Post on 07-Aug-2018
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A13 –Materials Selection in Design 1
Materials Selection in Design
References1. Ashby, Michael F., Materials Selection in Design, Butterworth-
Heinemann, n! "!ition, 1###.
. Cambridge Engineering Selector v3.1, $ranta Design %imite!,
&ambri!ge, '(, ))).
Introduction
How !oes an engineer choose, *rom a +ast menu, the material best
suite! to his !esign urose s it base! on e/erience s there a
systematic roce!ure that can be *ormulate! to ma0e a rational!ecision here is no !e*initi+e answer to these 2uestions,
howe+er the roce!ure can be somewhat aroache! in a
systematic manner. Ashbys boo0 an! the &ambri!ge "ngineering
Selector 4&"S5 so*tware she! some light on the materials selection
!ecision ma0ing rocess.
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A13 –Materials Selection in Design
From Ashby6 7Materials selection inherently must be base! on at
least 8 inter-relate! criteria6
• Function o* structural comonent• Materials a+ailable an! their roerties• Shae an! si9e o* structural comonent• :rocess use! to manu*acture structural comonent• &ost an! A+ailability 4both o* material an! rocess5
Function tyically !ictates the choice o* both material an! shae.
:rocess is in*luence! by the material selecte!. :rocess also
interacts with shae -- the rocess !etermines the shae, the si9e,
the recision an!, o* course, the cost. he interactions are two-
way6 seci*ication o* shae restricts the choice o* material an! rocess; but e2ually the seci*ication o* rocess limits the
materials you can use an! the shaes they can ta0e. he more
sohisticate! the !esign, the tighter the seci*ications an! the
greater the interaction. he interaction between *unction, material,
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A13 –Materials Selection in Design 3
shae an! rocess lies at the heart o* the materials selection
rocess.7
Engineering Materials and their Properties
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>hen one or more these materials tyes are combine! we obtain a
comosite material. n what *ollows, we will not consi!er the
metallurgy an! chemistry o* materials; rather we will *ocus on the+arious roerties o* the material tyes that are o* imortance to
engineers.
Metals ha+e relati+ely high mo!uli o* elasticity an! high strength.
Strength is usually accomlishe! by alloying an! by mechanical
an! heat treatment, but they remain !uctile, allowing them to be
*orme! by !e*ormation rocesses. yically strength is measure!
by the stress at yiel!ing. ensile an! comressi+e strength is
tyically 2uite close. Ductility o* metals may be as low as ?
4high strength steel5 but may be 2uite high. Metals are sub@ect to
*atigue an! tyically are the least resistant to corrosion. Some har!
metals may be !i**icult to machine.
&eramics an! glasses also ha+e high mo!uli, but, unli0e metals,
they are brittle. heir strength in tension means the brittle *racture
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strength; in comression it is the brittle crushing strength, which
about 18 times higher then the tensile strength. &eramics ha+e no
!uctility an! there*ore ha+e a low tolerance to stressconcentrations. Ductile metals tolerate stress concentration by
!e*orming inelastically 4so that loa! is re!istribute!5; but ceramics
are unable to !o this. Brittle materials ten! to ha+e a high scatter
in strength roerties. &eramics are sti**, har!, retain their strength
at high temeratures, are abrasion resistant, an! are corrosion
resistant.
:olymers an! elastomers are comletely !i**erent. hey ha+e
mo!uli that are low, roughly 8) times less than those o* metals !o,
but they can o*ten be nearly as strong as metals. &onse2uently,
elastic !e*ormations can be +ery large. hey can cree, e+en at
room temerature, an! their roerties ten! to +ery greatly with
temerature. :olymers are corrosion resistant. hey are easy to
shae through moul!ing rocesses.
