Čvrstoća materijala

download Čvrstoća materijala

of 104

Transcript of Čvrstoća materijala

  • 7/23/2019 vrstoa materijala

    1/104

    VIKSIL

    XSNKAOROS$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 9

    9$ ^ROK $$$$$$$$$$$ $$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 6

    3$ RSV[N OX[NSNNDLI $$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ >

    6$ DIXSN\IDLN$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 2

    ;$ KNBOSM IF@LI$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 98

    >$ MN^VOCDI OR@VDOV[ DIXSN\IDLI @ KN BO SM IF @LI $$$$$$$$$$$$$$$ 93

    2$ XSOSI^DVGO @ KOX^[NDO DI XS N\ ID LN $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 9>

    1$ IG V@LIJDO OX[NSNNDLN $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 92

    1$9 Idij`|i dixsn|idli ` knbosmif`li $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 921$3 Xsosi~d igv`lijdo ox{nsnnd`e{ixori$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 901$6 V{i{`g` dnoksnnd` |ikif`$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 331$; Xon{di ` {oxj`dvgi dixsn|idli$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 3;1$> Godfnd{sif`li dixsn|idli$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 30

    5$ V[IDLI DIXSN\IDLI $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 69

    5$9 Lnkdoovdo v{idln dixsn|idli$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 695$3 Kroovdo v{idln dixsn|idli$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 66

    5$3$9 Moesori gs~d`fi dixsn|idli$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 625$3$3 [idgov{`lndn {jidn xov~kn$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ ;8

    0$ VM@F IDLN$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ ;6r

    0$9 Idij`|i dixsn|idli ` knbosmif`li$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ ;60$3 Xsosi~d godv{s~gf`lvg`e njnmndi{i di vm`fidln$$$$$$$$$$$$$$$$$$$$$$$$$$$ ;2

    98$ ANOMN [S@LVGN GISIG[NS@V[@GN SIRD@E XS NV LN GI $$$$$$$$$$$$$$$$ ;0

    98$9 V{i{`g` momnd{ xors`dn$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ ;098$3 Momnd{` {somov{` xors`dn$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ ;098$6 Momnd{` o{xosi xors`dn$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ >;

    99 ^R@LIDLN$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ %>2Z L

    99$9 Dixsn|idli ` knbosmif`ln {ixori ogs~ajoa xsnvlngi $$$$$$$$$$$$$$$$$$$ >1

    9;-$3K`mnd|`od`sidln {ixori ox{nsnnd`e di ~r`lidln$$$$

    $$$$$$$$$$$$$$$$$$$$ 2399$6 V{i{ g` dnoksnnd` |ikif`$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 2>

    T 8

  • 7/23/2019 vrstoa materijala

    2/104

    93 $ VIR@LIDLN 21

    93$9 Sirdo `v{o vir`lidln$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 2593$3$9 Dixsn|idli ` knbosmif`ln {ixi$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 25

    93$3 Sirdo vir`lidln v`jimiT$ _______ -$$$$$$$$$$$$$$$$$$$$$$$$$$$$ *$$$$$$$$$$$$ 1993$3$9 Idij`|i dixsn|idli {i xi$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 1993$3$3 Xsosi~d rsv{on$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 1593$3$6 Njiv{`di j`d`li$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 5393$3$; V{i{`g` dnoksnnd` |ikif`$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 5>

    93$6 Govo vir`lidln$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 52

    96$ @\R@LIDLN$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 08

    96$9 @|r`lidln ~ njiv{`dom xoks~l~$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 0396$3 @|r`lidln ~ xjiv{`dom xoks~l~$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$96$6 Xsosi~d {ixori di `|r`lidln $$$$,

    9;$ VJONDO OX[NSNNDLN$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 01

    9;$9 [nos`ln rsv{on$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 01

    9;$3 Igv`lijdo ox{nsnndln ` vir`lidln {ixori$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 9889;$6 Vir`lidln ` ~r`lidln {ixori ogs~ajoa xsnvlngi$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 986

    KOKI[IG$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 999

    J@[NSI[^SI 991

  • 7/23/2019 vrstoa materijala

    3/104

    RSV[OI MI[NS@LIJI 6

    9$ ^ROK

    Vrigo rsv{o {`lnjo xok klnjoridlnm ridlvgoa ox {nsnndli m`lndli vrol ocj`g ` roj~mnd* i~ dlnm~ vn xolirjl~l~ ~d~{sidln v`jn$ Xsomlndi ocj`gi ` roj~mndi {`lnji di|`ri vn

    knbosmif`li* i vxnf`b`do ox{nsnndln {`lnji `|i|rido dlnaor`m ~d~{sidl`m v`jimi xsnkv{irjlidixsn|idln$

    Rnj``di ` ocj`g knbosmif`ln or`vn o ridlvgom ox{nsnndl~* {nmxnsi{~s` ` b`|`go-mneid`g`m vrolv{r`mi mi{ns`liji ok golna ln {`lnjo `|asindo$ Knbosmif`li siv{n vrn kog vndn ~vxov{ir` sirdo{ni `|mn~ ridlvg`e ` ~d~{sidl`e v`ji* giki {`lnjo xoxs`mi oksnnd`sirdo{nd` xojoil$ ^ {om vn xojoil~ knbosm`sido {`lnjo diji|` ~ dixsnad~{om v{idl~$

