Bsi bs en 02002 1 2005

BRITISH STANDARD AEROSPACE SERIES BS EN 2002 1 2005 Test methods — Part 1 Tensile testing at ambient temperature The European Standard EN 2002 1 2005 has the status of a British Standard ICS 49 025 05[.]

This Bri sh Stan ard was

published u der the authoriy

of the Stan ards Policy an

Strate y Commi e

on 3 J n ary 2 0

© BSI 3 J n ary 2 0

This British Stand rd is the oficial Eng lish lang uag e v er ion of

EN 20 2-1:20 5

ACE/ 61, Metal c materials for aerosp ce purposes, to S bcommit e

ACE/ 61/-/ 1, Mechanical testing of metal c materials, which has the

responsibi ty to:

— aid enquirer s to u der tand the text;

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interests informed;

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request to its sec etary

The British Stand rds which implement international or European

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This publ cation do s not purport to include al the neces ary provisions of a

contract User are responsible for its cor ect a pl cation

Compl anc with a British Standard do s not of itself c nfer im m unity

f om leg a l obl g ations

Sum m ary ofpag es

This document comprises a font cov er,an inside font cov er, the EN title p g e,

p g es 2 to 2 , an inside b ck cov er and a b ck cov er

The BSI copy rig ht notice display ed in this document indicates when the

d ocument was last is ued

The UK p rticip tion in its prep ration was entrusted b Tech ical Commit e

Aer ospace ser ies - Metal c materials - Test methods - Part 1:

Tensi e testing at ambient temperatur e

Sé e a r os atiale - Maté a x métal q e - Méth d s

d'e s is a plc ble - Par tie 1 : Es ais d tra tio à

temp ratur e ambia te

L f u d Ra mfa rt - Metal s h Wer kstofe

-Prüfv r fa r en - Tei 1: Zu v r su h b i Ra mtemp r atur

This Euro e n Sta d r d wa a pr ov d b CEN o 19 Se temb r 2 0

CEN memb r s ar e b u d to c mply w ith th CEN/CENELEC Inter nal Re ulatio s w hic stip late th c n itio s for givin this Euro e n

Sta d r d th statu of a n tio al sta d r d with ut a y alter atio Up-o-d te lsts a d biblo ra hic l r efer en e c n er nin s c n tio al

sta d r ds ma b o tain d o a plc tio to th Ce tral Se r eta at or to a y CEN memb r

This Eur op a Sta d r d e ists in thr ee oficial v rsio s (En ls ,Fr en h, Ger ma ) A v r sio in a y oth r la g a e ma e b tr an latio

u d r th r es o sibi ty of a CEN memb r into its own la g a e a d n tifie to th Ce tr al Se reta at h s th s me statu a th oficial

v r sio s

CEN memb r s are th n tio al sta d r ds b die of Au tr i , Belgium, Cy r us, Cz c Re u lc,De mark, Esto ia, Finla d,Fr an e,

Germa y, Gr ee e, Hu g r y,Ic la d, Ir ela d,Italy, L tvia, Lith a ia,L x mb ur g, Malta,Neth r l n s, Norw ay, Pola d, Por tu al Slo a ia,

Slo e ia,Sp in, Swe e , Sw itz r l n a d Unite K in d m

E U R OPE A N COMMI T TE E FOR ST A N DA RDIZ A TION

COMIT EUROPÉ N DE NORMALISATION

EUROPÄISCHES KOMIT E FÜR N RMUN

Management Cente: rue de Sta s r, 3 B-10 0 Brus els

Cont ents Pa e

F reword .3

Intro u tio

4 1 Sc pe 4

2 Normat ive referen e 4

3 Terms, definit i ns an sy mb ls .4

4 He lth an s fet y .7

5 Prin iple .7

6 Te tin req irement s .7

7 Te t rep rt .13 Annex A (n rmat ive) Ty pe of t est piece t o be us d for she t an st rip w it h t hick ne s le s t han or eq al to 8 mm .15 Annex B (n rmat ive) Ty pe of n n- mac ined t est piece t o be us d in t he ca e of bar, s c o an w ire w it h a diamet er or thickne s le s than or eq al to 8 mm .17 Annex C (n rmat ive) Ty pe of mac ined t est piece t o be us d in t he ca e of bar, s c o , plat e an w ire w it h diamet er or t hick ne s gre t er t han 8 mm an for forgin s an ca t i gs .18 Annex D (n rmat ive) Ty pe of t est piece t o be us d in t he ca e of t ube 21

