física dos materiais e mecânica

20
Or.c@ N6o - t4a/ [ourranj.dziaL: .tana"clzo' r, &\e.c€'o y'iut a I Esb-r,- o.' ) -la., a).-G-;ea- dLL r''-l \:_ 4<&,*,a-c r""'!Y- c'/'"@ Ao.]o\ -X pl qa-.^,J3* uuvlazr'..O'r dtprttct t-\erdtC )?,a,\ co# t c/YYa -!a LBYI gncfr- {e' .4 tr-,. a n--*ia-&g- . ^i\\ffi, a.r- ' ^.*r^-o.\,\r(- 4"-) -/ ds- c9li.o & & 4 <l[n ft !r.r-r Cr-.'1 O {ra 'r ..Ja- r- c.z& I *rlie-*-\ +or+L ) d.r os ;.fi- t-aLLa) 'c.a- g! - *.iqav.. dO Jl\^<,r- da '\*-\ wL d& Al1B to- A.y,-1,&\)* ( cAlcu,|* raaro yCornlz-ioa&A, c,sr--c la.rfr.r i& c;dJ, .q.O* s*sk^a, z a,--Li o.''!-, U* aul^L+4- d.r- dla\r,\>A^ t'r""o-\ N dc - Lt6q- L.- l^'-".,nc ("l .,P-rt.' ^t ""**;^ ) $ar.- L. o.x o,,v;.&a'z- ( . +- "* at- *t'.^Jda ) \'44^Lo vio,'rd at'<- Ulpr,^\ c.C ca)r!,O //\b.l*A ?a"a\, Q;a. r" -l-^ f..o,- tra-^cr., dl.: (,,.c\O lXttl\ rlrero- au l\ \a-!-oYt/! Y,n ra.o {e-;Pq t n . O pc-o <.al\o CO,-a-G.+i..a;S lccta/w tr-r6 pro c!i\1{ ,,0,^Jo ds+i.o allot6 na- X ^4:l-,* tlc* t ar.t- ^Ji.d.-o h iu,Los. 4.,'^ c L ^^- fM 6drt- S Jza,".--- | p(x"\1,.,-,r.,.rxo) p(x^ Irn -,) V t">t"-'> )t" 9- 1^^:vu n..Crr A-Ab'\.,/ G- fbaLi1i. dai^J dr- X anr.,u, r..rv O JalsL Y,. AO t^-4o".t', " , batsb., o^fu t*-v c 4,u{ 4Lo.,--!c,..r -D

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Page 1: Física dos Materiais e Mecânica

Or.c@

N6o - t4a/ [ourranj.dziaL: .tana"clzo'

r, &\e.c€'oy'iut a I

Esb-r,- o.'

)

-la., a).-G-;ea- dLL r''-l \:_4<&,*,a-c r""'!Y- c'/'"@

Ao.]o\ -X pl qa-.^,J3* uuvlazr'..O'r dtprttct t-\erdtC)?,a,\

co#t c/YYa -!a

LBYI

gncfr- {e' .4tr-,. a n--*ia-&g- .

^i\\ffi, a.r-

' ^.*r^-o.\,\r(- 4"-)

-/ds- c9li.o & & 4<l[n ft !r.r-r Cr-.'1 O

{ra'r ..Ja- r- c.z&

I*rlie-*-\+or+L ) d.r

os

;.fi- t-aLLa) 'c.a- g! -*.iqav.. dO

Jl\^<,r- da '\*-\

wL d&

Al1B

to-

A.y,-1,&\)* ( cAlcu,|* raaro yCornlz-ioa&A,c,sr--c la.rfr.r i& c;dJ, .q.O* s*sk^a, z a,--Li o.''!-,

U* aul^L+4- d.r- dla\r,\>A^ t'r""o-\

N dc - Lt6q- L.- l^'-".,nc

("l .,P-rt.' ^t ""**;^ )$ar.- L. o.x o,,v;.&a'z-( . +- "* at- *t'.^Jda )

\'44^Lo vio,'rd at'<-

Ulpr,^\ c.C

ca)r!,O //\b.l*A?a"a\,

Q;a. r" -l-^ f..o,- tra-^cr.,dl.: (,,.c\O lXttl\ rlrero- aul\\a-!-oYt/! Y,n ra.o {e-;Pq t n .