    Idij`|~ dixsn|idli ` knbosmif`li {`lnji ~ ogr`s~ mneid`gn rsv{`e {`lnji* moa~n lnxsornv{` di kri di`di gol` vn mn~vocdo si|j`g~l~ ~ xs`v{~x~ ` mn{okimi slniridli$ Xsr`di`d gos`v{` {nos`li njiv{`dov{`* |didv{rndi k`vf`xj`di goli ocsi~ln xsocjnm xodiidlirsv{`e {`lnji di ovdor` v{soa`e ` {od`e xov{irg`$ [`mn mi{nmi{`gn oxnsif`ln xs` slniridl~

    xov{il~ vjondn* ` xsnmki kil~ {odn sn|~j{i{n* moa~dov{ dl`eorn xsig{`dn xs`mlndn lnoasid`ndi$ Ks~a`* xsig{`d` di`d* gos`v{` di~gi o rsv{o` goli vroln mn{okn xsosi~diovd`ri di d`|~ xsn{xov{irg` xo{rsnd`e ngvxns`mnd{`mi* ij` ` di sn|~j{i{`mi koc`rnd`m vxomo~ {nos`ln njiv{`dov{`$ [o ln {ned`gi k`vf`xj`di goli xso~iri rsv{o~* gs~{ov{ `v{ic`jdov{ k`lnjori godv{s~gf`li ` v{solnri {n lnkdov{ird`l`e godv{s~gf`lvg`e flnj`di$

    rsv{oi godv{s~gf`ln ln dln|`di vxovocdov{ ki xsndnvn ox{nsnndln cn| jomi* {sild`eknbosmif`li `j` o{nndli %x~go{`di)$ Ki c` dngi godv{s~gf`li o~riji vrol~ rsv{o~* dilrnidixsn|idli di dln|`d`m gs`{`d`m mlnv{`mi dn vm`l~ c`{` rni ok kox~{nd`e rs`lnkdov{`dixsn|idli |i mi{ns`lij ok golna ln godv{s~gf`li `|asindi$ Vj`gi 9$9 xs`gi|~ln jom csokiVfendnf{ikp di kri k`lnji |coa dnkov{i{dn rsv{on godv{s~gf`ln$

    Gs~{ov{ godv{s~gf`ln xoksi|~m`lnri dln|`d~o{xosdov{ xsnmi knbosm`sidl~$ Xs` {omn* rnnknbosmif`ln moa~ kornv{` ko jomi godv{s~gf`ln* imidln moa~ xosnmn{`{` dln|`d~ b~dgf`odijdov{$\coa {oai vn |ie{`lnri ki dilrnn knbosmif`lngodv{s~gf`ln ov{id~ ~d~{is kox~{nd`e asid`fi$

    V{ic`jdov{ lnv{ vxovocdov{ godv{s~gf`ln ki|iks` xon{d` sirdo{nd` ocj`g$ A~c`{ig v{ic`jdoa

    sirdo{ndoa ocj`gi mon c`{` oxivid gio ` jomgodv{s~gf`ln* ln s csold` xs`mlns` `| xsigvn xogi|~l~ki dnv{ic`jdov{ sirdo{ndoa ocj`gi godv{s~gf`lndn`|clndo rok` xsnmi dln|`dom ~d`{ndl~$

    Vj`gi 9$9

    Xosnk or`e c`{d`e |ie{lnri* gol`mi ln ~rln{orid v`a~sid sik vrign {ned`gn godv{s~gf`ln*ok dln vn {si` ki c~kn ngodom`di i nv{o ` vi {o midlom rjiv{`{om {n`dom$ \ie{lnr`v`a~sdov{` ` ngodom`dov{` mn~vocdo v~ xso{~s`lnd`$ Xsr` |ie{`lnr` rokn gi xornidl~

    ~{sogi mi{ns`liji* i ks~a` gi vmidlndl~$ Xsocjnm ln xsodi` {igro slnndln godv{s~gf`ln golnln ~ ~rln{ `mi dosm ijdn ngvx joi{if`ln v`a~sdo ` `v{okocdo ngodom`do ~| ~{soig m`d`mijdngoj``dn mi{ns`liji$ @|d`ln{` |ie{`lnr`* oksn~l~ ovdordn |iki{gn di~gn o rsv{o`

  • 7/23/2019 vrstoa materijala

    4/104

    ; \ji{id G~jndor`

    V{risidln xsosi~dvg`e mn{ok i |i xsoflnd~ rsv{on* gs~{ov{` ` v{ic`jdov{` godv{s~gf`li* vf`jlnm xov{`|idli v`a~sdov{` ` ngodom`dov{` dl`eor`e xsig{`d`e `lnndli$

