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Innovative Cantilever

Children Swing: The Space

Saving Device

Submitted as a partial requirement

for the course INME!"": Machine Component Design "# $!!%&I Design Course for B.S. in Mechanical Engineering Department University of Puerto Rico at Mayagüez Mayagüez PR

Students:

Perez Nieves, IleanaUn!ergra!uate Stu!ent at Mechanical Engineering Department

University of Puerto Rico at Mayagüez Mayagüez PR

Mendoza Padron, RadaíUn!ergra!uate Stu!ent at Mechanical Engineering Department


Aviles Oliveras, RobertoUn!ergra!uate Stu!ent at Mechanical Engineering Department


'acult( )dvisor:

Caseres, Pablo Professor at Mechanical Engineering Department


Ma(# $!!%

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Objectives

Socialization is extremely important durin t!e development o" t!e !uman bein# $or t!e

c!ildren t!e s%ins are and !ave been an important part o" t!e recreation and t!ere"ore o" t!eir

socialization and development# &e as "uture enineers decided to improve t!e present s%ins so t!at

every c!ildren can !ave a s%in in t!eir bac'yards no matter o" t!e space t!ey !ave# (!e main

ob)ective o" our pro)ect is to desin an eronomic and sa"e cantilever s%in "or t!e averae "amily !ouse#

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Description

As %e all 'no% s%ins can be very "un %!en you are a 'id, t!ey can even be lots o" %!en

you visit t!e par' "or t!e "irst time in ten or "i"teen years# No one ever "orets t!e "irst time t!at

t!ey "elt t!at sensation t!at t!ey %ere oin to come o"" "lyin o" t!e s%in and !o% scary it ets

once you start ainin lots o" speed# (!e main purpose o" our pro)ect is to desin a s%in t!at

doesn*t !ave an excessive cost and %it! no need o" a lare bac'yard# Our main oal is to ma'e a

practical desin t!at at t!e same time is sa"e "or c!ildren "rom "our to ten years old#

An analysis %ill be made o" t!e moment, s!ear stress and o" "atiue to be able to

calculate t!e "actor o" sa"ety t!at t!is element can support# &e %ill consider t!e material to be

used and t!e di""erent eronomic aspects "or t!e %ell+bein and sa"ety o" t!e users# (a'in into

account t!ese speci"ications t!e calculations necessary %ill be made# &e %ill desin a s%in

%!ose structure could be analyzed as a cantilever# (!e cantilever %ill !ave t%o ropes or attac!ed

to t!e seat#

(!ere are some constraints imposed by our pro"essor, but %e as a team imposed ourselves

some oals t!at at t!e same time present ne% problems to our desin# (!e minimum

reuirements "or our pro)ect %ere t!at t!e desin must !ave one component sub)ected to

"luctuatin loads, %e must ma'e a ood material selection and it must !ave a minimum o" t%o

stress concentrators# &e %ant our device to be easy to install at !i! !ei!ts, %!ic! also implies

t!at is !as to be li!t%ei!t# In order to ac!ieve t!is %e must "iure out a %ay to assemble t!e

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us speci"ic in"ormation on !o% to build our speci"ic desin- by t!is %e mean stresses, strains,

some assumptions !ad to be made#

$inally once %e are done %it! t!e desin and t!e correspondin analysis o" critical parts,

our ob)ective is to !ave somet!in in !and t!at is really mar'etable#

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Design Details

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(!is desin and calculation tas' is very di""erent "rom %!at %e are used to doin %!ic! is

calculatin values o" stresses or "indin "orces %it! data t!at is already iven# .ere %e !ave to

study our desin t!orou!ly %!ic! %ill enable us to come up %it! reasonable estimates "or t!e