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&omosites can be !e+eloe! which combine the attracti+e
roerties o* the other classes o* materials while a+oi!ing some o*
their !rawbac0s. hey ten! to be light, sti** an! strong, an! can betough. Most rea!ily a+ailable comosites ha+e a olymer matri/
4usually eo/y or olyester5 rein*orce! by *ibers o* glass, carbon
or (e+lar. hey tyically cannot be use! abo+e 8)°& because the olymer matri/ so*tens. Metal matri/ comosites can be utili9e!
at much higher temeratures. &omosite comonents aree/ensi+e an! they are relati+ely !i**icult to *orm an! @oin. hus,
while ha+ing attracti+e roerties, the !esigner will use them only
when the a!!e! er*ormance @usti*ies the a!!e! cost.
Some important definitions for material properties
"lastic mo!ulus 4units6 si, M:a5 - the sloe o* the linear-elastic
art o* the stress-strain cur+e.
• oungs mo!ulus, ", !escribes tension or comression.
• he shear mo!ulus, $, !escribes shear loa!ing.
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• :oissons ratio, ν, is !imensionless an! is the negati+e ratio o* thelateral strain to the a/ial strain in a/ial loa!ing.
• Accurate mo!uli are o*ten measure! !ynamically by e/citing thenatural +ibrations o* a beam or wire, or by measuring the see!o* soun! wa+es in the material.
Strength, f σ 4units6 si, M:a5
• For metals, the strength f σ is i!enti*ie! by the ).? o**set yiel!strength, yσ .
• For olymers, the strength f σ is i!enti*ie! as the stress yσ atwhich the stress-strain cur+e becomes signi*icantly nonlinear;
tyically a strain o* 1?.
• Strength *or ceramics an! glasses !een!s strongly on the mo!eo* loa!ing - in tension strength means the *racture strength
t f σ
while in comression it means the crushing strengthc f σ which is
1) to 18 times larger.
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For metals, yiel! un!er multia/ial loa!s are relate! to that in
simle tension by a yiel! *unction; *or e/amle the +onMises yiel!
*unction6 1 3 3 14 5 4 5 4 5 f σ σ σ σ σ σ σ − + − + − =
'ltimate ensile Strength, uσ 4units6 si, M:a5he nominal stress at which a roun! bar o* the material, loa!e! in
tension, searates. For brittle materials 4ceramics, glasses an! brittle olymers5 it is the same as the *ailure strength in tension.
For metals, !uctile olymers an! most comosites, it larger than
the strength f σ by a *actor o* 1.1 to 3 because o* the wor0
har!ening, or, *or comosites because o* loa! trans*er to the
rein*orcing *ibers.
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Eesilience, E 4units 3 J m 5
he ma/imum energy store! elastically without any!amage to the material, an! which is release! again
on unloa!ing, i.e., the area un!er the elastic ortion
o* the stress-strain cur+e.
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Har!ness, H 4units6 si, M:a5
A measure o* its strength. t is measure! by ressing a ointe!
!iamon! or har!ene! steel ball into the sur*ace o* the material;
!e*ine! as the in!enter *orce !i+i!e! by the ro@ecte! area o* the
in!ent.
oughness, cG 4units6 FkJ m 5 an! *racture toughness, c K 4units61
si in ,1
M!a m 5A measure o* the resistance o* the material to the roagation o* a
crac0. he *racture toughness is measure! by loa!ing a samle in
tension that contains a !eliberately intro!uce! crac0 o* length c
4which is eren!icular to loa!5, an! the !etermining the tensile
stress cσ at which the crac0 roagates. Fracture toughness is
!e*ine! byc
c K " c
σ
π = , an! the toughness is
41 5
cc
K G
E ν =
+
, where
is a geometric *actor, near 1, which !een!s on the samle
geometry.
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%oss coe**icient, η 4!imensionless5A measure o* the !egree to which a material !issiates energy in
cyclic loa!ing. "ssentially, the ratio o* energy !issiate! to the
elastic energy 4*or a gi+en stress that the material is loa!e! to5.
Eelate! to the !aming caacity o* a material 4how much !aming
a material has5. * the loss coe**icient is 9ero, there is no !aming.