    Xs`mlndi koc`rnd`e xsosi~dvg`e mn{oki |i oksn`ridln lnkdn ok moa~`e dnxo|did`fi{sindoa dilcojlna %ox{`mijdoa) slnndli si|mi{sidn godv{s~gf`ln ~ or`vdov{` o dln|`doldimlnd`* i {o ln ocj`g* k `mnd|`ln* kox~{ndo ox{nsnndln `j` mi{ns`lij$

    Mi{nmi{`go ox`v`ridln okdovi `|mn~ ridlvgoa ox{nsnndli* dixsn|idli ` knbosmif`li*|di{do o{niril~ vjond` ocj`f` snijd`e rsv{`e {`lnji {n si|dorsvdi b`|`go-mne id`gi vrolv{ridl`eor`e mi{ns`liji$ \i{o vn ~ di~f` o rsv{o` ~rokn oksnndn xsn{xov{irgn o vrolv{r`mimi{ns`liji ` o di`d~ knbosm`sidli goln `knij`|`sil~ rsv{i {`lnji$ [`mn vn ~ |di{dol mlns`ojigiril~ ` xolnkdov{irjl~l~ ~{rs`ridln xomnd~{`e okdovi* xs` nm~ xoasngi ~ajirdomov{iln ~d~{is asid`fi `dndlnsvgn {odov{` %: > .)$

    Ovdordn xsn{xov{irgn v~

    c) f)

    Vj`gi 9$3

    Xjoi ln godv{s~gf`lvg` njnmnd{ gok golna ln lnkd i k`mnd|`li %kncjl`di) |di{do midliok ov{ij`e$ Vsnkdli xors`di xjon ln sirdi ` xsnxojirjli dln|`d~ kncjl`d~* vj`gi 9$3c$

    J l~ vgi ln godv{s~gf`lvg` njnmnd{ gol` `mi |igs`rjlnd~ vsnkdl~ xors`d~* vj`gi 9$3f$

    3$ RSV[N OX[NSNNDLI

    Ridlvgn v`jn goln klnj~l~ di rsv{o {`lnjo xo{ln~ ok ks~a`e {`lnji ~ dlnaorom ogs~ndl~$Xsnmi m lnv{~ klnjoridli orn v`jn moa~ c`{` xors`dvgn ` roj~mndvgn* vj`gi 3$9$

    Xors`dvgn v`jn klnj~l~ di f`lnjolxors`d` {`lnji `j` dilnkdom dln|`dom k`lnj~* i dnor`vn o miv` {`lnji %dxs$ mn~vocd` xs`{`vig {`lnjixs` kok`s~* {jig {ng~`dn `j` xj`di di {`lnjo `{k$)$Igo ln xors`di di gol~ klnj~ln xors`dvgi v`jirsjo mijndi %{ogi)* aoros` vn o godfnd{s`sidolv`j`$ ^ v~xso{dom* sik` vn o god{`d~`sidom ox{nsnndl~ goln mon c`{` sirdomlnsdo `j`dnsirdomlnsdo sivxok `lnjlndo xo xors`d`$

    Roj~mndvgn v`jn klnj~l~ di vrig` klnj`{`lnji ` ~ rn`d` vj~ilnri si|mlnsdn v~ dlnaorolmiv` %dxs$ asir`{if`lvgn v`jn* `dnsf`lvgn v`jn `{k$)$

    Or`vdo o xsomlnd` {`lngom rsnmndi* ridlvgn v`jn moa~ c`{` v{i{`gn %v{ijdn) ` k`dim`gn%xsomlndjl`rn)$ @vg~v{ro ` `vx`{`ridli xogi|ij` v~ ki ln `|ksjl`rov{ godv{s~gf`lvg`e njnmndi{ixs` k`dim`gom oxnsnndl~ d`i dnao xs` v{i{`gom$

    Gigrn n knbosmif`ln rsv{oa {`lnji div{~x`{` xok ~{lnfilnm ridlvg`e v`ji* or`v` o rsv{`ox{nsnndli$ [o vn mon xogi|i{` di xs`mlns~ {ixi gio dilrid`lna ` dillnkdov{ird`lna

    godv{s~gf`lvgoa njnmnd{i$

    V`ji* momnd{ v`jn ` vxsna v`ji gio ovdord` v{i{`g` njnmnd{`* ~|sog~l~ vjlnknn ovdordnrsv{n ox{nsnndli!$

    Vj`gi 3$9

  • 7/23/2019 vrstoa materijala

    6/104

    2

    I

    \ji{id G~jndor`

    Igv`lijd o %ovdo) ox{nsnndln$ V`jn klnj~l~ ~|k~ ov` {ixi* {igo ki dlnaoro ox{nsnndlnmon c`{` rjido %siv{n|idln)* {o `|i|`ri xsok~jlndln {ixi* vj`gi 3 $3 i* `j` {jido %vic`lidln)*goln xso`|rok` vgsindln {ixi* vj`gi 3 $3 c$

    Vm`fidln* V`jn klnj~l~ ~ sird`d` xoxsndoa xsnvlngi {ixi ` div{oln `|i|ri{` gj`|idlnlnkdoa dlnaoroa k`lnji ~ okdov~ di k s~ a `* vj`gi 3 $3 f$

