a13 materials selection in design (1)

8/21/2019 A13 Materials Selection in Design (1)

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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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shae an! rocess lies at the heart o* the materials selection

rocess.7

Engineering Materials and their Properties


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A13 –Materials Selection in Design =

>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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A13 –Materials Selection in Design C

• :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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A1 - Design *or &olumn an! :late Buc0ling #


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A1 - Design *or &olumn an! :late Buc0ling 1)

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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A1 - Design *or &olumn an! :late Buc0ling 11

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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A1 - Design *or &olumn an! :late Buc0ling 1=

Here are some charts *rom Ashby an! the &ambri!ge "ngineering

Selector +3.1 so*tware 4&"S5.


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A1 - Design *or &olumn an! :late Buc0ling 1C


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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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A1 - Design *or &olumn an! :late Buc0ling 1#

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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A1 - Design *or &olumn an! :late Buc0ling )

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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A1 - Design *or &olumn an! :late Buc0ling

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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A1 - Design *or &olumn an! :late Buc0ling =

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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A1 - Design *or &olumn an! :late Buc0ling C

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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A1 - Design *or &olumn an! :late Buc0ling #

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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A1 - Design *or &olumn an! :late Buc0ling 3)

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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A1 - Design *or &olumn an! :late Buc0ling 3=

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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A1 - Design *or &olumn an! :late Buc0ling 3C

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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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 ".

a13 materials selection in design (1)

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