Foreword

This Euro e n St an ard (EN 2 0 -0 1:2 0 ) h s b e pre are b t he Euro e n Ass ciat io of Aero p c

Ma ufa t urers - St an ardiz t io (AECMA -STAN)

Aft er e q irie a d v t es c rie o t in ac cord n e wit h t he rule of t his Ass ciat io , t his Sta d rd h s

re eiv d t he a pro al of t he Nat io al Ass c iat io s a d t he Oficial Serv ic s of t he memb r c u t rie of

AECMA, prior t o it s pre e t at io t o CE

This Euro e n Sta d rd s al b giv n t he st at us of a n tio al sta d rd, eit her b p blc t io of a id nt ic al

t ex t or b e d rs me t , at t he lat est b Ma 2 0 , a d c nflc t in n t io al sta d rd s al b wit hdrawn at t he

lat est b Ma 2 0

At t ent io is drawn t o t he p s ibi t y th t s me of t he eleme t s of t his d c me t ma b t he s bje t of p t ent

rig t s CEN [ an /or CE ELEC] s al n t b h ld re p n ible for id nt ify in a y or al s c p t ent rig t s

Acc ordin to t he CE /CENELEC Intern l Re ulat io s, t he n t io al st an ard org niz t io s of t he folowin

c u t rie are b u d t o impleme t t his Euro e n Sta d rd: Austria, Belgium, Cy pru , Cz c R ep blc,

De mark , Est onia, Finla d, Fra c e, Germa y, Gre c , Hu g ry , Ic la d, Irela d, It aly , L t v ia, Lith a ia,

L x emb urg, Malt a, Neth rla d , Norw ay , Pola d, Port ug l, Slov ak ia, Slov enia, Sp in, Sw ed n, Swit zerla d

a d t he Unit ed K in d m

Int roduction

This st an ard is p rt of t he s rie of E met al c mat erial st an ard for a ro p c e a plc atio s Th g n ral

org niz t io of t his s rie is d s rib d in E 4 5

This st an ard s e ifie t he re uireme t s for t he te sie t est in of met al c materials at ambie t t emp rat ure for

a ro p c e a plc at io s

It s al b a ple whe refere t o in t he E t ec hnic l s e ific t io or mat erial st an ard u le s ot herwis

s e ifie o th drawin , ord r or in p ct io sc he ule

Th folow in refere c d d c ume t s are in is e s ble for t he a plc atio of t his d c me t For d t ed

refere c es, o ly t he e itio c ite a ple For u d t ed refere c es, t he lat est e it io of t he refere c d

d c ume t in lu in a y ame dme t s) a ple

EN ISO 7 0 -1, Metal c m aterials – Verific tio n o f s tatic uniaxial testing m ac ine s – Part 1: Tens io n/

com pres sio n testing machines – Verificatio n a d c lbration o fthe fo rce-measuring s ystem

EN ISO 9 13, Metalc materials – Calbration ofe tens ome ters use d in u niaxial te sting

EN 4 5 , Aero spa e series – Metalc materials – G eneral organiz tio n ofsta dardiz tion – Links b twe n

ty e s ofEN sta dards a d the ir use

EN 4 5 , Ae ro space series – Me talc materials – D efinitio n ofgeneral te rm s

1)

A TM E-1012, Sta dard p ra tice fo r v rific tion ofspecim en algnm ent und rtensile lo ading

2)

For t he p rp s s of t his st an ard, t he t erms, d finit io s a d sy mb ls giv n in E 4 5 a d t he folowin giv en

in Ta le 1 a ply



1) Publs ed as A ECMA Prest an ardat t he date of publc at ion of t his st an ard

2) This stan ard is publs ed by: A meric an Society for T st in an Materials (ASTM), 10 Bar Harb r Driv e,