Deen!s on the *re2uency o* the loa!ing.
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Materials Selection Charts
Mechanical, thermal an! other roerties *or materials may be
!islaye! in a +ariety o* ways. >hat is nee!e! is a way tocomare materials in a use*ul way *or roerties that are imortant
*or the !esign roblem un!er consi!eration.
For e/amle,
• * we want a structure to sti** but light, then we want to choose amaterial that has a high sti**ness 4"5 to !ensity 4ρ5 ratio.
• * we want a structure to be strong but light, then we want tochoose a material that has a high strength 4 f σ 5 to !ensity 4ρ5ratio.
• * we want a structure that is tough 4resistant to crac0 *ormationor roagation5 an! light, then we want to choose a material that
has a high *racture toughness 4 #C K 5 to !ensity 4ρ5 ratio.
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Here are some charts *rom Ashby an! the &ambri!ge "ngineering
Selector +3.1 so*tware 4&"S5.
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Materials Selection - the basics
%ets ta0e a loo0 at the basics o* material selection. First we nee!
to !e*ine the concet o* material indices. he !esign o* any
structural element is seci*ie! by three things6 the *unctional
re2uirement 4F5, the geometry 4$5 an! the roerties o* the
material o* which it is ma!e 4M5. he er*ormance 4:5 is
!escribe! *unctionally by an e2uation o* the *orm6
Functional $eometric Material, ,
Ee2uirements, :arameters, :roerties,
4 , , 5
f $ G M
f $ G M
=
=
he 2uantity !escribes some asect o* the er*ormance o* the
comonent6 its mass, or +olume, or cost, or li*e, etc.
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n many cases, the three grous o* arameters are searable so that can be written as6
1 3
4 5 4 5 4 5 f $ f G f M =
>hen the grous are searable, the otimum choice o* material
becomes in!een!ent o* the other !etails o* the !esign, i.e., it is the
same *or all geometries, $, an! *or all the +alues o* the *unctional
re2uirement, F. he otimum subset o* materials can now be
i!enti*ie! without sol+ing the comlete !esign roblem, i.e.,
without consi!ering or e+en 0now all the !etails o* $ an! G . he
*unction 34 5 f M is calle! the material e**icient coe**icient, or
material inde%. %ets ta0e a loo0 at an e/amle to see how this
wor0s.
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Example 1: Material index for a light strong axial bar !rod"
>e want to !esign a bar o* length & to carry a tensile *orce $
without *ailure; an! to be o* minimum mass. hus, ma/imi9ing
er*ormance means minimi9ing the mass while still carrying the
loa! F sa*ely. Function, ob@ecti+e an! constraints may be liste! as6
Function6 A/ial ro!
e nee! an e2uation !escribing the 2uantity to be ma/imi9e! or
minimi9e!. his is the mass m o* the ro!. his e2uation, calle!
the ob'ective function, is gi+en by6
m (& ρ =
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where ( is the cross-sectional area o* the ro! an! ρ is the !ensityo* the material out o* which it is ma!e. he length & an! *orce $
are seci*ie! an! are there*ore *i/e!; the cross-sectional area A is
*ree to choose.
>e coul! ob+iously re!uce the mass by re!ucing the cross-
sectional area (, but there is a constraint; the area must be
su**icient to carry the loa! an! not *ail, i.e.,
f
$
(σ ≤
where f σ
is the *ailure strength. "liminating ( *rom the last twoe2uations gi+es6
4 54 5 f
m $ & ρ
σ
≥
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Gotice that the *irst term contains the seci*ie! loa! $ while the
secon! term contains the seci*ie! length & . he last term
contains the material roerties. Hence, the lightest bar which will
carry $ sa*ely is that ma!e o* the material with smallest +alue o* f ρ σ . Gote6 we shoul! be inclu!ing the sa*ety *actor S$ here
so that becomes f $ ( S$ σ ≤ . Howe+er, i* the same sa*ety*actor is use! *or each material in a roblem, its +alue !oes not
enter into the material selection.I
t might be easier, or more natural, to as0 what must be ma/imi9e!
in or!er to ma/imi9e er*ormance. >e there*ore in+ert the
material roerties in an! !e*ine the material inde% M as
f M
σ
ρ =
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The lightest bar that will safely carry the load $ without failing
is that with the largest value of the material index M # his in!e/
is sometimes calle! the secific strengt).