"orces and stresses, %!ic! are "orce concentrations, t!at %ill be present in critical elements o" our

desin# /y doin so %e %ill be able to !andle our data and desin t!e elements o" our s%in

accordin to t!e maximum values observed in t!e analyzed elements# Also %e !ave to consider

t!e mec!anical and p!ysical properties o" t!e material to 'no% !o% t!e loads %ill a""ect it# (!e

main concentration o" stresses in our pro)ect %ill be localized at t!e "illet %!ere t!e beam %ill be

attac!ed at t!e %all#

(!e "irst assumption t!at %e made %as t!at t!e maximum allo%able %ei!t o" t!e user

s!ould be around 011lbs# (!e )usti"ication "or t!is assumption is t!e "act t!at t!e s%in is

intended "or t!e use o" a speci"ic type o" public, %!ic! are 'ids bet%een t!e aes o" six and

t!irteen years old# Accordin to 2ids Nutrition %ebpae t!e %ei!t o" c!ildren bet%een t!e aes

o" six and t!irteen s!ould be bet%een 01+34 lbs# As %e all 'no% t!ere are some cases %!ere

t!ese values are exceeded so in order to accommodate a larer amount o" public %e placed t!e

%ei!t limit above t!e maximum "iure s!o%n above#

&it! t!ese values %e %ill be able to determine t!e appropriate materials t!at are best

suited "or eac! component and also t!e dimensions o" t!e component so t!at t!ey do not "ail

under any type o" preventable circumstance# Also by determinin t!e materials %e %ill et a

better picture o" !o% muc! maintenance %ill be reuired by t!e s%in i" any# A"ter "ollo%in

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certain criteria t!e material %e c!oose %as AISI 5161 a steel# (!is material is cold rolled and it

!as a sima yield 41711 psi and a ultimate tensile strent! o" 81311 psi#

(o calculate t!e principal stresses %e "orm a matrix %it! t!e applied loads, %it! t!is %e

calculate t!e 9eviatoric matrix and "inally t!e principal stresses#

Matrix

9eviatoric Matrix

Principal Stress

No% calculatin to "inally calculate t!e sa"ety "actor "or static stae

Sa"ety $actor

(!e dimensions o" t!e beam t!at %as desin are: !ei!t 0in, lent! ;;in and %idt! ;in

in# A"ter t!e beam %as done a support %as created so t!at it could be placed in t!e %all# (!e

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component li"e o" our material is in"inite# A "illet %as done %it! a radius o" 1#8in and an . o"

6in# In order to calculate t!e critical section, stresses and sa"ety "actor under dynamic loads, t!e

area, t!e "irst moment o" inertia and t!e second moment o" inertia %ere "ound#

I b !

0⋅56

:=


10/32

and to t!e S!ear "orce# (!e momentum %as "ound by multiplyin t!e "orce in a neative

direction times t!e distance at %!ic! t!e "orce is located, M=+@#7 x 510

inlb# (!en t!e

momentum o" A/ %as "ound Mab

=4#; x 510

inlb# (!en x=a t!ere"ore t!e de"lection at A/ and

and /C %ere "ound# (!e values o" t!ese de"lections are +3#86 x 51+0

in# (!e maximum

de"lection %as 1#116in#

δab$ x

6⋅

8 ?⋅ I⋅

x 0 a⋅−B C⋅:=

δ bc$ x

6⋅8 ?⋅ I⋅

a 0 x⋅−B C⋅:=

Dmax$ a

6⋅

8 I⋅ ?⋅

6a 0 b⋅+B C⋅:=

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R 5 $:=

M5 $− a⋅:=

M

ab

$ >

beam

a−( )⋅:=


11/32

(!e material selected in t!is desin %as AISI 5161 a lo% carbon steel %it! an ultimate

strent! o" 81#3'si# $or t!is ultimate strent! an endurance limit euation %as "ound in t!e

course material, t!e endurance limit %as 01'si# (!is type o" lo% carbon steel !as been cold

rolled, t!ere"ore t!e sur"ace "actor calculated %as o" 1#313# (!e size "actor "or a nonrotatin

rectanle is determined by calculatin t!e A34 and a deuivalent# (!e euivalent diameter %as o"

1#717in t!ere"ore "or 1#0in E deuivalent E 51in a t!e size "actor %as calculated %it! t!e euation "or

