J- CM J in «-t CM U% j- w-i CM CM ro to I • I 1 1 l i l 1 1 I 1 t 1 1 1 1 • 1 i i 1 1
CD O CD P «= C3 : a P= C5 CD CD CD CD O ep CP r- cs CD C? CD e CP f= e= o •= • 11 1 i I 1 » 1 1 I 1 1 1 1 i : 1 1 1 1 1 1 I 1 I I 1 1
LU LU U- Lu LU u U- li_ tl.' LU u U- LU Lu UJ Lu' LU LU LU LU LU Lu' Lu UJ LU LU LU fw fO ro h «o m N eo CVJ v0 CO \D C" N- o J- cr CM iC CD OO CM V0 h- 4-t CM ^ J" <T 10 J- -T <X) JT j- u; J" -T \D in u> eo <JO V0 10 J- P- CM «-• 4-4 es O' J" CM
^ JO *T) r" ro fr> r«o ro ro ro ro ro ro ro rr rr- r ro ro ro CM 4-1 4-t cr cr eo in vo 00 «D OP co ec cr- ; CO CO 0P 00 a' 0P or ec ou ao on eo eo OP eo a- r- h- r«- OL- «r
i
ro fO fi rr rr ro wt |r. fo ro l»; rr r; r» ro ro ro ro t~. to ro r»: rr m .T
f W o K- K J- «-< »-4 cr V0 i0 ro CD es K .* -* 4-J <r cr »r K »<- CO K. CM «D J- J- o in in ^H h r- CM eo CO ^ O CD in «H 4-f r^ CM CM eo -* * CD in. J" M w* <-l o <o ac N. in in u- CM CM rl O e? CO N. r*- in ^ j- CV. 4-t 4-1 cs eo ** ** h- N- t? CM CVJ in co CO r-t J- j- r- c c= tv IT. in 00 4-< •H J- »N. r»- CD CM
x •v. ?-• m U> cs .* ^ oo pvj *VJ fw w-l »^ in fp »P J- CO CO CM K. r*. •M in in CD ** in K CD co ° rt *H CVJ J- J- ir< K. r^ co «D e= w-t CM CM it in in K eo ao CS 4-i
. ,* *» J- ^ in in . in in in in in IT. m m vo «0 V0 \D U0 10 «0 \0 V0 <S) iDK K
. .1 . . i— — — 1 . .. J -i • L— . ^ _ ., i.._ .i -. _. 1 .
87
>
A,
. • r: ■
;3 UJ X
-j I
m «M «M O O «9 • I I
UJ UJ UJ «o in K. «H O K. -4- \0 CM
OWN
o o o I I I
UJ UJ UJ -* fO O* <T> o o O J" CM ro «-* CT> t£ ro «-•
.»• CVJ CM opo I I f
Uj UI UJ in CM en «D in CJ .* o ro
in ro ro
f*> CM CM O O O I I I
UJ UJ UI ro ro \o (T> CO i-t (OfOlO *D -* r»
*0 CM CM OPO I I I
UJ UJ UJ PO <T» « \D v/j) n win J-
WWW ooo I I I
Ui UJ UJ vO «-) ee «o «o o fv 0* CM ro o r»-
•-«•«• CM OOO I I I
UJ UI UJ in .* K. N. CO CM CO CP ro W WO O rO K.
o o o P a CM o I 14 + 44.
UJ UJ UJ UI UJ UI U\ «o CM €3 vD cr» CO CX> (P CM h. IO in J" v-4 O \D CO NKtOoNW CO OVCM CM lO K.
•
wtCVJ vfl 1 1 1 www
CO CM vO 1 1 1 www
N. CM vO 1 • 1
W M f)
CM CM vO 1 1 1
ro PO ro
r>» CM m i i i
ro ro ro
«D CM -*
ro ro ro
<r4 *4 rO
WWW
en CM »»i «-• CM ro 1 • • 1 1
ro KO ro ro ro ro 1 e e fa
ui ui UJ K. CO *H CO CO o
ooo 4- + * Ui Ui Ui K. as -* OOOO
O O O 4 4- 4 LU UJ UI is e o to co o
ooo + 4> * UJ Ui UJ r- co ro co «o o
ooo ♦ 4 4- UJ Ui UI O vDifl CX> CP »-l
o ca o 4- * 4> Ui UJ UI (VJtOO ooo
ooo 4*4- UJ UJ UJ N. *-4 CO co CM en
O O O o o o 4 4*4-44 UJ UI UJ UI UJ LU in vo en in in ua co ^ o <J> in .»