O pc-o <.al\o

CO,-a-G.+i..a;S

lccta/w tr-r6 pro c!i\1{ ,,0,^Jo ds+i.oallot6 na- X ^4:l-,*

tlc*

t ar.t- ^Ji.d.-o h iu,Los. 4.,'^ c L ^^- fM

6drt- S Jza,".--- |

p(x"\1,.,-,r.,.rxo) p(x^ Irn -,) V t">t"-'> )t"9- 1^^:vu n..Crr A-Ab'\.,/ G-

fbaLi1i. dai^J dr- X anr.,u, r..rv OJalsL Y,. AO t^-4o".t', " , batsb., o^fu t*-v c 4,u{ 4Lo.,--!c,..r -D

Page 2: Física dos Materiais e Mecânica

C,a.'^^ X nO {++19c tn-l

Q(rn) f 9(r.\x^-) P(*"-)

h a"\n ,r!a,'.4, ; rr^ret-ur) +d a- y,.,.-^- a-,o f.r:e\-re-N6a - H,a ,t-,.p rN zr.,Y'a!.

'J).O.fYwcor- dJ- S^tla--r"

.-Q-dr.;.o e!,.,A-+,.._o

(91-- o P.^ra-d-o

A*r^r€\

S^^A^+:ro tHpni +ora.*,-fo( +.,p+a"'^", 9^'a--c" "^-). r r6J V^e- {r-.rr +o a5*:

dz!!r-,r..r-rt rregra .veev |,OI^{- O **1,; r_** . 1

A .y.,C^ "; tioAp,'ol! +:r* ,q/.;.e- o.fu"6.1^

f.

a.- Q- o<*L;,e.,/=- /:o_rO

Drtb\sr aa ll-'lLl-c€aI./lo* tC\ ?€lr qj.^aat-glr^

a,;- V,.o-.lrtzr ,,

f\ototl4.-'-'

'K Kro K

I

a^.^b

' i\ar.,.n, l\o rv a.,- 6 i+ l-l*eio*+ 4-69 {\o""o t J};,q

d-ye,,fi.o p-^."'.^ry"O

>& * l'\K-^^ e-r1 C,-,o,-

q^^-l- \rr'da da - z.,uSk,rraz.-

'. ci-r.,\(.^{ v-rrv a a^-*A^ico- 61a 6\le-r,.q-

d- a,r,-'j;?.-.Jo-

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83larr-'-.,o..' buaoq,*.ao cE.n&r"-cin rr\O.e\L4,9\ f,n1*dur^u<-^.

J;v",\r-

C,O

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. 'd-Cif a.{ r-v\, o^k^.aUr.,,.. O9.-.4^9CAj\.. r- -D 01 ..R.q F.c.*L. afu*r,w.o^. +rlo\ 'a---,^ L ;^.ww*Q i*ro"a, ce,-' <). O

Page 3: Física dos Materiais e Mecânica

*.r.-lr;a-/o- fa"'o' Yda^- k<-4'a4-o q^aL

==u UPirFe\ a4' baco 6,R:N\ciA

(,r,'

\a.-\

lo>\€>UC*,)

tr)l€) \)C*

\o<o,\2'

a,td u '

\o>\€"L+Dr r) lc.e))

(u,.\o) tx'\i) '-r("I "zo lo)lE.('o)) tarlr)\-er(tD

3.t ) =-r.r,*(3"lilJ - otJ't- o."xa'<e.tt\ lE"tt)

xrvj (au)l v,CrD I*\.a

ftro)

l/. J /.rJ )/*

o

a

O0p.j8.r&

ooo.ooaoo

oo

o oO)/z

O.Ooooot(z

o\d 2--

2r>

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ab*d\'>

'W* ^r,,^

zwSErYq, ?l6-/i't,o

JCt) = u tt) 3i c.rt tt )

(rg!1>),r^ .,

Ns\6-"..,a-' aLt'\*o

-I-(too> <o,o | + ia r)1 r rl

\Sc4a.d.o, Eg a(r. Sa-,"6"ud5".n

UL\)= 6i1**/s

)

$*c7""n?* .C^-\.AJ a^}r]^i^ alo

a4; qr^t L..icacl rnrrr-gsl"-..c- ! aa'td-& .ia.7;\L^6, ..taJaie- d.t\ \7)

3r(t)- -r-r** -[_.rttl tf,.e **r)U"(r) ]

Page 4: Física dos Materiais e Mecânica

lV*;-E--

a

Knf KJ

n^.,* o o

Ko< nac

€ x;S\4- a; \nr.,-e^:t ^. abr aO4<-> 1b"@, d.e4cra- o6,-c da\_ \.fu' ^.-;,-ftn <-a- r J. *o'o