    ^r`lidln %{os|`li)$ {ix ln ox{nsnnd vxsnaor`mi v`ji gol` jnn ~ sird`d` dlnaoroaxoxsndoa xsnvlngi* vj`gi 3 $3 k$

    Vir`lidln$ [igro ox{nsnndln {ixi mon c`{` vxsnaor`mi v`ji* vj`gi 3$3n* `j` v`jimi ~sird`d` goli xsoji|` gso| dlnaor~ ov* vj`gi 3$3b$ ^ xsrom vn vj~il~ sik` o `v{om vir`lidl~*kog ks~a` vj~il x snkv{irjli vir`lidln v`jimi$

    @|r` lidln$ [jido ox{nsnndln r`{goa {ixi %k~a ` {idig {ix)* giki v`ji xs`lnn oksnnd~asid`d~ rs`lnkdov{* korok` ko `vgs`rjlndli ov` {ixi* {l$ ko dlnaoroa codoa `|r`lidli* vj`gi3$3a$ @|r`lidln ln* |ixsiro* a~c`{ig njiv{`dn v{ic`jdov{` {ixi$

    ^ xsigv` v~ nv{` ` vj~ilnr` `v{okocdoa ox{nsnndli {ixori v kri `j` r`n ovdord`e rsv{iox{nsnndli$ ^ {om vn vj~il~ aoros` o vjondom ox{nsnndl~$

    Igo di dngo {`lnjo klnj~l~ ridlvgn v`jn* odn div{oln ki xs`cj`n `j` si|kroln xolnk`dnnv{`fn {`lnji* nm~ vn v~xso{v{irjlil~ ~d~{sidln v`jn goln klnj~l~ mn~ nv{`fimi$

    Xsn{xov{ir`mo ki vn {`lnjo xok klnjoridlnm ridlvg`e v`ji B* %7 = 9*3*$$$* d) diji|` ~ sirdo{n`$

    Oro |di` ki ln ~vxov{irjlndi sirdo{ni `|mn~ ridlvg`e ` ~d~{sidl`e v`ji ` ki lnknbosm`sidln |irsndo$ \i oksn`ridln dnxo|di{`e ~d~{sid`e v`ji xs`mlndl~ln vn mn{oki

    Bi)

    c)

    f)

    Vj`gi 3$3

    6$ DIXSN\IDLN

  • 7/23/2019 vrstoa materijala

    7/104

    RSV[OI MI[NS@LIJI 1

    xsn vlngi* xsnmi golol {`lnjo |im`jlndo xsnv`lnfimo sird`dom di kri k`lnji$ Vrig` k`o {`lnjimosi ov{i{` ~ sirdo{n` xok klnjoridlnm ridlvg`e v`ji goln di dlnai klnj~l~* {n ~d~{sid`e v`jigoln |imlndl~l~ ~{lnfil okv{sidlndoa k`lnji$ ^ oxnm vj~il~* {n ~d~{sidln v`jn `mil~dnsirdomlnsd~ sivxoklnj~ xo xsnvlng~$ Mlnsi `d{nd|`{n{i or`e v`ji di|`ri vn dixsn|idln* `xoksi|~ m`lnri rnj``d~ ~d~{sidln v`jn di lnk`d`f~ xors`dn ~ xsomi{sidol {og` xsnvlngi$

    Dngi ~ dngol {og` O xsnvlngi* goli vn diji|` di njnmnd{isdol xors`d`II* klnj~ln

    njnmnd{isdi ~d~{sidli v`ji IB * vj`gi 6$9$

    Dixsn |i dln ~ {og` O xsnvlngi knb`d`sido ln rng{osom$3

    Di k`liasim~ siv{n|idli ~oiril~ vn gisig{ns`v{`dn rs`lnkdov{` dixsn|idli< asid`fi xso xosf `o dijdov{ ` fsx* asi d`fi njiv{`dov{` "n * asid`fi {nndli i b * asid`fi rsv{on `asid`fi g`kidli :Lg $

    Kog ln dixsn|idln midln ok x * or`vdov{ dixsn|idli ` knbosmif`ln ln j`dnisdi %OX -xsirif)$ Gik dixsn|idli xov{idn rnn ok x * {i or`vdov{ xov{iln dnj`dnisdi* ij` vn mi{ns`lij `kijln xodii njiv{`do* {o |di` ki vn nxs~rn{i digod siv{nsnndli rsii ~ xsroc`{d` ocj`g `k`mnd|`ln$ Digod {o dixsn|idln xov{idn rnn ok n * mi{ns`lij vn xo`dln xodii{`

    dnnjiv{`do `j` xji v{ ` do* lns digod siv{nsnndli ~ mi{ns`lij~ |iov{il~ {sildn `j` xjiv{`dnknbosmif`ln % vxj* vj`gi >$3)$ Gik dixsn|idln kov{`adn { * knbosmif`ln kijln siv{~ cn|

    xornidli dixsn|idli* goln ig mon ` mijo xiki{`$ Ori vn xoliri di|`ri {nndln mi{ns`liji$