How !o we !etermine the can!i!ate materials with the best
4largest5 f σ
ρ ratio >e use the
f σ
ρ chart in Fig. =.= *rom Ashby,
or generate the chart using the &"S so*tware.
Gote6 he material in!e/ *or stiff , light bar is similarly obtaine! as
the largest +alue *or the *ollowing material in!e/ M .
E M
ρ =
>e now use the E
ρ chart in Fig. =.3 *rom Ashby 4or &"S5.
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Example $: Material index for a light stiff simpl% supported
beam
&onsi!er a simly suorte! beam o* length & , s2uare cross-
section 4b/b5, an! sub@ecte! to a trans+erse *orce $ at mi!-san.
>e want to !esign a beam which must meet a constraint on its
sti**ness S , i.e., it must not !e*lect more than δ un!er the loa! $ .
Function6 Beamhat !oes the term stiffness mean Eecall that *or a cantile+er
beam with a loa! $ at its en!, the !e*lection is gi+en by3
3
$&
E# δ =
L/2 L/2
F
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which can be written as3
3 E# $ S
& δ = = . he term
3
3 E# S
&≡ is calle!
the stiffness an! is similar to a sti**ness coe**icient in a *initeelement analysis. Hence, *or the cantile+ere! beam6
$ S
δ = .
For the roblem at han! 4simly suorte! beam with oint loa! at
the center5, beam theory gi+es the ma/imum !e*lection 4at thecenter o* the beam5 as6
3
=
$& $
E# S δ = =
where 3= E# S &=J7sti**ness7 o* the simly suorte! beam 4*or a
oint loa! at the center5. he constraint e2uation than re2uires that
3
= $ E# S
&δ
= ≥
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he moment o* inertia is gi+en by6
3 =
4 54 51 1 1
base )eig)t b ( # = = =
Gote that the length 4 &5 is seci*ie! an! the sti**ness S is seci*ie!
by e2uation . he area ( is *ree to be !etermine!.
he mass o* the beam 4ob@ecti+e *unction5 is gi+en by6
m (& ρ =
he mass can be re!uce! by re!ucing the area, but only so *ar that
the sti**ness constraint e2uation I is still met.
Substituting # *rom e2uation into gi+es
3
= $ E(S
&δ
= ≥
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Substituting ( *rom e2uation into e2uation gi+es6
( )
1 3
1
1 3
=
4 5 4 5 4 5
S
m & & E
f $ f G f M
ρ ≥ ⇒
Gote that we ha+e searate! the !esign roblem into the three
arameters6 *unction 4F5, geometry 4$5 an! material 4M5. *)e
best materials for a lig)t+ stiff beam are t)ose ,)ic) ma%imi-e t)e
material inde% M 61 E
M ρ
=
t will turn out that the abo+e result is +ali! *or beams with any
suort con!ition an! with any tye o* ben!ing loa! location or
!istribution. >e now use the1F E
ρ gui!eline in the
E
ρ chart in Fig.
=.3 *rom Ashby 4or &"S5 to !etermine the best can!i!ate materials.
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Example &: Material index for a light strong simpl% supported
beam
n sti**ness-limite! alications, it is elastic !e*lection that is the
acti+e constraint, i.e., !e*lection limits er*ormance. n strength-
limite! alications, !e*lection is accetable ro+i!e! the
comonent !oes not *ail, i.e., strength is the acti+e constraint.