W est Con hohoc k en, PA 194 8-29 9,U A

Table 1 — Terms, definit i ns an sy mb ls

– – Te t piec e Th p rt io of t he t est s mple o whic h t he t en ie t est is

c arie o t

– – Pro ort io al te t pie e A t est pie e w it h a origin l g u e le gt h (L

0) h vin a

s ec ifie relat io s ip t o t he s u re ro t of t he c ro

s-s c t io al are (S

0) Th pro ort io alt y c oeficie t , K, h s

th int ern t io aly rec og iz d v alu of 5,6 for t est

piec es of circ lar cro s-s c t io Th g u e le gt h of a

pro ort io al t est piec e is t herefore e u l t o 5,6

0

S

Cert ain mat erial st an ard u e pro ort io al t est pie e

w it h ot her t ha t he 5,6 pro ortio alt y c efic ie t In this

c as , s e A

xfor th p rc ent ag elo g tio s mb l u e

– – No -pro ortio al t est piec e A t est piec e where t he origin l g u e le gt h is

in e e d nt of th c ro s-s ct io al are

Th in re s of t he ex t en omet er g u e le gt h (L

e) at

a y mome t d rin th t est

– MPa Limit of pro ort io alty Th st re s at whic t he st re s-st rain (or forc e-ex t en io )

relat io s ip d viat es from a st raig t ln

(pro ortio al t est pie e)

NOTE F r non-st an ard

pro ortional t est piece, se Ax

Elo g t io aft er fra t ure ex pre s d a a p rc ent ag of

th origin l g u e le gt h (L

0) for a pro ort io al t est pie e

n-pro ort io al te t pie e)

Elo g t io aft er frac ture ex pre s d a a p rc nt ag of

t he origin l g u e le gt h (L

0) for a n n-pro ort io al t est

piec e wit h a origin l g u e le gt h of L

0 For a n n-

pro ort io al t est piec e, t he origin l g u e le gt h is giv en

in mi metre , e.g A

5m

% Perc ent ag elo g t io (n n

st an ard pro ort io al t est

pie e)

Elo g t io aft er fra t ure ex pre s d a a p rc ent ag of

origin l g u e le gt h (L

0) for a n n-sta d rd pro ort io al

t est pie e wit h a origin l g u e le gt h of L

0

= x (e.g A

4D)

A n n-st an ard pro ort io al te t piec e is o e in w hic

th pro ort io alt y c oefic ie t h s a v alu oth r t ha 5,6

In t he ex ample a ov e th g u e le gt h is fo r t ime t he

diamet er, e uiv ale t o a pro ort io alt y coeficie t of 4,51

a mm Te t pie e t hick ne s Thick ne s of a t est piec e of re t an ular cro s-s c t io or

wal t hick ne s of a t ub

b mm Te t piec e widt h W idt h of t est piec es of rec t an ular cro s-s c tio ,

av era e widt h of t he lo git udin l st rip t ak en from a t ub

or widt h of a flat wire

D mm Tu e ex t ern l diameter Ex t ern l diamet er of a t ub

d mm Te t piec e diamet er Diamet er of t he p ralel le gt h of a c irc ular t est piec e or

diamet er of ro n wire or intern l diamet er of a t ub

c on n ed

Table 1 — T erms, definit i ns an sy mb ls (co nclu e )

E GPa Y ou g's mo ulu of ela t ic it y Th v alu of t he in reme t in st re s div id d b t he

c ore p n in inc reme t in st rain for t he st raig t p rtio

of t he st re s-st rain (or forc -ex t en io ) dia ram

of t he t est pie e Th c on e t of p ralel le gt h is

re la e b t he c nc ept of dist an e b twee grip for

n n-mac hin d t est piec es

s c t io al are (S

0) of t he t est piec e

b a s fix giv in t he pre c rib d p rc enta e of t he

origin l g u e le gt h for ex ample: R

aft er frac t ure

The ma imum d cre s o f th cro ss- se tio al are ( S

0 – S

u

ex pre s d a a p rc ent ag of th origin l cro s-s c t io al

are (S

0) i.e Z =

σ

origin l c ro s-s ct io are (S

0) of t he t est piec e

θ

°C Sp c ifie t emp rature Th t emp rat ure at whic h t he t est is t o b c rie o t

4 Healt h and safety

R es urc s, t est pie e , t est s mple , t est mat erials, t est e uipme t a d t est proc ed re s al c omply wit h t he

c re t h alt h a d s fet y re ulat io s/laws of t he c ou trie where t he t est is t o b c arie o t