' size s!o%n belo%# (!e load "actor is determined by per"ormin tests "or t!e modes o" cyclic

loadin# Our desin %as sub)ected to bendin, torsion and s!ear- t!ere"ore t!e load "actor %as 5#

A cantilever c!ildren s%in is placed in bac'yards, par's, etc### conseuently it is at ambient

temperature so its temperature "actor is 5# It %as assumed t!at t!e s%in !ad a reliability o"

33#3F t!ere"ore t!e reliability "actor %as 1#@40# (!e endurance limit must be corrected by usin

t!e Se#c euation s!o%n belo%#

S#e 1#4 S#ut⋅:=

A#34σ 1#14 b⋅ !⋅:=

' size 1#783 de,1#13@−⋅:=

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' sur"ace a Sultimate be⋅:=

deuivalent

A34σ

1#1@88:=

Se#c ' sur"ace ' size⋅ ' load⋅ ' temperature⋅ ' reliability⋅ Se⋅:=


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(!is desin !as a "illet o" 1#18in t!ere"ore a stress concentration "or a rectanular plate

%it! "illet must be "ound in its correspondin rap!, t!ere"ore ' t is 5#6# A"ter t!at a ' t !as to be

calculated by "indin and substitutin it on t!e ' " euation t!en ' " %ill be 5#503#

A maximum and minimum "orce must be determined# (!e %ei!t o" a c!ildren %ill be o" 011lb

and t!e %ei!t o" t!e beam %ill be o" approximately 541lb# (!e lent! o" t!e rope is 88 in and

its %ei!t %it! t!e c!air is 4lb# (!e potential enery must be eual to t!e cinetical enery a"ter

doin t!is euality %e solve "or t!e velocity and "ind t!at t!e velocity is approximately 668inGs 6#

(!e maximum "orce %ill be t!e determined by addin t!e centri"ual "orce plus t!e %ei!t o" t!e

beam# &e %ill consider t!e mass o" t!e c!ild and o" t!e s%in %!en calculatin t!is "orce# (!e

minimum "orce is t!e %ei!t o" t!e beam plus t!e %ei!t o" t!e s%in# (!e minimum "orce is

544lb" and t!e maximum "orce is @81lb"#

v >soa ⋅ 6⋅:=

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5

5arootsuare

r

+

:=

' " 5 ' t 5−( )⋅+:=


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$cmax

ms%in mc!ildren+( ) v6⋅

>soa:=

(!e amplitude "orce and t!e mean "orce are "ound because %e !ave dynamic loads in our

desin# (!ese "orces are determined %it! t!e euations s!o%n belo% "or $a and $ b# (!e

amplitude "orce is 010lb" and t!e mean "orce is ;4@lb"#

(!ere is a bendin and torsion at point A and t!ey are sub)ected to "luctuatin "orces#

(!ere"ore a maximum and minimum moment %as determined and sima bendin mean and

sima bendin amplitude %ere calculated "or point A, t!e values o" t!is numbers are 8'si and

5'si respectively#

σ#bm ' #" Mmax c#M⋅

I

⋅:=

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$max $cmax % bea+:=

$min % beam %s%in+:=

$m$max $min+

6:=

$a$max $min−

6:=

σ ba ' " Mmin cM⋅

I ⋅:=


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A visual analysis o" t!e loads in a uadrant o" t!e cross section o" t!e beam %as

per"ormed# &e let point A be t!e top point, point / be t!e le"t side point, point C be t!e bottom

point and point 9 be t!e ri!t side point Bsee appendix# &e deduced t!at t!e critical point %ill

be "ound in t!e top point A or in t!e le"t side point /#

A torue is produced at bot! points and t!ere"ore a (ao torsion must be "ound "or mean

and amplitude# (!e (ao torsion "or mean and amplitude are ;'si and 8'si, respectively# A s!ear

is produced at point / "or amplitude and mean "orces t!e values o" t!is are 58'si and 64'si,

respectively#

τ#s!ear#m0

6#

$#m

A#5⋅

' #⋅:=

A sima Hon Misses !as to be "ound because %e need a property t!at unites sima "orces

and tao "orces# Hon Misses !as to be "ound at point A and /# At point A sima Hon Misses

amplitude and mean are @'psi and 56'psi respectively# In order to "ind Hon Misses at point /