',., o( H <,q

l. ft .,..,o.' "o!x.-_

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l4apa- $. * b Lf€,) Di- (/6s\-p1,

{- p.e !. ,rr e }r+f (Ca1l)

6 Ge")

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CAn'''la hly,'.,&- ? e.^jH.ro

4

= hSge;lu!t) r W <"ul.,rta)d,

T-X=J C?eR&DoR=S crl-

KP <OS

K^,a^r <"- )ov.i

d

Z K"- KdI-),a-*., ) u r.? r)<,.pr \ u. l-,.5)) )'1sd2),(..r,)u.t-t" l..-rj) = I. j't .J "'

I.

Otr No{ea,- tQ,). l"q"d,;*" \

d&

A

+q\ lr'.',a,- r?^rle- r-

Page 5: Física dos Materiais e Mecânica

E V,v>lra. "v*a,t .ru- olh- UaM-

1|a*q^r^';lq3)

Opfp {"--, r..r,f"rf 9-*'F d<' < (a}r'i'

q d& liquoi llc - se-' N< ume-n

A^-1Ptot \ .('q a* r'^ePt ^''-t')

|6 fod.O "af\

( K: <" = 4-)

4

d L

ht

d*

+ $tt)= do(&co) )

4SA= / (dewco))- #" trtdr)drk d*

= 6" 6i'(l*)4""-* a' '^vtt*tu

\v

S**Pt V'^-aq : biod&) *toe'* q'*ac<

\EA rg..'.o- dr- D"dA;*^', rL o Q.IJ" ar{\g c./-al'o a'#*zrJ- dO\^,

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( . a^Ai,Vah'o.. e-

w As L i"r-;+-"o^o, (4.' 1-^e ey'tanrlt\

6r)o.6q.V$t.re

Ua,J-dL l;"d(A/

Ou-

?. q<sr5lo.,'-; - ko S'a,l',,co Y*;- &t azqi*e^ -L.*uW- O

Page 6: Física dos Materiais e Mecânica

?rop & ia-,'-a'.VPo; $" f v !s)otQJu

= Z x*:gr)r^I

+s (

cP

Jcttat) - do* 3t,"1

O q/"r \,4, ur'fii\ cf(^,,als\"^ cr&- Y^a)',,t>

u2c++ct) vyt+)+ A't QqO,*r;Jc.ortt-?o ' d an- erae-- ar At

-+ k*Jt+lKJ "" l€ K* .lE L*

(*)

k,yt+y go - -?c+) 4 k" = d''6,Arr

Ui u- , L K-n r<.d+a

<lo

--r -er^ .rra..4" + a:,cA,O\ \ur>k$z.n

-,H

A/{ r-^+.i;*

Lu,tu"

LtikfcL

6=F

= (4t cj6t)14+6At) +*+ Z l*u<fo

'd + (6+cr')& tat> r"I.t, +9(tt')

EdJ\. q dr- {etrrt .. ar,-t- 9(d-P- bta*o.

+ L<

.SrtsUi+u^-"oo -0..,-- (x)'

,.i(t+at)= (4+rnar) 3cr.) (t+r,.,at) t41 |^i<Jz[.t'io

= J,Lt) + lt (hg +.ph) " At Zlo L. ld

L= J(+) - i At fl,f1 +Llo

L.! t:. 5iLu" ,3Y

@,,

Page 7: Física dos Materiais e Mecânica

.j't+rat ) - fc+\ fl

c";r*< a'o

[r*f[-5-ldi"+ Ld" ,,\/""&0

L*4tut) =& E{O

t*

ifilL"- L.

A

\ r.rk a"ca2 '

G,-p '^ ' in}tra-

*""U-"

c-go }.oco- ( a4 'e'1t' '

*- ar rae-locat- WtJev

daJa"r u-1,6 ior-^

nA;t"a'aae'

dq- bndLLaa' ?oau- tt^'

cb&t, co'oJ<^/l *ioar: ?ile

ctStiPaaU ca-

\;>,o

'+-.-6"^ a9; oab-

O....L'e<t' e'

o

&B*^^)o

)r.- r"9

1",(N

* *lroU ta *\ *'

)

Pear^en.'n@?at\

P\o^l"or-o-"^. {*., ", -- {*1,,

(-cue0 +*L^lra, *A 4e4,*do-

,o a- u)a|-t';'Q- t',c/r-a' '€.>

0r,o V]c>s>o

'DL.'!