&onsi!er the selection o* a simly suorte! beam 4s2uare cross-
section5 *or a strength-limite! alication. he !imensions are as
in the re+ious case. he !esign
re2uirements are summari9e! by6
Function6 Beam
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he ob@ecti+e *unction is still on mass e2uation I but the
constraint is now that o* strength, i.e., the beam must the suort
the loa! without *ailing. he ben!ing moment is a ma/imum at
the center an! is e2ual to = M $&= . he stress at the to sur*ace4 ma/ y y= 5 is gi+en by ma/ ma/4 5 F 4 5 F4= 5 My # $&y # σ = = . Hence Fis gi+en by ma/4= 5 4 5 $ # &yσ = . he *ailure loa! f $ occurs when
f σ σ = , or
ma/
f f
# $ C y &
σ =
where C is a constant !een!ing uon suort con!itions an!
loa! alication!istribution, an! ma/ y is the !istance between the
neutral 4centroi!al5 a/is o* the beam an! its outer most *iber. Gote
that *or the simly suorte! beam with oint loa! at the center,
=C = 4as !eri+e! abo+e5 an! ma/ y b= 4hal* the height5. 'singe2uation an! e2uation to eliminate ( *rom the ob@ecti+e *unction
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in e2uation gi+es the mass o* the beam that will suort the loa!
f $ 6 3
3
3
f
f
$ m &C &
ρ
σ =
Gote that f σ is tyically yσ *or !uctile metals. he mass is now
minimi9e! by selecting materials that ma/imi9e the material in!e/M6
3 f
M σ
ρ =
As state! be*ore, the !esign re2uirement is characteri9e! by6
*unction, an ob@ecti+e an! constraints. >hat is the !i**erence
between constraints an! an ob@ecti+e A constraint is a *eature o*
the !esign that must be met at a seci*ie! le+el 4*or e/amle,
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!e*lection or sti**ness5. An ob@ecti+e is a *eature *or which a
ma/imum or minimum is sought 4mass in the last *ew cases5.
he ob@ecti+e *unction is sometimes not easy to choose because
there may be many otions. For e/amle, the ob@ecti+e *unction
might be cost, it might be corrosion resistance, it might be elastic
energy storage 4*or a sring5, it might be thermal e**iciency *or an
insulation system, an! the list goes on.
>e note *rom these three cases, that the satis*action o* the
ob@ecti+e *unction re2uires choosing materials where is a ratio is
ma/imi9e!. :lotting these sti**ness to mass 4weight5 or strength to
mass ratios *or broa! classes o* materials allows one to +ery
2uic0ly see which materials are 7better.7 Gote also that, li0e the
last e/amle, it is o*ten not a simle ratio li0e F f σ ρ but
something more comle/ li0e3F
F f σ ρ , or *or the !e*lection-
limite! case 1 E ρ .
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Example ': Material index for a cheap stiff column
>e !esire the cheaest cylin!rical column o* length & an!
!iameter r that will sa*ely suort a comressi+e loa! $ without
buc0ling. he re2uirements are6
Function6 &olumn
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elastically i* $ e/cee!s the "uler critical loa! crit $ . he solution is
sa*e i*
crit E# $ $ n &π ≤ =
where n is a constant that !een!s on the en! con!itions 4nJ1 *or
inne!-inne! con!ition, nJ= *or clame!-clame! con!ition5.
For the cylin!rical cross-section , the moment o* inertia is
= = 4= 5 # r (π π = =
where A is the cross-sectional area. Gote that the loa! $ an! the
length & are seci*ie!; the *ree +ariable is the cross-sectional area
(. Substituting into gi+es
=crit
E( $ $ n
&
π ≤ = . Substituting A
*rom into this last result gi+es
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1F 1F 3
1F
= mC $ C &n & E
ρ
π
≥ ÷ ÷ ÷
As be*ore, we obtain the *unctional, geometry an! material
arameters. he cost o* the column is minimi9e! by choosing
materials with largest (alue of the material index gi+en by6
1F
m
E M C ρ
=
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Table 6.6 Procedure for derivin material indices (from Ashby)
Ste (ction
1 Define t)e design reuirements/
4a5 Function6 what !oes the comonent !o
4b5
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= De+elo euations *or the constraints 4no yiel!; no *racture;
no buc0ling, etc.5.