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τtorsion#a# ' " (a cM⋅


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τ#total#a τ#s!ear#a τ#torsion#a#+:=

τ#total#m τ#s!ear#m τ#torsion#m+:=

σ#vm#amplitude 0 τ#total#a6

⋅:=

σ#vm#mean 0 τ#total#m

6⋅:=

t!e torsion and s!ear "orces are added to "ind a total (ao amplitude and mean# (!en Hon Misses

amplitude and mean are "ound# (!e values are @'psi and 55'psi#

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)fter all this anal(sis was done a safet( factor was found using the modified&*oodman

Criteria+ )t point ) the safet( factor "+,-" and at point . the safet( factor is "+%/$+ 0ur lowest safet(

will determine the critical section of the beam+ The lowest safet( factor was at point ) # therefore the

critical point is at )+

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Discussion

The cantilever swing has man( advantages than other t(pe of swings+ It is space saving

because the ma1orit( of home swings are designed to be on ground at the bac2(ard+ ) swing

of this 2ind can be an obstacle in home tas2s li2e cut the grass3 a 2id can hit himself

running when he is pla(ing in the bac2(ard+ The swing was designed to graduall( change

the seat while the 2id is growing# because of this so man( t(pe of seats will ad1ust to the

design+ .ecause of the versatilit( of the seat t(pe is a good option to a housewife leave her

bab( close to her while she is doing some outdoor tas2s li2e fi4 the garden or simpl( seated

outside ta2ing a breath or spending a good time+ The beam alone can also be used in other

applications# li2e to hang punching bags# pi5atas and other things under /!!lb+ 0ur

design is also eas( to install because it has onl( four ma1or parts that are the beam# the

ropes and the seat+ It can be used b( almost an(one because is designed up to /!! pounds

surpassing the weight of an average adult "67+6 pounds according to Accordin to t!e

National Center "or .ealt! Statistics BSee Appendix+ The cantilever swing cost would be

relativel( low because of the material selected+ 0ne ma1or disadvantage and the main

problem of our design is that the beam will alwa(s be hanging out of the wall and it wil not

be considered esthethicall( appalling+ .ecause of this disadvantage another future design

was thought with a pivot point attached to the wall so the beam can be bending toward the

wall 8See )pendi49+ This could be considered the storage wa( of the new design+

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Conclusions

A"ter desin and analyze t!e cantilever s%in %e determinate t!at t!e critical part o" t!e

desin %ould be t!e beam# (!is %as a simple desin, but it %as really di""icult because it %as an

idea beins "rom practically cero# (!e beam %as analyzed in to points, A and /# Resultin A t!e

critical one because it*s lo%er sa"ety "actor# (!e di""erence bet%een t!e t%o sa"ety "actors %as

1#1@4 but "or us %as very important to desin as sa"e as possible# (!e material selection part %as

a very critical one in our pro)ect because it involves all aspects o" our desin# &e %anted a li!t

material because to install t!e beam it is need to be raised approximate @ or 7 "eet above t!e

round# I" t!e beam is too !eavy t!e installer could result in)ured because t!e beam "alls and !it

!im or because a muscular or bac' !urt because o" t!e %ei!t o" t!e beam# (!e type o" material

also determine !o% muc! t!e cost o" t!e s%in %ould be, t!at is %anted to 'eep lo% because o"

t!e merc!antability o" t!e product# And o" course t!e most important part o" t!e material

selection, %e do not %ant t!e s%in to brea' %!ile it is in use because t!e security o" t!e people,

specially t!e 'ids %!ic! are t!e ma)or users o" t!is type o" desins#

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AppendixA# Important &eb Paes Hisited