$,= 4"s #. v +>+b

a+ eq. Vu>*a' 'ro'

. @<...,dqr<))o!v'.+ a- $"alt*-':*

+ [6.n is]o 6/do.n"g,\ an- tat*&)\t c"at'' l:

\4.$i\t- q*n- &..-e rr,-'Y@\/YYt€f\ d2- V1lt<x,ovlA+[O

@<^O aEl,C, .L'd;- r<'la'c- eta'ao Cp,r''\ 6- i d!9-

c.,c' i-.;i,oQ- *- r,.D<e/e>g.,.,,rto JrO',-. Har[,o,r-""^"e.?\4 ar>

AAni

d..o 7'4Ysz)

Page 8: Física dos Materiais e Mecânica

NaO - Pa^J", (iaz-na,.. ae-f..-i-a";-a- cp*, pY4P

Var"^oo \.0/Y>\ 1r-r-/,- f-g\ qrX- tta,rSlraz--'

' eD1a,, i a!a-.

|,q67. -;^OA. a- dJ":&*-i 'r.- ct"J v'.;'.' <fbi+

e( [4a.Lovia^q-

N cA*w ?*@ qdD ^Ya ?** eu- AS''\o>

?

Lo t t., I n+,r

tntt

€r. Ndo - \-4a"U-a wa-'-t

{o l'-At

Ai..v )

,.ico1 7 ro)<o \

S(At) = 1-ox s(o)ox I r, o+ .Go)dL-z-a

O(

da

01

01\ S."*, = S-)

Page 9: Física dos Materiais e Mecânica

3cp\ lr)(r\

to L,

7

La

----)

-47

{ r.+d-

{"

D(o\- t-s(arl= oD(o) ' 't

?".

Ca-;ary-Jr,'.o- hrel.r+

Ii^lE,rac;o.'Irraw

R-c^r-Pxac'rr) ds :I^{*' a@

r6a ttt*,.',.er-' a"'' d-r''fir* Yo do- ?^*b

-FrrA" c1r-,P^-';L71, a. di-&"iva: '2

da

€,< o'n rpto

att d*'reta*ie 'd$

c,A".a"f.igtaQ

?-

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A^4 ir^^" a,i n&].a'to- ai"t t''*Q. p"a-o. tt^-, q!r- ^eo

natisp5rat a- c.e''+;roIdq

)

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qL,JJ* dLl',wda' ?ca.a-'t\- ?o"n- d'o-

d,a- ?a^b F9.or"ce^^

. $rC) = 61 6+.Pd n&*yol*(+fou'qtdq, Ot = ll)<p I e. O-- loXr\ [.p & "i""{o o a^-i1,,,i1^Pb

Page 10: Física dos Materiais e Mecânica

b."^t*laa Ao Y- au;3-$cL'(r'91 -/^cB 1-* a,.JA-

€.: €)*^6ddr.u- a;snpa. fo ra.aod3-

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\ -.1-

I act&-o

I JCrt. 4"(9)= -. Ll+s gl *

P?'Ja-r<lr-;4f;./

dt- (

{t'*.,f })

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ff^kiq^n.jo tr (4J6r- 5 (u".,fl);[*,3.1 * t',(r,(P.)t(, S,(p")iy4.. 1t)

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'*|aaa d.L i- qr"Jd',+

"i. = +tt) It p,,<+)Q t o,-t+)o+ + Zt)o:

..rs,< &. = IK><L\

J,

Page 11: Física dos Materiais e Mecânica

(tr(t )

\tr.r )"i,

(t )p.(t )

l-o &

= ?it+ ) r-dr\oo(,

r P.C+)

)

/X. O\, aC+) (;,,:-q) dt\o -l"l

t &(+ )(-i'!- Do:

pCel = -E r lP,(+) + (.9' Ct)

d(t)= Yra.r(()-(-h-L+)

oat+ )- J^-Q)t.ao)

, -!r+(a)t { r: 4,/'4Xtt)-1to)e*"-'+P [-a ]

- -Gr{')l r r!rr+ ) ' gaot a tP, ll -

- ((,*(r.Q.

d' +(.,? L?x =(.

hi o\\o u/

Xrt(a.r

?.Jo'"'o' a,.lo. arhlX-o tsoq"a l

Page 12: Física dos Materiais e Mecânica
Page 13: Física dos Materiais e Mecânica

Ai^la"L C,P CF

Marvl.,o-, a'^-: &aae' " 4o" = $.t's fi'oN &o -F^a-\t-o' o; ande".' { ",o = Vr,s ds,o

I-6Po-,- NP

1 'for-o M'b'"- Sr- r.e-r ,-r.rA,pa. L

r ?e-r q^^L ,;--jl-,;t a,". r.66 - t "!t".o

i'"^',-". t'& iTle+nnaJal?