UJ X ►»■ z
i •
CT» en o CJ> <J» O w w -r
<J> 0> o «T> CT> «p W CO -*
<J> CT O (P CP O
(T <7» C? CT> <y> o ro n .*•
CP CP O CT> O* O WW4
ooo ooo ,* Jt -*■
CP CP r*. CT> <T> CP ro ro po
N. \D UJ in wt en en en en en o «H ro ro ro ro rf •>■
ooo
ff>«p'r
CM CO J" J- CM •* *H «* r-
.» o
N- S?
m co CM
ooo
K .* «-» in *~i r» c N in CM in co
ooo
«•* CT \D K CM co m j- CM cu ri Jt
O O o
iflWo co -* o MrtD j- r~ «z
OK.* Olft H eoK P CM U\
I
in
en CM
in ^ CO »-•
O O O Q O O
m «p K. r es K CM CO J- J- o m j- CM *-i *-• e? co
K. w* in in N> co .*■ i» JT
U> O .*• eood j- in in i
.* «D CM
in m in i
NKrl J- ir> N. m m m
.i
«-i in o P ^- CO «= •-» CM 10 vO (D
I
CO CM ^ CM ^ in vO %D %C
I
IAN BCD B rt <Ot0iOiOr*S
88
(y
■ Ul s e a o e e o a a
«4 *S •H «-t CM CM CM CM «H ! »- O CD CD CD D CD o o o ,3 ♦ 4 ■4. 4- 4 4 + * +•
Ul UJ Ul U UJ UJ Ul Ul Ul o J- cr CM <T> (T> CO vO CT«
»-• ro in «P U> OD UJ o OD h«- X CM >H O ao .T «H ro ^-i in
1 ro -*■ CM ro aO f*5 m f*5 -^t CM CM a» cr «3 CM CM co in • • • • • • • • •
«~i in CM • ft
CM —1 CM CM CM -»
.* J- J- fO w m w o o o o CD O C5 o o 1 1 1 1 • 1 1 1 t
UJ Ul UJ Ul UJ u UJ Ul UJ •^ ro CM in 0> CM -t 1-5 W
IM CS 1*5 10 1*5 in CD CT^ cr> o> X CO in CD *-t CM C3 «P V0 C a © tO tO J- •H CO go CO o CD •H CM CM CM •-• 1*5 1*5 l*» N. • • • • • • • • •
M ro CM CM U> CVi CM in N. I i 1 1
CM CM CM CM CM CM CM CM CM o a O CS IP O O ep es «+> ■■* 4- 4. + + * i" * Ul UJ Ul U> UJ Ui U- LU UJ cr cr CT CT> <r> <r cr a* cr>
M' CM CM CM rv CM CM CM CM CV x; •H >H ■H «H •H ,-t -H «H ^
*' ,<r cr cr a> cr cr 0^ cr cr> <r o> <T» CT (f o> <T> <r> o> • •« * * • t • • •
l t0 tO tO <x> >0 «JD V0 v0 10
CM |M CM CM CM CM CM CM CM 1 o o o a o o CS o es i 1 II 1 1 1 1 1 1 1
U. Ul U! Ui u UJ UJ U- UJ t0 CO CM K
r>» in •H r««. in r> rv
1-4 x in in r» -H : »»i v0 (T>
■d- in CM CM KD O o •H J" 0> a *-l •H -H rr 1*5 ec «-< N. CT CD CD ■H CM CM W 05 • . • • • • • • • •
in in 10 t0 \D v0 , <0 10 10
CM £9 eo CD O C3 j ea er in e? p o P ea c.' C3 C3 O
» F ♦ 4- ■*■ * •*• * 4> Ul Ul u u U UJ i UJ UJ Ul e= h- ,* CM CO -H ' in p> J- * r* cr ■ T vO vO rl «f «-• fs. iH cr tn 10 •»-! or a> cr>
a O CM CM ro CT> C a> CD CT1
*Sft at «e> TH CO CO r^ in • - i* • • ■ • • • CM (H 1*5 ro r- N- ' N. CM fO
» ; I 1 1
CP p *-t JH r* »-i j T-I cv K O F O C3 ; C a o
I II 1 l i i ; 1 1 1 UJ U' UJ UJ UJ UJ LL Ul U' K t» M mp* <T N. fw
to in J- CM j- in : -T <H OD cr> o-> cr eo oo ■»-l ^H
X O i» er «n f^ CO CO «M J- JT i» -x ;» J CM ! CM J- CM
j
• i • • • • • • «H «H <H >H >H N C^
1 K.L «H JH cr vo <0 in «H r*. f>~ CM CO CO ■* (H CO f>- in m J- CM CM ■H P CM in OD <o •^ ^ 4NP • !• • ■ • • ' • « •
•4" (O CM f- N <H *w in cs X , «-< «M ■* I* in N K oo e=
Kf- r» K KK ; SN «5
a o o CD CD a a c= O e eo CD ea CD CD
•H CM CM CM CM CM CM CM «-4 «4 «-i •H m* CM CM o a O O C3 CD CD CD CD CD CD CD CD O O
+ + ■♦• 4> 4> 4> + 4- 4> 4 4 4 4 4. 4