• 'idsnutrition#or• mat%eb#com

• mdsolids#com• !ttp:GG%%%#rantadesin#comGproductsGopsGrevie%#!tm

/# M9 Solids /eam Analysis

Analysis o" t!e H and M o" t!e loads applied to t!e Cantilever /eam bein study#

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C# Calculation o" sa"ety "actor in steady state usin matrix

Calculation o" t!e sa"ety "actor in steady state usin matrix:

,

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Matrix

9eviatoric Matrix

=

Principal Stress

, ,

Calculatin

Sa"ety $actor

Calculation o" t!e sa"ety "actor in steady state usin matrix:

&e "irst calculate t!e area, inertia,

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22/32

,

9# Representation o" !o% t!e "orces are actin on t!e "our principal sur"aces o" t!e

Cantilever /ase /eam

?# Solid &or's 9ra%in

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'illet Close&up in the between green and red area+

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Cantilever Swing Design

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Improved design model

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Support of the improved design

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9# Cosmos /eam Analysis

Deflection anal(sis made in Cosmos pres+ The deflection magnitude is show form blue to

red+

Stress distribution in the fillet area+ The stress intensit( goes form blue to red respectivel(+

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$# Material Selected Bmat%eb#com

Subcategory: AISI 1000 Series Steel; Carbon Steel; Ferrous Metal; Lo Carbon Steel; Metal

Key Words: !"S #10200$ AMS 5032$ AMS 5045$ AS%M A29$ AS%M A108$ AS%M A510$ AS%M A519$ AS%M A29$ A108$ A510$ A512$ A513$ A519$ A544$ A575 M10120$ A576$ A635$ A659$ A827$ A830$ &S 970040A20$ 050A20 '(n2C)$ 050A20 '(n2*)$ 060A20$ &S 970 +art 1 070M20$ *(F S%A"95,1,1 C1020$SA( -412$ SA( -414$ *I" 1.0402$ AF"/ CC 20$ !"I C 20$ SS14 1450 'Seen)$ SA( -403

Component Wt.

C 0.17 , 0.23

Fe 99.08 , 99.53

Mn 0.3 , 0.6

+ Ma 0.04

S Ma 0.05

!aterial "otes:1020 steel resons ell to ol or an eat treatin. elabilit is :air.

Applications: Sa:ts$ litl stresse ears$ ar earin sur:aes$ ins$ ains an ase arenearts ere ore strent is not ritial.

1020 is suitable :or ase arene arts ere ore strent is not ritial.

#$ysical #roperties !etric %nglis$ Comments

*ensit 7.87 0.284 lbin<

!ec$anical #roperties

=arness$ &rinell 121 121

=arness$ >noo 140 140 Con?erte :rom&rinell arness.

=arness$ oell & 68 68 Con?erte :rom&rinell arness.

=arness$ @iers 126 126 Con?erte :rom

&rinell arness.%ensile Strent$ !ltimate 420 M+a 60900 si

%ensile Strent$ iel 350 M+a 50800 si

(lonation at &rea 15 B 15 B In 50 mm

30 | I n m e 4 0 1 1

http://www.matweb.com/search/GetUnits.asp?convertfrom=43&value=7.87http://www.matweb.com/search/GetUnits.asp?convertfrom=109&value=420http://www.matweb.com/search/GetUnits.asp?convertfrom=109&value=350http://www.matweb.com/search/GetUnits.asp?convertfrom=138&value=15http://www.matweb.com/search/GetUnits.asp?convertfrom=43&value=7.87http://www.matweb.com/search/GetUnits.asp?convertfrom=109&value=420http://www.matweb.com/search/GetUnits.asp?convertfrom=109&value=350http://www.matweb.com/search/GetUnits.asp?convertfrom=138&value=15


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eution o: Area 40 B 40 B

Moulus o: (lastiit 205 #+a 29700 si %ial :or steel

&ul Moulus 140 #+a 20300 si %ial :or steel

+oissons atio 0.29 0.29

Mainabilit 65 B 65 B &ase on AISI 1212

steel. as 100Bmainabilit

Sear Moulus 80 #+a 11600 si %ial :or steel

%lectrical #roperties

(letrial esisti?it 1.59e,005 om,m 1.59e,005 om,m onition unnon;0DC '32DF)