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cP -

(4^et') (3) >o&-P --------, ( d*e'p) (-?) > o

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t"o"^C-

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!e /"(rc-e rc.-)

3'e L(K*e rq^)

3. T fi }t><r't

Stsl= ! c,5 Str";><;t)

Malr"z Ctie'

L5

o.- n-r.,-t c{n.,5^^ic'o- 1- tr l)^l)t 1;$iI

{tC) -r;r(c (aef-))

LL

Z p rr)1\ ."!J<j \9A,,. \i) !t)j !-={J

6ri Q," d,|,

?r.9 (H)S\)@

Page 14: Física dos Materiais e Mecânica

Tda. i*p.rra,<io a.o std A*^- b. -ta,--fido; e a& CAg, , +*,ulr^ cl6.yr,aaa, cl* zrafuizdL.ar;"a.,\

Te.o-7c,CCt,s)r Ur1 '?@A -P,N'aV ,f cS-tt,(++ot*ae,pa ruh'.ro r*) a x4^Jl.*- tl-@- .vP o P",l,1' .-:at

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J? tf

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d-o rna,p.,, -+ VTbt-ra,. a;l: oL, {or^oqraip A- at-?"\,O oQlyt,o

+ ar-wc" \o uori^!--fi-

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O NM?

d^ -6,rr,'r;r,a-

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r

c,q1,R,

G-\ d. -+.,\ rwacaa

-12t1. *rnla- de ).\f1 '.

<r& ca,*ro,-di 'v-I

t>of(g*irl, d"t ")) ( &(r',o) V

@

Page 15: Física dos Materiais e Mecânica

\(a Nqn-u--l

\t lll;-w "l-Sl''feQ\<""7''

tWq** l^rrvt w lia,-,^.,c

t\f.(all\r (llAl\r.

?"w-e- HwC <.Aryr*a, ql't- e ww

d.- Nef .n.- OLL

r-.,oka

|':O W P. t>9tv.z--j* M-

A &.,+a'-.a,C -,--, K

q.L^4- 7'4 K^^E- o t<acc t &

po',,i,Urro |r4-;d)'111':d' L>O

?'\r/9^oada r(d(a) IIr= (lAil,

q.^,^e- -*@ L r.e-unto>'af do. "r'r8r. rwa- ?

CA.,A."lrr..r- o\RP'a'-'

,y-,,4& Poli,\'so Al''r^'-r' af;;a.P I n'a)>

a+- rrafut; + dwou&'c>!Q-e^, 1e ^{, sarA=A*

\ 146vr.u) A\\.< a

-to

.l e: a""lo'

4

Zt\+xi:\ -[lxl \rur<11A]

..( 1\dtln)l\,' I\d(a-)l\ =

116t1\+ i\[\\= \\a\\r

\\ 0 ( s) l\^ = \\ d(a*) - dtr) l\ '

+ g, Vt,s e- cP =* Xe Vt,s a >en'lfi uo

A L(PLaa lL

L Vo,, j \^ao c) .r exrsk- T4, .rr-e.r.vs1 rr,F eg

h,.^.-\a---cverne,

g-^€k- r:\'C a-

Page 16: Física dos Materiais e Mecânica

Ce..-o tSlc o- J-h, t "e

o Tnu)1ffi d.-a- I ^,t S."^a-+io)

A=qE-ta-a)f- ( o-^ ^o(.*- et Lr'--6o^-'o )

/'f\J/1,snp t^,|;*oe at- u\1ad-g x

Q= t/a_t

(8^n-", , /;'o ' ?;ilo 'BLt ?RL- t'os ,2d1ol (z-ooq)

-9.J.rJ)

O(&, ?): l\ (f,-p") j\j l4A/.,1., \ri &.,e-

?,obu;u aaa-, dt- olr-!(T ra^ ctx,o Zu",- q Ni{,o'.-

?LP. *rc{ z^o( (zol5)

o{Yw

-b(f (r^)

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Page 17: Física dos Materiais e Mecânica

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Page 18: Física dos Materiais e Mecânica

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Page 19: Física dos Materiais e Mecânica

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Page 20: Física dos Materiais e Mecânica