UJ Ul Ul Ui UJ UJ UJ Ul Ul u Ul Ul Ul UJ U >H *-l 10 N. cr in K. eo cr J- ▼-t r*. oo «e s a) cr> a *-l V0 «-t <-l in CD in cr •H vX) CD CD
<r CM CM CM in in m in -* J- U5 ro ro eo eo J- o> \0 10 -a- cr cr •»4 r^ N. «-» J- j- -* cr in c=> s. rw eo in in CM vO V0 r*. ^-i •H CD V0
a «-4 «H «H •H «H >H «H OO ao 10 f> h- «H »-4 1 1 1 1 1 1 1 1 • • 1 III
fO 1*5 ro ro ro ro ro ro ro ro CO ro ro ro ro O o c CP o c=> o CD CD CP CD CD CD o o
1 1 1 l 1 « 1 I 1 1 1 1 1 1 1 Ul Ui Ul Ul Ul UJ Ul Ul Ul U. Ui Ul UJ Ui U eo o •-»- in \0 CO r- oo r*» s CM CD r s N in m -* ro ro in to ao CO <r ao •H T*O«
«H in •-I •H in r» rv CM •H «-4 e> CO OO CD 10 a ^4 tn ro CO ao ao J- f«- r- ro CM CM -* CM r»- u\ ao ao cr ■H •H in eo es N> -»■ .* CD .* • • • • • • • • • • • • • • •
N. ft. 10 v0 in in in •* ••*■
^ ro ro ro 1*5 CM
CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM O O e CO c ea C O CD CD e= C= CD CD CD
+ + •¥ ■*■ + <♦■ + 4> 4 4 4 4 * .4 4 UJ UJ Ui UJ Ul UJ U Ul Ul UJ UJ Ui U UJ UJ cr -* in v0 r^> c? o J- tO 10 er in in CD ro CM r- in in ro CM CM cr CM CM ru r-' co r^ ro 1 •r* C3 ro ro CO CM CM CD cr <r »-t CD es cr ■H 0> TH ro 1*5 «0 CM CM O o eo in ro ro j- H 0*> C3 CD CD CD ■H T-t CM ro ro -*■ t0 vO <0 •*-!
V0 t«- K r> K r«. N- r- r-. N. N. N r-N oo
, CM CM CM CM CM CM CM r* »-i *-< »H —t •H ^H w* O O o CD CD CD CD CD CD CD CD CD ceo
1 1 1 t 1 1 1 1 t • 1 1 1 1 1 UJ U' Ul Ul u< Ul Ul U Ul UJ u u. u, UJ U eo ao CM ao C3 r>- o ao vl •H in CM CM CM ro co CM CM CM C3 r>- eo (^ in Ui CM ro K, r< S ,* «-< 10 <0 J- w-l «H cr CM CV tO cr cr CD «0 «H <T> »i ■H IO CD CD tO CD CD -4- cr cr vo CM
; vo cr 10 V0 -a- in in CD CM CM r« j- ^ 10 CO ^ • • • • • • • • • • • • » • • i vDvCf» N- eo cr cr , • »H «H CD O cr e CD CD c: er en E> CD C?.«H i C P CD CD f& P CD CD CP P CD CD er eo o ! •*■ 4- *■ * '* 4- 4- + 4 4 4 4 4 4 4
Ui Ul Ul u Ul u U u> u; UJ UJ UJ U Ul U1
i cr cr 10 ro no cr ro CM CM J- CM cr CM U> f^- J- f5 cr •ri cr ro or .* cv wri ec, CM in cr r*- (0 LTl IT. N. j- cr ao ro or ec r-~ cr (Tn J- CT1 «H j- ^t j- cr cr *-i *-! »H in r- N- c: J UN BO i0 vO •H cr CT' K- o CD in. CD ea j*: ro
CM f»5 -H 1 1
u> 1
in l
CM in u^ tO u\ in »-i i
ro eo «H 1 1 1
CM CM »H »-i w-l T-l *H «H ■H ■w-l TH r* «-l «H >H O C= CD O CS fP cr. CD e= CD a C-i e= op c 2T 1 1 1 I 1 1 1 • 1 1 1 1 1 1 1
U' UJ U! U' Ul UJ U U' u U UJ Ul LU UJ U' 1- ■* «H cr cr 1*5 »-i ao CD ao ■-O CD »-4 eD ro oo CK O'1 ro eu eo C\J in -X CD K. r>- CM a. eo oo eo «« ^ J- <0 i0 r in in cr rtj CM in CD CD h- tO U ro «= c c; f er e? nj n-t *-l to cr o- oo ^r
CM rr> t=> CD r° t0 to ao CD er *-i CM CM r j- \-i ~J C\ 40 «-» ■H ■H T-I »H «H CM CM CM CM CM CM CM W 1 1 t 1 1 I • 1 1 1 • 1 • 1 t T er- f> r^ K P- r~ ro r^. er er r»i N N C ^ in o ro t0 «0 C3 ro ro tO CD CD K" tO tO cr ro
& r»> to tO CD r. ro to CD O f; to to o ro 2 cp ro \D V0 CD ro tn tO C CD ro tO tO cr ro