  • 7/23/2019 vrstoa materijala

    14/104

    9; \ji{id G~jndor`

    Digod oksnndn knbosmif`ln* dixsn|idln xodordo siv{n* kov{`n migv`mijd~ rs`lnkdov{ %?m

    goli vn di|`ri ` rjidi rsv{oi* i |i{`m xiki ko :l g * giki vn nxs~rn{i jom`$Xsok~jlndln nxs~rn{n xs` siv{n|idl~* xsi{` v~ndln dln|`doa xoxsndoa xsnvlngi$ Ko xolirn

    {nndli mi{ns`liji {o ln v~ndln lnkdo j`go xo f`lnjol k~jl`d`* i lnkdoj`g i v~ ` dixsn|idli `knbosmif`ln ~ f`lnjol nxs~rn{`$ Gik vn dixsn|idln xs`cj`` asid`f` {nndli* xo`dln diajov~ndln dilnkdom mlnv{~ nxs~rn{n %rsi{)* akln dixsn|idli ` knbosmif`ln xov{il~ `|si|`{o rnndnao ~ ov{ijom k`lnj~ nxs~rn{n$ \i{o vn vrn ko {ogn [ k`liasimi siv{n|idli* godrndf`odijdo `v{risdo dixsn|idln dn|di{do si|j`g~l~* i xovj`ln {n {ogn dl`eorn si|j`gn xov{il~ vrn rnn$

    K`liasim` siv{n|idli si|j``{`e {ned`g`emi{ns`liji rsjo v~ si|j``{` xo ocj`g~ `rs`lnkdov{`mi dixsn|idli* ij` vn `xig moa~vrsv{i{` ~ n{`s` ovdordn vg~x`dn* gigo {o xogi|~ln

    vj`gi >$6$Xog~v` vic`lidli kil~ vj`dn i - v k`liasimn

    gio ` xog~v` siv{n|idli$ Gok siv{n|jl`r`emi{ns`liji %dxs$ mng` nj`g* cigis* csodfi `{k$)*asid`f` {nndli xs` siv{n|idl~ okaorisi asid`fi adlnndli xs` vic`lidl~* giki xo`dl~ |di{d`lnxjiv{`dn knbosmif`ln mi{ns`liji$ Rjidol rsv{o`okaorisi asid`fi rsv{on xs` vic`lidl~ `j` {jidirsv{oi$

    Gseg` mi{ns`lij` %dxs$ gijlnd` nj`g* v`r` j`lnr*cn{od `{k$) dn moa~ vn xjiv{`do knbosm`si{`* {o|di` ki digod njiv{`d`e knbosmif`li xsig{`g`okmie koji|` ko si|isidli mn{ns`liji$ [snci`v{igd~{` ki ln gok gseg`e mi{ns`liji {jidirsv{oi |di{do rni ok rjidn rsv{on %dxs$ |iv`r` j`lnr xs`cj`do ; x~{i)$

    \i vrn rsv{n k`liasimi siv{n|idli* vj`gi >$6* xs` mij`m knbosmif`limi xov{ol` j`dnisdior`vdov{ okdovdo xsoxosf`odijdov{ dixsn|idli i ` knbosmif`li v $ [i v~ xoks~li ~k`liasim~ `|r~ndi kncjlom fs{om$ [igons* xog~v`mi ln xogi|ido ki xov{ol`

    xsoxosf`odijdov{ `|mn~ xoxsndn n X ` ~|k~dn k~jl`dvgn knbosmif`ln v * xs` nm~ v~ odn~r`lng v~xso{doa xsnk|d igi %xs` siv{n|idl~ nxs~rn{i vn xsok~jl~ln ~| vmidlndln xsnvlngi* i xs`vic`lidl~ div{~xi vgsindln nxs~rn{n ~| xornidln xsnvlngi)$ [n kr`ln |igod`{ov{` moa~ vnxs`gi|i{` `|si|`mi$;)

    Or` `|si|` xsnkv{irjlil~ E oognor |i god lnkdoovdoa v{idli dixsn|idli$ [o ln {nmnjld`|i go d di~gn o rsv {o`* lns vri koc`rndi slnndli rs`lnkn ~ dlnaor`m asid`fimi* {l$ ko

    asid`fn xsoxosf`odijdov{` i x $

    Gonb`f`lnd{` xsoxosf`odijdov{` ~ `|si|`mi %>$;)* v~< N - Po~daor mok ~j njiv{`dov{` ` r -Xo`vvo`{or gonb`f`lnd{$

    [o v~ godv{id{dn rnj``dn |i oksnnd` mi{ns`lij$ Mok~j njiv{`dov{` `mi k`mnd|`l~dixsn|idli xi m~ ln lnk`d`fi xivg ij$ Dxs$ |i nj`g ln N = 398 AXi$ Xo`vvodor gonb`f`lnd{ ln

    Vj`gi >$6

  • 7/23/2019 vrstoa materijala

    15/104

    RSV[OI MI[NS@LIJI 9>

    cn|k`mnd|`lvgi rnj``di goli |i `|o{soxdn mi{ns`lijn `|dov` 8 : r: 8*>$ \ i rn`d~ m n{iji ln r