W here mat erials a d/or re g nt s t hat ma b h z rd u t o h alt h are s ec ifie , a pro riat e pre a t io s in

c nformit y wit h loc al re ulat io s a d/ or laws s al b t ak en

5 Principle

Th t est inv olv s st rainin a t est piec e b a t en ie forc at ambie t t emp rat ure t o frac ture for t he p rp s of

d t erminin o e or more of, Y ou g’s mo ulu of ela t ic it y, pro f st re s, t en ie st re gt h, elo g t io , re u t io

Te t in mac hin a c ra y s al b v erifie at int erv als n t ex ce din 12 mo t hs in a c ord n e w ith

EN ISO 7 0 -1 a d s al b c ert ifie t o cla s 1 or b t t er

It s d sig s al p rmit a t omat ic lo din alg me t Th lo din sy st em alg me t s al b c e k ed at le st

a n aly with a st rain-g u e t est pie e Th difere c b twee th re ord d max imum a d minimum st rain

s al n t ex c ee 10 % of t he me n st rain at a a pro riat e v erific t io forc relat iv e t o t he forc es ex pe t ed

d rin a s b e u nt s rie of t est s R efere c e ma b ma e t o ASTM E1012 for a v erific t io met ho

It ma b c omp t er c ontrole a d c ap ble of a t omat ic c lc ulat io a d re ordin of Yo n ’s mo ulu of

ela t icit y, pro f st re s, t en ie st re gt h a d elo g t io

6.1.1.2 Ex t ensometer

Th ex t en omet er ac curac y s al b v erifie at int erv als n t ex ce din 12 mo t hs in a c ord nc e with

EN ISO 9 13 a d s al b c ert ifie for d t ermin t io of:

 Yo n ’s mo ulu of ela t ic it y t o c la s 0,5 or b t t er a d a t y pe t hat is c ap ble of me s rin ex te sio o

b t h sid s of a t est pie e a d alows re din s t o b a era e is prefere

 Pro f st re s t o cla s 1 or b t ter

Grip for t ub s may , in a dit io , u e plu s t hat s al b of:

 a a pro riat e diamet er in ord r to b grip e at b t h e d ;

 a le gt h at le st e u l t o t hat of t he grip a d ma projec t b y on t he grip for a max imum le gt h e u l

t o t he ex t ern l diamet er of t he t ub ;

 a s a e t hat s al h v n efec t o t he d format io of t he g u e le gt h

6.1.2 Mat erials/re gent s

Mat erials/ re g nts ma inc lu e s it able:

 d gre sin fluid ;

 rec ordin p p r;

 me n of elec t ro ic rec ordin , if a pro riat e;

 mark in ink s

6.1.3 Qualficat i n of perso nel

Te t in t o t he re uireme t s of t his t est met ho s al o ly b u d rtak en a d/ or s p rvis d b p rs n el w ho

h v e d mo st rat ed t heir c omp t en e b a s it able e uc at io or a pro riat e trainin a d ex perie c e Su h

c omp t enc e s al b d c ume t ed in a a pro riat e form

6.2 Te t s mple /te t pie e

Th s a e a d dime sio s of th t est pie e d p n o t he s a e a d dime sio s of t he met al c pro uc t a d

t he mec ha ic al pro ert ie whic h are t o b d t ermin d

Where s fic ie t mat erial is a aia le t he t est piec e s al b o t ain d b ma hinin a s mple from t he pro u t

in a c ord n e wit h A nn x A, C or D Howev r, pro uc t of c on t ant c ro s-s c t io (s ct io , b r a d wire in

ac cord nc e wit h Ann x B) ma b s bje t ed to t est wit ho t b in mac hin d

A mac hin d te t piec e s al inc orp rat e a t ra sit io ra iu b t w ee t he grip e e d a d t he p ralel le gt h if

t he e h v difere t dime sio s Th dime sio s a d t olera c es a d t he t ra sit io ra iu of a t est pie e s al

b in a c rd n e wit h t he a pro riat e a n x (s e 6.2.2)

Th grip e e d ma b of a y s a e t o s it t he grip of t he t est in mac hin (s e 6.3.3) Th p ralel le gth

(L

c

or, in th c s wh re t he t est pie e h s n t ra sit io ra iu , t he fre le gt h b twee t he grip , s al

alway s b gre t er t ha th origin l g u e le gt h (L

0)