er ro V0 V0 CS ro ro 10 CD CD ro t0 to o ro X cr> cr cr cr CD CD e= CD wi w-i »H •H
t
H N (\J
89
t
\
* S
Ifk <H N. * r«- u\ Nino • • •
C\J J-
I
*-f (T tf» ^ ev «o in j- <\j «0 wl .4 • • •
CM N ,H «»■ m N-
■ \ eoo OWd «4 »4 «4 1 f • «9 e> o O O O OBO ♦ ♦ ♦ + * + 4- ■*■ *•
< UJ UJ UJ UJ UJ UJ UJ UJ UJ K- ts \D \D \D *o to fO (T» .*■ UJ <T> ■* CVJ tn \0 o C\J in N- X tONQ us ■* in <T> in .* *- 0> N- vO ■*4 U\ O* <J\ <X> tn X. (OIAS OO <\i 10 tfi .# W
• • • • • • • • • TO <H CO • 1
tO tO tO
CO W 10 t0 CO «•<
W f> W fO CVJ ▼* BOO O O «3 o o o * ♦ * * * ♦ + + ♦
«t UJ UJ UJ UJ UJ UJ UJ UJ fr_ «\» o< <\J K. M »-l (OS «J ui p> o o OO ^ OJ •H -» O x o» w *-» O CM CO CO «-t «o ym <rimo> o"» oo »-( w co co Z ,* •* .* «* •* w M -*■ vO • • • • • • • • •
*»4 «H «-» v4 «-l *-( •H • <H
I
eo ^
• » *■* tn K. CO
e-
IP
4> * * UJ UJ UJ CO CO cO ooogt j- J- to lOOvt w> .* tn t • •
«■« to in t i
cs o o ♦ ♦ ♦ UJ UJ UJ in .* to COP vO ■H ro <r>
N. *0'C\J t t •
»-• W K
+ + + UJ UJ UJ 0 W CVJ W CVJ CO 4-vO a ■«-• W tO tn «o «-i • • •
in in in 1 i • www o o o + * * UJ UJ UJ 00 s. in vO *o «-i a> oo <JJ> J- CVJ C9 • •
1 I
t\J
•
I
UJ UJ UJ CP M <P eo f) KO 0 ^ h. W t\j a r400 • • •
v\ ** to I I I
to to n O O C9 ♦ + *.
! L' U.'
*-i cs a> o> J- .M
MlftK • • •
•r* +4 w4 1 I I
Ul UJ UJ win co co \0 «H K. N. \c oio> e» jt in • ■ •
M t\J c\J I I I www oeo ■♦■ + -f UJ Ul UJ w4 tO N> a« s. cy
O* O* h^ r«» a» ^H • • •
^H "-• <M • • I
* ■♦■ ♦ UJ UJ UJ Jt ** J» w(\Jtn to in ao
in in j- • • •
NWlft I I I
to t* to Boo
* * "^ Ul UJ UJ
<r> a> tn ■S tO ~4 N. -* <J» •H W J- • • c
CVJ PJ <\l II I
f\J
I
< • • • U o o o o o o oao
iir.
U.I T C K> ^ to C=J r*5 io
o tn %D
« cr PO iD
K r- t~ fC K. cr vO c= tr ro vO C3 lO o n K) «o C3 a> C5 1*5 IT «r cs • • • • • •
-4
to . IE
vO o
POO
er< K. (v •=> K> «D
• • i • PKlO
POO
;
K c< t*
»o o to
t • •
52- -i'' ^^M ^•^^ ^t^ri HHH r-4
90
i
'X a. x
x a CD
I a.
■a o • a C9 CO O O C9 CD a o
«M CM CVJ CM CVJ CVJ CVJ CVJ CVJ CVJ CVJ CVJ CP o to o e o coo CD CO CO * 4. ♦ * * +• ■4 * 4. * 4- 4. lu UJ UJ u- U. UJ UJ U. UJ UJ UJ UJ to in j- CD v0 a N- ^ «B «~t CVJ vO o o ro *? O CVJ r4 HO a» J- j- e to T-l ^ T* CVJ CVJ «=> CVJ CVJ J- N. <r vt in s vO cr j" CVJ m in J- <o \0 tO N. rA <r to CP N. vO tO -*• tO • t .• • "X • • • • • • t
UH CVJ W ro j. to tO tO vO to in cvj 1 1 I i 1 1 1 • 1 i i i
ro ro in irwn M tO CVJ CVJ CVJ CVJ e> o o a o o o a o CD o o 1 1 1 1 1 1 I 1 l 1 1 1
UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ !* cr to <-• KO S (OiCN in J- .* CT tO m O* tO T4 CJ> tO to to to cr» to r- cr T-l co «o h- tO w to CVJ CVJ CM cr OO IV CVJ OO OSS S vO tO cr -♦ to ro o in in in es e- ro in • • • • * • • • • • • •
IN w* T-l T-I CVJ cr J- fw »-( ■»H »-l «H
» 1 I 1 I 1 1 1 1 1 fcj CM CM ; CVJ CVJ CVJ cvj CVJ ro ro ro i>o