    8*6$Xog~v`mi vm`fidli mon vn ~{rsk`{` or`vdov{

    `|mn~ {idandf`lijd`e dixsn|idli s ` g~{d`eknbosmif`li p |i dng` mi{ns`lij$ [igri vn or`vdov{

    xs`gi|~ln u - p k`liasimom * gol` ln vj`id i - v k`liasim~* vj`gi >$;$ @ ~ orom vj~il~ xogi|ido ln kixov{ol` xoks~ln xsoxosf`odijdov{` dixsn|idli `knbosmif`ln* {o |di` ki Eoognor |i god vm`fidliajiv`$>)

    Gonb`f`lnd{ xsoxosf`odijdov{` ~ orom `|si|~ ln< A -mo k~j vm`fidli %gj`|idli)$

    Mok~j vm`fidli ln {igons godv{id{di rnj``di |ioksnnd` mi{ns`lij$ Dlnao ri lnk`d `fi ln xivgij$ Dxs$ |inj`g rs`lnk` A = 58 AXi$

    Xo{o gisig{ns`|`sil~ njiv{`di vrolv{ri rsv{oai {`lnji* rnj``dn N* A ` r * di|`ril~ vngodv{id{n njiv{`dov{`$ Dl`eorn vn rnj``dn |i si|j``{n {ned`gn mi{ns`lijn moa~ xsodi` ~{ned`g`m xs`s~d`f`mi$

    2$ XSOSI^DVGO @ KOX^[NDO DIXSN\IDLN

    Njnmnd{` {ned`g`e godv{s~gf`li xsosi~diril~ vn {igo ki c~k~ ~ ngvxjoi{if`lvg`m~rln{`mi v`a~sd`* {o |di` ki vn xok klnjoridlnm ox{nsnndli dn knbosm`sil~ {sildo `j` ki dnkov{`ad~ asid`f~ jomi$ Ki c` vn xsosi~d dixsn|idli `/`j` knbosmif`li godv{s~gf`lvg`enjnmndi{i moaio xsornv{`* si|m i{sid~ godv{s~gf`l~ xo{sncdo ln moknj`si{` gigo anomn{s`lvg`*{igo ` xo ovdor` oxnsnndli$ \coa {oai vn v{risdi godv{s~gf`li xs`gi|~ln xso si~dvg om venmom* di golol v~ ~fs{idn vimo ajirdn k`mnd|`ln ` xsn{xov{irjlndo ox{nsnndln$ Di vj`f`2$9i* gio xs`mlns* xs`g i|i dln nj`d` dovi [ xsob`ji gol` ln dil nkd om gsil~ rsv{o |irisnd |irns{`gijd~ v{`lndg~* i di dlnaorom vjocokdom gsil~ xs`rsnd ln njng{somo{os$

    Di xsosi~dvgol venm` {n godv{s~gf`ln ocj`gi god|ojn* vj`gi 2$9c* ox{nsnndln ln xs`gi|ido{n`dom god|ojn Ag* {n`dom njng{somo{osi An m ` xsomlndjl`rom fnd{s`b~aijdom v`jom

    Bf = mn i 3* akln v~< m *n Z fo - mivi* ngvfnd{s`f`{n{ ` g~{di cs|`di so{osi njng{somo{osi$

    i) T c) B

    Vj`gi >$;

  • 7/23/2019 vrstoa materijala

    16/104

    92 \ji{id G~jndor`

    \coa origroa xs`v{~xi xs` xsosi~d~* {snci si|j`gori{` v{risdo ` xsosi~dvgo dixsn|idln$V{risdo dixsn|idln ln odo goln vn ~ godv{s~gf`lvgom njnmnd{~ xolirjl~ln ~ sikd`m ~rln{`mi*i xso si ~dvg o dixsn |idln xsnkv{irjli ong`rid~ rs`lnkdov{ dixsn|idli ~ godv{s~gf`lvgom

    njnmnd{~ koc`rnd~ xsosi~dom$Xsosi~dvgo dixsn|idln si|j`g~ln vn ok v{risdoai* i |i {o xov{ol` r`n si|joai< dnkorojldo

    xo|diridln ox{nsnndli goln klnj~ln di godv{s~gf`l~* dnokaorisil~` `|cos xsosi~dvgn venmngolom d`v~ ~|n{` ~ oc|`s vr` kn{ijl` v{risdn godv{s~gf`ln* oasid`ndi {odov{ `|si|i gol` vngos`v{n ~ di~f` o rsv{o`* xov{olidln koki{d`e dixsn|idli %xon{di* mod{idi ` {oxj`dvgi)goli v~ dilnn dnxo|di{i* `{k$ \coa vrnai {oai* xsosi~dvgo dixsn|idln vimo ln xsoflndi v{risdoa dixsn|idli$

    Ki vn godv{s~gf`li dn c` vjom`ji* livdo ln ki v{risdo dixsn|idln mosi c`{` midln okrsv{on mi{ns`liji$ Mn~{`m* ~ mdoa`m vj~ilnr`mi dn vm`ln vn kox~v{`{` xoliri d`{`dilmidln xjiv{`dn knbosmif`ln$ Xsnmi {omn* v{risdo dixsn|idln ~ siv{n|jl`r`m mi{ns`lij`mi