6.2.2 Ty pe

Th main t y pe of t est piec e are giv en in A nn x es A t o D ac c ordin t o t he s a e a d t y pe of pro u t a

s own in Ta le 2

Bar, s c t io , plat e a d w ire of diamet er or

t hic k ne s > 8 mm a d for forgin s a d c ast in s

C

6.2.3 Preparat i n of t est piece

Mac hinin , if re uire , s al b c arie o t at ambie t t emp rat ure in a c ord nc e wit h a ma hinin proc ed re

Pre a t io s s al b t ak en t o minimiz s p rfic ial c old w ork in , a pre ia le h at in of t he p rt or s rfa e

ire ularit ie t hat c uld afec t t he re ult s of t he t es

Th s rfa e finis of t he p ralel le gt h s al h v a R

a

v alu n t ex ce din 0,8 µm

In t he c as of material wit h a elo g tio s ec ifie in t he mat erial st an ard to b le s t ha 10 %, t en ie t est

pie e of ot her t ha c irc ular cro s-s c t io s al h v e th e g s alo g t he p ralel le gt h a d t he t ra sit io

6.3.1.1 Determinat i n of t he original cros -s c o al are (S

0)

Th origin l c ro s-s c t io al are s al b c lc late from me s reme t of t he a pro riat e dime sio s, wit h

a ac cura y of 0,2 % or 0,0 5 mm, whic ev er th gre t er v alu , for e c dime sio

In t he c as of a le gt h of tu e, t he origin l cro s-s c t io al are (S

0) s al b c lc ulat ed a folows:

S

0

= πa (D – a)

W he u in t est pie e c on ist in of a lo git udin l strip c t rom a t ub , t he origin l c ro s-s c t io al are s al

b c alc ulat ed ac cordin t o o e of t he folowin e u t io s:

W he 0,17 ≤

Db

)2(61

2

aDDb

6.3.1.2 Det erminat i n of final cros - sec o al are (S

u

Th dime sio s of th t est pie e s al b me s re at t he lo at io of th fra t ure t o a a c ra y of 0,01 mm,

a d b u e t o c lc ulat e t he fin l cro s-s ct io al are

In th c as of a le gt h of t ub or lo git udin l t est pie e c ut rom a tu e, t he fin l cro s-s c tio al are s al b

c alc lat ed a c ordin t o t he e u t io s in 6.3.1.1

6.3.2 Mark in t he original gau e len t h (L

0)

For pro ort io al te t piec es, t he c lc lat ed v lu of t he origin l g u e le gt h s al b ro n e to t he n are t

1 mm Th origin l g u e le gt h s al b mark ed or me s re t o a ac cura y of ± 1 %

A fin sc rib d ln or a smal p nc he d t s al mark e c e d of t he origin l g u e le gt h

In is d s rib d ln s or p n h d d t s s al n t b u e o low d c t ilt y mat erials, o whic s c h mark in s

ma c au e premat ure faiure Th re omme d d met ho of mark in g u e le gt hs is u in st an ard

e gin erin mark in o t prac t ic e, b p int in t he p ralel le gt h of th t est piec e wit h a s it able mark in

me ia, s c h a q ic k -dry in in a d t he lg t ly s ribin t hro g t his c oatin

If t he p ralel le gt h (L

c

is muc h in ex c es of t he origin l g u e le gt h, for in t anc e, wit h n n-ma hin d t est

pie e , a s rie of ov erla pin origin l g u e le gt hs s al b mark ed; s me of t he e le gt hs ma ex t en u

t o t he grip

6.3.3 Met ho of grip in

Th grip s al b of a a pro riat e t y pe s e ifie in 6.1.1.3

For pro f st re s d t ermin tio , it is rec omme d d t hat pin grip s o ld b u e for al flat t est piec es u le s

t he t est pie e is to n row

Th e d of a lo git udin l t est piec e c ut rom t he w al of a t ub ma b flat t en d t o aid grip in , prov id d t hat

t he p ralel le gt h is n t afe t ed b t he flat t enin

6.3.4 Ex t ensomet er

Th ex t en omet er s al b at t ac he t o t he p ralel le gt h in s c a ma n r t hat it ac c urat ely me s re t he

ex t en io wit ho t d ma e to th g u e le gth

6.3.5 Temperat ure of t est

Th t est s al b c arie o t at 10 ≤ θ ≤ 3 ) °C u le s ot herwis s ec ifie In c as s of dis ut e t he t est s al

b p rforme at θ = (2 ± 5) °C

6.3.6 Spe d of t est i g

6.3.6.1 Y ou g’s mo ulus of ela t i it y (E)

Th t est s al b p rforme at t he s e d giv en in 6.3.6.2

6.3.6.2 Pro f st re s (R

p)