r ° ° i .CD to to coo O CO o * * 4. ! * * 4- 4. 4- + 4r 4- 4. UJ UJ UJ UJ UJ UJ UiUiUi UJ UJ UJ ro r*» er a* to cr> o> »-t ,»■ -*• K) CD f!iC«0 tO © TJ. ^H s cr <r> cy> s w-t m o CO TH N- NlftN K vOiH T-I T-I tfl tO C* -* ^j- vO ro nsn H J- h- t*- w4 in in cr> o «D O ^-t
1 • • • • • » • • • • • • bo oo co. oo <r o^ o*> cr> »4 •»-! »H T-t
•» e o o o coo CD CD CD
1 1 1 1 i 1 1 1 1 1 1 1 UJ UJ K> CVJ
UJ UJ UJ UJ UJ lb lu U. U. UJ tO ; to a> cs »-< -* m tO cv; «c
r^ -* *"• 1 T-l a Si tO «-4 S S TH O tO vO in in N- ■* J- OO tO to C7> in CM c tO tO CVJ N- N. 0> oo CO CM *H BC CT> *-i «-i ro ^-
^ U^ tO iDSN
JJ • • • • • • • • • • CVJ ! CV) CVJ CVi CVJ CVJ f«J fu CVJ CM
H *-• '*"' 1 T-l w4 «H TH O ■•H *-» »H T-l P O o 1 O o o O CD O ooo 4 4- * i * 4- * 4- 4- 4. 4- 4- 4- jj U1 UJ UJ UJ UJ UJ U. UJ U> UJ UJ x> co VD ! oc> •rJ AT to ■^ to J" tO OO S- tO in in in o w1 to cr «r «-i CM CT CVJ «o : OO cv in in oo to tO CT> tO t* K T-I i «-i f- ** rtWlO OO CT> CM fo N- er C3 or in in CVJ CD co r^ j- !• • • I • • i • • ! • •_ • • • H *"* CV. ! CM w4 «H rtlAH ^ WiD
U <H "H | • 1 1 1
*-t »H CVJ CM CM »-( CO O 0 i £3 «= F= c o e Poc
II ' I i 1 1 1 1 I 1 .' » ' UJ u UJ ! UJ U UJ Ui »J-' UJ UJ U- U cr> to in , r- a> CVJ in to to vO in CM
*» ■» tO «JD tv m mu\H vor IT to CO tO ! ro to a. tO to cr> cr co cr cr IP s l N. ou m in u <r (T<Trl
r * IT) . i»- ^-> oo «t f tO tO C CM
Ki CVJ CVJ ' CV CVJ «-■ «r< «-< tO lO T< r(
ro N- I I i t 1 1 1 1
co 1 CD K N- S C3 f ro s c f>0 tO K> tO
to C to tO tOCffl W vDo «= , €3 fO tC vOPK, ro tt> o
f> »o c to ro UJ to co ro ro tt cr :». • • 1 • • • • • • • • • fo tO CD . e> ro to to co ro to tO o CVJ cvj to i f to to . «44 j- J- in
f4**"^ i w4 •-4 •-< ^-1
. .1 Hrlf4
C3 ca e O O a a CO C9 CO o a
CM CVJ CVJ CVJ CVJ CM CM T4 T4 T-l T4 T-I CO CO o CO (O CD O CO CO CJ to a 4i 4> * 4> 4- 4> 4/ * 4- 4> 4» 4> UJ UJ UI UJ UJ UJ UJ UJ UJ UJ UJ UJ K. to in CO «4 oo tO CVJ in in vO in tn |w to tO vO T< CO aD CO T-l in ro IS. a in S OO ro tO N. cr tO T-l T-l vO tO «-) T-l vO <S OO CM vO in to a* tO s ^ -» <T ro to in «-• T-l CM s • • • • • • • • • • • •'
CVJ tO J" J- CM *4 T4 ro T4 T4 CM T4
1 I 1 1 1 CM CM ro fo ro cr cr cr cr -*■ cr cr CD co a a co o CD CD O CO to CO
1 1 I 1 l 1 1 1 1 1 1 » UJ UI UJ UJ UJ UJ UJ UJ UJ UJ UI UJ ro O CM o oo CO tO to cr CD CVJ T4
<T> tO N. -3- in OO CT« S <H OO ro ro CM rv ^ ro *H CO cr> •H S cr ro to tO «-i K. r*. in ao cr co OO o* CM tO
CM cK in ct r** ro ro tO vO cr to tO ■ • • • • • • • • • • • • *-» «H OO «o ro cr ' *>os N. in CM
• 1 1 ( l i • ro ro ro ro ro ro ro ro r<« ro r^ ro a a co O CD CD CD O "C' o to o 4> * 4> 4- 4- 4- * 4- 4. 4- 4> *
» UJ UJ UJ ; Ui UJ UI UJ U, UJ UJ UJ UJ *-4 in r«- in -*■ cr CM cr o to in cr r- CT> CT> cr ro T^ T-l cr» «o CO S fv «-< ro ro ro -* CO CD T^ in in CO CO ■»-• o> ro ro J- cr cr ro CM CVJ CM TH
»-t «H CM , CM CM CM CM CM CM CM CM CM