    {snci ki c~kn midln ok asid`fn {nndli* i gok gseg`e mi{ns`liji |di{do midln ok asid`fnrsv{on$ C~k~` ki v{risdo dixsn|idln mon c`{` rnn ok xsosi~dvgoa* xo{sncdo ln ov`a~si{`ki dilrnn xsosi~dvgo dixsn|idln c~kn midln ok dngoa kox~{ndoa dixsn |idli :Lk* okdovdo

    {k * vj`gi 2 $3 $

    Kox~{ndo dixsn|idln siv{n|jl`r`e mi{ns`lijiknb`d`si vn `|si|`mi* ij` xodngik mon c`{` ` V 4 98

    %1 $ IGV@LIJDO OX[NSNNDLN

    1$9 IDIJ@\I DIXSN\IDLI @ KNBOSMIF@LI

    Dngi ln sird` xs`|mi{`d` {ix xso`|rojldoa xoxsndoa xsnvlngi* di gsilnr`miox{nsnnd godfnd{s`sid`m v`jimi B goln klnj~l~ k~ dlnaorn ov` |* vj`gi 1$9i$

  • 7/23/2019 vrstoa materijala

    17/104

    RSV[OI MI[NS@LIJI 91

    Vj`gi 1$9

    {ix vn diji|` ~ dixsnad~ {om v{idl~* {o |di` ki vn ~ dlnm~ xolir jl~l~ ~d~{sidln v`jn$ \ioksn`ridln rnj``dn ` sivxoklnjn {`e v`ji* gos`v{`{ nmo mn{ok~ xsnvlngi$ Xsnv`lnf`mo xoxsndo{ix sird`dom di kri k`lnji* i ~{lnfil okcindoa k`lnji |im`lnd`mo v~v{irom ~d~{sidl`e v`jisivxok`lnjlnd`e xo xors`d` xsnvlngi$ Dl`eori sn|~j{id{i klnj~ln ~ {n`{~ [ xsnvlngi ` `mixsirif ov` {ixi* xi xsnkv{irjli ~|k~d~ v`j~ D ~ xsomi{sidom xsnvlng~$ ^ orom ln vj~il~~|k~di v`ji xo|`{`rdi lns ln ox{nsnndln {ixi rjido$ Xs` {jidom ox{nsnndl~ {ixi* ~|k~div`ji ln dnai{`rdi$

    Livdo ln ki v~ ` xsirf` vr`e ~d~{sidl`e v`ji xisijnjd` ov` {ixi |* {o |di` ki vn ~ vrigol

    {og` xsnvlngi xors`dn I* lirjli vimo dosmijdo dixsn|idln i $ Di vrigol njnmnd{isdolxors`d` kI klnj~ln ~d~{sidli v`ji i-kI* gigo {o xogi|~ln vj`gi 1$9c$ Xsomi{sid` k`o {ixidiji|` vn ~ sirdo{n`* x i mosi c`{` `vx~dlnd ~rln{-98!

    >88-98# = 08 MXi

    Xsomlndn k~jl`di8-8*>

    I/ 3 =

    I/*

    NI ! 3 8 8 -o89oO

    @O# 2

    D 3j3 6>-9

    NI 3 8 8 oOD

    JIOo@O#2

    T 6 ;>-9*>

    NI 388-982->88-98#

    = 3*>- 9 8 ; m

    = 6 *>-@O! ; m

    = 2*1>-@O#; m

    ^

    U N I

    b;

    D *

  • 7/23/2019 vrstoa materijala

    21/104

    RSV[OI MI[NS@LIJI 39

    ^g~xdi xsomlndi k~jl`dn* ~ orom vj~il~ `|k~nd`n {ixi* `|dov` ' 6*> ' 2*1>) @O! ; = 93*1> @O#; m = 9*31> mm

    XS@MLNS 3

    Gs~{i eos`|od{ijdi asnki IC |idnmisjl`rn{n`dn* ovjodlndi ln |ajocdo ~ {og` I i ~ {og`C xorn|idi ln v rns{`gijd`m cigsnd`m {ixomCF* xsirog~{doa xsnvlngi gio di vj`f`$ Oksnk`{`xo{sncdn k`mnd|`ln xoxsndoa xsnvlngi {ixiCF {n xomig {ogn C* igo vn asnki IC ox{nsn{`

    sirdomlnsdo sivxok`lnjlnd`m god{`d~`sid`mox{nsnndlnm y$\ikido

    {nmxnsi{~sn$ ^ xsrom vj~il~ sik` vn o xon{d `m dixsn|idl `m i* kog vn ~ ks~aom vj~il~xolirjl~l~ {oxj`dvgi dixsn|idli$ [igri dixsn|id li rsjo v~ oxivdi ln s vn {ngo o{gs`ril~* i xs`ox{nsnndl~ godv{s~gf `ln |csilil~ vn v dixsn|idl`mi goln `|i|`ri ridlvgo ox{nsnndln$Sn|~j{i{ mon c`{` jomgodv{s~gf`ln* `igo ln dixsn|idln

    goln xo{lnn ok ridlvgoaox{nsnndli midln ok kox~{ndoa$

    Xolir~ xon{doa dixsn|idlixogi`mo di xs`mlns~ eos`|od{ijdngs~{n asnkn gol~ {snci xorn|i{` vkri rns{`gijdi {ixi* vj`gi 1$2$