(letrial esisti?it at (le?ate %emerature 2.19e,005 om,m 2.19e,005 om,m onition unnon;100DC '212DF)

(letrial esisti?it at (le?ate %emerature 2.92e,005 om,m 2.92e,005 om,m onition unnon;200DC '390DF)

&$ermal #roperties

C%($ linear 20DC 11.7 Emm,DC 6.5 Einin,DF 0,100C

C%($ linear 250DC 12.8 Emm,DC 7.11 Einin,DF 0,300DC '68,570DF)

C%($ linear 500DC 13.9 Emm,DC 7.72 Einin,DF 0,500DC '68,930DF)

Sei:i =eat Caait 0.486 -,DC 0.116 &%!lb,DF onition unnon;50,100DC '122,

212DF)

Sei:i =eat Caait at (le?ate %emerature 0.519 -,DC 0.124 &%!lb,DF onition unnon;150,200DC '302,

390DF)

Sei:i =eat Caait at (le?ate %emerature 0.599 -,DC 0.143 &%!lb,DF onition unnon;350,400DC '662,

752DF)

%ermal Conuti?it 51.9 m,> 360 &%!,inr,:tG,DF %ial steel

31 | I n m e 4 0 1 1

http://www.matweb.com/search/GetUnits.asp?convertfrom=138&value=40http://www.matweb.com/search/GetUnits.asp?convertfrom=45&value=205http://www.matweb.com/search/GetUnits.asp?convertfrom=45&value=140http://www.matweb.com/search/GetUnits.asp?convertfrom=138&value=65http://www.matweb.com/search/GetUnits.asp?convertfrom=45&value=80http://www.matweb.com/search/GetUnits.asp?convertfrom=116&value=1.59e-005http://www.matweb.com/search/GetUnits.asp?convertfrom=116&value=2.19e-005http://www.matweb.com/search/GetUnits.asp?convertfrom=116&value=2.92e-005http://www.matweb.com/search/GetUnits.asp?convertfrom=5&value=11.7http://www.matweb.com/search/GetUnits.asp?convertfrom=5&value=12.8http://www.matweb.com/search/GetUnits.asp?convertfrom=5&value=13.9http://www.matweb.com/search/GetUnits.asp?convertfrom=65&value=0.486http://www.matweb.com/search/GetUnits.asp?convertfrom=65&value=0.519http://www.matweb.com/search/GetUnits.asp?convertfrom=65&value=0.599http://www.matweb.com/search/GetUnits.asp?convertfrom=137&value=51.9http://www.matweb.com/search/GetUnits.asp?convertfrom=138&value=40http://www.matweb.com/search/GetUnits.asp?convertfrom=45&value=205http://www.matweb.com/search/GetUnits.asp?convertfrom=45&value=140http://www.matweb.com/search/GetUnits.asp?convertfrom=138&value=65http://www.matweb.com/search/GetUnits.asp?convertfrom=45&value=80http://www.matweb.com/search/GetUnits.asp?convertfrom=116&value=1.59e-005http://www.matweb.com/search/GetUnits.asp?convertfrom=116&value=2.19e-005http://www.matweb.com/search/GetUnits.asp?convertfrom=116&value=2.92e-005http://www.matweb.com/search/GetUnits.asp?convertfrom=5&value=11.7http://www.matweb.com/search/GetUnits.asp?convertfrom=5&value=12.8http://www.matweb.com/search/GetUnits.asp?convertfrom=5&value=13.9http://www.matweb.com/search/GetUnits.asp?convertfrom=65&value=0.486http://www.matweb.com/search/GetUnits.asp?convertfrom=65&value=0.519http://www.matweb.com/search/GetUnits.asp?convertfrom=65&value=0.599http://www.matweb.com/search/GetUnits.asp?convertfrom=137&value=51.9


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# Similar 9esins

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