CD O CO co a CD CO co co CO to to » I I 1 t 1 1 1 ! 1 1 1
Ui UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ U- o OO OO tO S K- in to ^t J- ro r>. «-t *-t ro K? m «H T-l in T-* T- T-l U in CO CM CM OO cr cr cr to tO c; m w-t CM "> in ro CD CD tO CM CM CJ> if>
r> f- tO to in ^t cr CM T4 T-l CT> OO ' • • • • • ■ • • • • • • • ^ CM C\J CM CM PJ CM CM CM CM T-l «-l
|H *-* to «3 TH b CO CO CO to CVJ »H CD O CO co co CO CD «P o CD a co *• * 4- 4> 4. 4> 4> 4- 4- 4- 1 1 UJ UJ UJ UJ U- u, UJ UJ U- u UJ u s ro ec CM CO CD cr e= in U^ h. to r-t K OO 00 «0 OO C5 cr —I f^ 00 CM tO .* ■* J" TH T< T-l fv CVJ CM S (T* CM N. h-i CV. tO cr or.- CM uv U> to CO jf in oo OO CD T-l T-l r J" * a to
ro to T-i in in T4 uu oo '■^t T-l T-l CM m i l I t 1 1 1 1
—{ •-i «-< *-i *J »H T-l T-l T-l TH •H TH o c= O CO CD CO co CO to «= to C> CD
Z 1 1 1 • 1 I 1 1 I 1 1 1 U! UJ U, UJ U U u. u.' u. UJ UJ UJ
1- C5 J- ^ oo h- ■* aO lO fJ CO in r*. ae cx> tr> ro cr CD CD tL» ro oo oo cr in <r J- ro t2 CD CJ> to in r- CD CO OO CD Q. «H in to to O' in in r- cr es ro CM
CV. a* cr> cr o' ro tr ro to ro CM CM
_J •-! r»* in IT tO h- N- N S r- N- S UJ x r- O CD O CO c CD er co co o to CO CO CO o CD er to en co to CD er cr
CO C CD = CO CD CD CO CO (=3 o o Z t= cf op ec CM tO tO c -» cr ao CM t-t • • • • • • • • • • • • <X CO wH CM CM .* in in r- oo CO 0^ T-l r irk in in in in in in in in in in >o
»H «-l »4 »4 T-l »4 T* T-l T-l T-l ▼4 T4
91
■7
x;
o o o ♦ ♦ ♦ UJ UJ UJ NW« <T» CT> -H «o «o in \DO(M
X Mj* -4 _t «-»
CM CM CM OOO * + + Ul UJ UJ CM a* CM
in in CM J-
CM CM CM ooo 4> UJ
oo «o
00 oo
f*. N.
UJ UJ <r ro CM ro
to CM 00 N.
CM CM <H ooo ♦ * + UJ UJ UJ in ^ CM N5 Jf \D
CM 10 <0 ** CM in
UJ
in «o *4 » i i
to ro ro o o^o * * *- UJ UJ UJ
ro ro ^ «-«in o <p o N- J>vDo) • • •
(CM «M CM
I I I ro fO ro O O O * + ♦ UJ UJ UJ
*-t «-t o o oo ro N. vD «o
• • • CM CM CM I I I
I I I to ro ro
UJ UJ UJ o» ifi in o N- oo K) «± CM oo o ro u\ -f *-• • • •
CM CM CM I I f
OOO
ro«oo CM CM ro
o fO *0 ro
v0 o ro
»-• «-i ro l l l www ooo •♦■ + ♦ UJ UJ UJ 0> CM N» 0O fC o> CM w* O ro «o «o <•■< r* ro
a • • CM m* «4 I I I
! 1
i I
j i
fO K. O ;
fO «C C
o r<- N- e w ifi en ic cr ro tL
K «=» r»* »o e t« v0 P K vo «= ro
W»Co ro a. o Kite
j- J- in
•4 CM CM ooo * * ♦ UJ LUUJ
<T> CM N.
vo in o> in in in • • •
ro «-4 «-t •
ro CM CM ooo * <¥ 4> UJ UJ UJ <r» oo .# a> o »H o o «~» ao wl to ro in vo
CM CM -H OOO * * ♦ UJ UJ UJ in tr» CM CM *4 10 CM J- 0O a» p -H won • • t
CM ro ro ooo ♦ * + UJ ID UJ ao tO J- ** .* r^ CM CM CM ro ro oo u> CM ro
UJ UJ UJ -± .* in in m in oo •«-< ro CM oo N-
• • • -*" oo vO
I to ro to ooo ♦ * ♦ UJ UJ UJ CJ^ CJ^ to in in vD CM ro u> «o N. *-< ro w ro
I <
o o o ♦ * 4. UJ UJ UJ o o \0 O <T» fvj ro o eo in «-* in vo »4 in • • •
vD (T» iO I I t
ro ro ro o o o * + + UJ UJ UJ *-• —i to vo in vo vo in in ▼H vO tO « CM CM
ro i j i
O; Zi
1 i j . 1 !