8 Substitute *or the *ree +ariables *rom the constraint
e2uations into the ob@ecti+e *unction.
Grou t)e variables into three grous6 *unctional
re2uirements 4F5, geometry 4$5, an! material roerties 4M5;
thus
:er*ormance characteristic 1 34 5 4 5 4 5 f $ f G f M ≤
or :er*ormance characteristic 1 34 5 4 5 4 5 f $ f G f M ≥
C ead off the material in!e/, e/resse! as a 2uantity M,which otimi9es the er*ormance characteristic.
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Table !." E#amples of material indices (from Ashby)
$unction+ 2b'ective and Constraint #nde%
)ar, minimum weight, sti**ness rescribe! E
ρ
)eam, minimum weight, sti**ness rescribe!1 E
ρ
)eam, minimum weight, strength rescribe!
3 yσ
ρ
)eam, minimum cost, sti**ness rescribe!1
m
E
C ρ
)eam, minimum cost, strength rescribe!
3 y
mC
σ
ρ
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A1 - Design *or &olumn an! :late Buc0ling 3
Column, minimum cost, buc0ling loa! rescribe!1
m
E
C ρ
Spring, minimum weight *or gi+en energy storage
y
E
σ
ρ
*hermal insulation minimum cost, heat *lu/ rescribe!1
mC λ ρ
Electromagnet ma/imum *iel!, temerature rise rescribe! C κ ρ
4 ρ J !ensity; " J oungs mo!ulus; yσ J elastic limit;
mC J cost0g; λ J thermal con!ucti+ity; κ electrical con!ucti+ity;
C J seci*ic heat5
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A1 - Design *or &olumn an! :late Buc0ling 3#
n the material selection charts shown re+iously 4*rom &"S5, note
that the +arious material roerties are lotte! on log-log scales. he
reason *or this is as *ollows. For a con!ition li0e
1 E C
ρ =
where & is a constant; we can ta0e the log o* each si!e to obtain
1
log log log E C ρ − =or
log log log E C ρ = +
>hen lotte! as log E +s. log ρ 4or " +s. ρ on log-log scale5, thise2uation reresents a *amily o* straight arallel lines with a sloe
o* an! an intercet on the log E -a/is o* logC ; an! each line
correson!s to a +alue o* the constant &. hese lines are re*erre!
to as selection guide lines in &"S. Any material *alling on a gi+en
straight line will ha+e e2ual +alues o*
1
E ρ , i.e., be o* e2ual
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A1 - Design *or &olumn an! :late Buc0ling =)
7goo!ness7 in satis*ying a material in!e/ *or sti**ness to weight
ratio. Selecting a higher cur+e 4greater &5 in the *amily o* cur+es
is e2ui+alent to selecting a *amily o* materials with higher sti**ness
to weight ratio.
here are many go-no go limits that may limit the +alues o*
seci*ic roerties. For e/amle, in "/amle = 4column buc0ling5,
i* the !iameter is constraine! to Kr , this will re2uire a material
with a mo!ulus greater than *oun! by in+erting e2uation I
3 =
=K
4 K5
$& E
n r π =
!roerty limits ,ill lot as )ori-ontal or vertical lines on material
selection c)arts. he restriction on rK lea!s to a lower boun! *or "then gi+en by the e2uation abo+e. t might also be a !esign
re2uirement that the column !iameter lie within certain limits 4*or
e/amle, the column !iameter must satis*y 1 r r r ≤ ≤ 5. n thiscase, we woul! ha+e both uer an! lower limits on the !iameter
an! thus uer an! lower limits on the mo!ulus ".