Th t est s al b p rforme at a c ont role strain rat e of:

0,0 3 to 0,0 7 (0,3 % t o 0,7 %) p r min a st rain rat e of 0,0 5 (0,5 %) p r min is prefere

For s e ial a plc t io s or mat erials, ot her t est in rat es ma a ply a d s al b s ec ifie in t he mat erial or

t ec hnic l st an ard or o t he draw in , ord r or in p ct io s h d le

6.3.6.3 Tensie st ren t h

(R

m)

If t he t est is t o b c ont in e t o fra t ure, t he st rain rat e of th p ralel le gt h ma b in re s d b y on t he

pro f st re s b t s al n t ex c ee a v alu of 0,1 (10 %) p r min

6.3.7 You g’s mo ulus of ela t i it y (E), s lec o of t est met ho

Y ou g’s mo ulu of ela t icit y s al b d t ermin d b o e of t hre meth d of whic h Met ho 1 is th mo t

a c urat e a d Met ho 3 t he le st ac curat e Met ho 3 s al o ly b u e whe n it her Met ho 1 n r Met ho 2

c an b a ple In c as of dis ut e Met ho 1 s al b u e

Met ho 1

Th te t pie e s al b lo d d t o a st re s b low t he lmit of pro ortio alt y a d u lo d d This s al b

re e t ed twic more Y ou g’s mo ulu of ela tic it y s al b tak en a t he a era e of t he t hre v alu s It is

rec omme d d t hat t he loc at io of t he ex t en omet er b c a g d for e c s c c es iv e d t ermin t io

Th init ial p rt of t he st re s-st rain (or forc -ex te sio ) ln ma b omit t ed t o c omp n at e for a y n n-ln arit y

at t he st art of t he t es

Met ho 2

Th t est pie e s al b lo d d t o a st re s b low t he lmit of pro ort io alty a d lo din s al c ont in e wit ho t

int eru t io t o d t ermin t he 0,2 % pro f st re s (R

p,2)

Th init ial p rt of t he st re s-st rain (or forc e-ex t en io ) ln ma b omit t ed t o c omp n at e for a y

n n-ln arit y at t he start of th t es

Met ho 3

Th t est pie e s al b lo d d wit ho t int eru t io t o d t ermin th 0,2 % pro f st re s (R

p ,2) It s al t he b

u lo d d t o 10 % of t he 0,2 % pro f st re s (R

p ,2) a d re-lo d d t o ju t a o e t he pro f st re s t o pro uc e a

hy st ere is lo p Y ou g’s mo ulu of ela t icity s al b d t ermin d from t he ln p s in thro g t he hy stere is

int erc pt s

6.4 Det ermination a d ex pre sion of re ults

6.4.1 Det erminat i n of You g’s mo ulus of ela t i it y (E)

Comp ter c ont role ma hin s are c p ble of c alc latin Y ou g’s mo ulu of ela t ic it y a t omat ic aly In whic

c as draw in of a stre s-st rain (or forc -ex t en io ) dia ram, alth u h re omme d d, is n t n c s ary

Oth rwis t he mo ulu s al b c alc lat ed b d t erminin t he slo e of t he st raig t p rt io of t he c rv o t he

dia ram W he st re s-st rain (or forc -ex t en io ) d t a is o t ain d in n meric al form, t he b st it t o t he slo e of

t he st raig t -ln p rt io of t he c rv ma b d t ermin d b st atistic al met ho s

Th v alu for Yo n ’s mo ulu of ela ticity s al b giv en in GPa u le s s e ifie ot herwis a d t he meth d

of it s d t ermin t io s al b stat ed

6.4.2 Determinat i n of pro f st re s (R

p)

Comp ter c nt role ma hin s are c p ble of c lc lat in pro f st re s a t omat ic aly , in w hic h c as draw in a

st re s-st rain (or forc -ex t en io ) dia ram, alt ho g rec omme d d, is n t e s nt ial Ot herw is t he pro f st re s

(or stre s s) s al b d t ermin d from a ac curat ely drawn c rv o t he dia ram