o. OOO. ooo o a o ooo
_J i 1 1 j -I UJ
i ;
x r~ e> o cec o cr o OOO] </) o o o ooo ooo boo
ooo ° e o ooo Poo 2 c j- oo / 0C CM %D tO t 4 J- oo CM 1-4 • « • "J • • ■ • . • • I • • •
«OHW CM Jt in in K «o » <r V* x in in in in in in in in in in in «o
•H »"• «-l *••»-»«-« «■« «-l w4 n*4H '•N .1 i " -L i I
92
1 [ e © «9 O a o o o r> O |B e> es er a cs a is
I.I «-l o o o *H *-i ot «H O a a ▼-i «-t ^t «-i 1-1 er cv
Z o o o a O CD a er cr er o a cr er er cr cr cr
.♦ ♦ * ♦ 1 1 1 1 * *■ + ♦ ■* * * * * * a Ui u. UJ UI Ui UI UI UI u. Ul UJ UJ Ui UJ UJ Ul UJ Ul
10 a o» »-i CP \0 in ao a tO iO o ro in in CD »-l <T>
X <Vi o vO cr »H in CV cr in ro cr ■a CV cr m J- -3- -» o tn CV «-i ^ re .*■ ■«H CV er cr cr ro co a *-4 ro j- -° J- v£> iv v£) j- tw vO CV in r^ er u\ *-■ cv eo O •»-!
X f*. K r- in N. in wH CVJ J- eo in ro ro -* cr <T> cv m
•H o> w ro m CVJ cv CV CV ~* I i 1 l i 1 .» m in in in in in in in in in J> J- J" -* .* ro -a- e c o er o O o a er er o cr o c CD o O cr
1 I • 1 1 i 1 l 1 i 1 • 1 1 1 1 1 1 LU UI UI UI UJ UJ U* UI Ui UJ UJ UI Ul UJ Ul u_ UJ UJ r^- ro in cv CP o J- CO <T> in vO \D o*> o-> in in eo r»
*•* X a o
«o in rv er <X) in CV ao J- .» v£> CV ro eo CO ■a 1^ ^ J- cr •H N- cr ro CO vO cr CV -* ro j- ro rr> N. r^ ro •v ro in fO cvi ao ^-t i-t CV cr ro .* CO CJ f- ■»-l J- «P -* -4" ro —( N. CT» N. CV CV N- CO J- ^t CV J- in cv »v
M il> CV
1 CV
1 ■4-
1 1 -*■ ro l 1
CV -H 1
•-i «-t -4- CO CO wi uD
www ro to W M ro I-) ro ro ro ro ro ro ro ro ro O O to er CD a cr a cr a a er. D e= CD cr o er * * '♦ * * + + *■ * 4- + * + + + ♦ >♦■ * UI Ui U- . UJ U- UI UJ UI u, UI UJ u. u u. UJ UJ UJ Ui
, ro in '/ r- cr
»-f <T> CT> -* cr J-eo eo r«- «-i eo ro CD tn ro a> in .*- IV -» J- cr «-i er eo m ^H vO in ▼H cr iv
X CK S N. \D in in ro cr <T> CV ro ro cr -* ^f cr cr »•< *H «-< <H «H *-i t-t ▼H CD er a cr tr> t>~ \D OJ vO J- O-
z CV CV CV cvi CVJ CM CV CV CV CV CV ▼H ~4 T4 V* «H ** CV
t ▼H CV CV CV cv CV CV cv cv
«9 O O er a CD er o cr o er o o o o a a cr
1 • UI Ui
... lO O ll. 1 1 • 1 1 1 1 1 1 » 1 1 1 1 1
u> UJ UJ UJ Ui UJ UJ Ui UJ u UJ UJ U. Ui UJ ' * N- in in v£> J- «=> ro <r> r* eo eo TH ro ro ro iv U\ CV *-< ▼-I o N r- ro »- \u ro f- CV ro r- cr cr cr>
»-4 in TH ID vC C3 CV r.1 j- J» J- o J- -4- in iO in K co X in cv eo CO Ul ^-4 ■>-t N- ro ro -* CV CV er a <T> cv cv a to N- IT m -* r> n »H cr er cr in in «-( vC vO ro er
«H ~* *-i I
v* >r-t «H «-H *-> eo »- r^- U2 i
j- j- ro cv
*4 *H »-4 1
w 1 CV CV »-< •H ^1 «-) •-< *-< ■r* •-) er -r*
C3 «? ks O c o IP o a ' o cr cr ep cr c; cr er o 1 1 i 1 1 1 • l 1 "1 1 1 I 1 1 1 + *
• UI U/ Lu Ui U, U UJ UJ UJ UJ U> UJ u, Ui U UJ UJ U- ' wt PI (r, en in fvj ro er »H «=. c -3-
-» in J- IV r*- cv
»© f*- ^ sO er vO <r> CV r>. ro in fT> eo K m •-• ^ CD J- lO ro e CL .* in aj re ^ e? eo ro m-i in cr rv jh in cr v£> e= a> CT> cr cv cr u> ro c: -4- N- en cr eo
cr C^«X) iO IV er T-I J- ro t= ^( ee K in CT- en in v£> & • •
r- • ; • • • • • • • • » • • • • •
in J- CV ^H in "~* «-■ *H ^1 cv I* J1 rv ao •
eo 1 1 1
o cr P Cr c a e> cr c. O o cr CD er CD CD o er 1 • ii 1 • l i 1 f 1 1 1 1 1 1 1 • 1
U-' UI U. UJ UJ U' UJ lu U. Ul Lu UJ UJ UJ U U- Ul o -» CF> K «-l TH er J- N- eo T-I »- CV eo ro vO KD eo m IM B3 cr UA ^. iO il) ■-• er cv tr« er> ro ed r»> U^ cv C O' N ID e; CV CV C! -* j- a> UO r^ IV rr -T err ^,
^ CV ro N r>- CVJ UL- VO C3 K- r» ir. to \D r^ J- J- 1-- eo CV CM CV OJ rr> f ro -* ^r -3" -T JT ■S j- m ro ▼H CT>
I^N r- N» N f^ r^ » N- N- N- N. r^ K K IV r- *o
CJ C5 er e? e er er er er e=> er> er er er er CJ CD er C9 tD cr e? o cr IP cr Cr C3 CZ> CD cr es CD c; tn er o e> D C? «= o IP O CP •P cr- er O cr CD - er e=. o cv <x» C3 c J- ao CO CV vC UJ er rf J" CO CV CV vD C
I •-< cv .* J- in v£> v£) «p (P a> «-< CV CV ro in in vD cd X . «£> *C lO IO vO «X> vO \D iD «ONr« s- f-- N- K rw iv
' __ . :' * 1. . J_. i i.- - i _.^
93
\
I. ' 00*4 •4'T« <«H *4 *-4 «4 w-t 0 0 O «-4 O (9 «-l *4 e e «P a 0 19 0 e 0 B O (9 0 a 0 000 ♦ ♦ 1 1 1 • 1 1 1 1 * * ♦ I ■*• * ♦ *
'^' tu UJ UJ UJ LU UJ UJ UJ UJ UJ UJ UJ UJ W UJ UJ UJ UJ t- *-4 W K- in »-» *-4 wt a* m (Or4K in w \D tT» tT CM UJ O N- ^1 in «-• uo w 0 ^ -H 0* r*- MCOO ro w 0 X CM er> jf ^ in .* ^ vO CM •* w in »o •«-» w u> in o> l-i w in .* o> -*■ J- ^ «o J- ■* co m w w ^ ^ f- «o
*. in CM a> -*■ CM o> in «o w* r> ^ •H CM «H K. 10 W 10
(Of4 Q> (J> T-l w & ■& N. CO »■* CM CM <J> K. N. W l«w 1 1 1 1 1 1 t 1 WWW w w w www www WWW W W CM 0 0 0 e 0 a 00a O O C9 e 0 a OOO ♦ * •♦ ♦ ♦ * + 4. * +*>•*■ + + ♦ 4> * *
<r UJ Ul UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ k. e 0 N. W 0» <T> 00 0 OO W t= *. .* CM CO C3 UJ Ul vO cs-CM CM a m inss «0 eO CM ^ CM CO in in ^
Ift •* w W N- CM CM co in in CM vO vO S (T 0 w rj W CM «M CM CM w w w -* -* in in in j- 0 *-) CM o> CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM NH J
_ j
1
1
i
i ]
i i
O O O O 0 a 00a 0 C9 0 0 0 0 0 0 0
COD CBD 'OP C
CM «0 CS
e> e o ceo opo ceo p c o oeo CStPO pop COO c 4 co eo CM a. a> c? .?
000 .? CO C\J
*-• CVJ j-
t L
^ in v0 U3 U3 \D
\0 «0 tT> 03 lO MD
a» «H CM tONK
CM w in *• N N-
in u? co f^ K K
_>a 1 —
9^
Jh
::A
Ar
~ -)' jl. -.'■■' CR.Zrn."''1'?.":" '0, :JZ
In.t'ri^ial ; r,'..-".
r . a c j i an i1 c 3 J. /i- ■' '■1 J^CO'^J;
-^ ---^ —. v^ p ,.
■ •"-> ,~ /~> -i ,"> ■■ -, ; fw
197' i"5 "10.'.'.''.'''3-'
. .C Ci a-llcal -ill""! —
no or in;; "n Ja:iaar;r "015 •* After June 1?7;<,
'■:or''-in"-; :°cr the Vonosnolan -.oirochor:ical Inatitr.to at their
■ 7i.il cortini'
Central inf"? iioorin~ V^iiicoc at Garacaa, Vonenreha
oc
7