    `|sikn gisi` |i 5 ok xo{sncdnk~jl`dn$ \i vxilidln* xo{sncdo ln`v{okocdo vic`{` {ix 9 |i Ie * `

    siv{nad~{` {ix3

    |i Ie $

    Gio sn|~j{i{ {igroa xov{~xgi ~ {ixor`mi v xors`dimi xsnvlngi ; ` ` * * xolirjl~l~ vn v`jn

    V* ` T 3 * goln `|i|`ril~xon{di dixsn|idli) @O1 -938-@O2 ->-98 #;

    Kigjn* {nmxnsi{~si vn mosi xorni{` |i 56*6 F$

    c) Giki dnv{iln v`ji ~ f`j`dks~ 9* rijlig 3 xsn~|`mi vir {nsn{$

    B3 = 8 =4%9)=4BU=A =>4%3)=4

    I { _ A ________________ T8______________ = _36 a f%i * - i 3) N jIj %93>-92>) 981 -398-982 98-98 ;

    ^ orom ln vj~il~ xo{sncdo vmidl`{` {nmxnsi{~s~ |i 36*5 F$

    f) Rijlig 9 ` f`j`dkis 3 lnkdi go v~ ox{nsnnd`$

    B * = B 3 =4%)=4 Bu = B 3 = @ =4%3)=4

    I{ = - A% ` t i 3 )

    9 9

    Z N W I w N 3I 3 l= $$$ = 30*5 F

    Xo{sncdo ln |ias`li{` v~v{ir |i 30*5 F$

  • 7/23/2019 vrstoa materijala

    29/104

    RSV[OI MI[NS@LIJI 30

    1$> GODFN D[SIF@LI DIXSN\IDLI

    ^ xsigv` v~ gok igv`lijdo ox{nsnnd`e k`lnjori ocj`gi {ixi* |coa godv{s~gf`lvg`e `j`ngvxjoi{if`lvg`e si|joai* nv{o xs`v~{d` si|j``{` ocj`f` diajn xsomlndn dlnaoroa xoxsndoa

    xsnvlngi< v~ndli* |isn|`* ~{os`* o{ros` ` v`$* gigo {o xogi|~ln vj`gi 1$0$

    Di mlnv{`mi {igr`e anomn{s`lvg`e k`vgod{`d~`{n{i gol` ovjicjl~l~ xsnvlng {ixi* ij` ` dimlnv{`m i klnjoridli godfnd{s`sid`e v`ji {f moa~`e* knbngi{i ~ v{s~g{~s` mi {ns`liji* sivxoklnjidixsn|idli r`n d`ln lnkdoj`gi* lns koji|` ko jogijdoa xornidli dixsn|idli$ [i vn xoliridi|`ri godfnd{sif~li dixsn|idli* xs` nm~ di vrigom {igrom mlnv{~ migv`mijdo

    dixsn|idln mon r`nv{s~go xsnmi`{` xsosi~dvgo dixsn|idln ` kornv{` ~ x`{idln dov`rov{godv{s~gf`ln$

    Oksn`ridln dixsn|idli ~ cj`|`d` k`vgod{`d~`{n{i rsjo ln vjondo ` dn mon c`{`dixsirjlndo idij`{`g`m mn{okimi di~gn o rsv{o`$ @igo v~ dng` lnkdov{ird`l` ` |i xsigv~rid` vj~ilnr` s`lnnd` mn{okimi {nos`ln njiv{`dov{`* kidiv vn xsocjnm` godfnd{sif`lndixsn|idli slniril~ ngvxns`mnd{ijd`m ` d~mns`g`m mn{okimi$ Godfnd{sif`li dixsn|idliigv`lijdo ox{nsnndoa {ixi gol~ `|i|`ril~ kri xoj~gs~di ~{osi xs`gi|idi ln di vj`f` 1$98$

    Vj`gi 1$98

    Gio mlnsi godfnd{sif`ln dixsn|idli vj~` gonb`f`lnd{ godfnd{sif`ln dixsn|idli i G$Od xsnkv{irjli omlns migv`mijdoa jogijdoa dixsn|idli :smiu ` di|`rdoa %xsosi~dvgoa*

    xsovlndoa) dixsn|idli fsd ~ ovjicjlndom xsnvlng~ xors`dn Id * {l

  • 7/23/2019 vrstoa materijala

    30/104

    68 \ji{id G~jndor`

    i G = ?LVVJ %1$9>)i d

    i Bakln ln< i = $;*

    Gonb`f`lnd{ godfnd{sif`ln dixsn|idli i G or`v` ok ocj`gi ` rnj``dn anomn{s`lvgoa

    k`vgod{`mk{n{i* {n ok rsv{n ox{nsnndli$

    Vj`gi 1$99 Vj`gi 1$93

    @j~v{sif`l~ sivxoklnjn dixsn|idli ogo vsnk`dlna gs~doa o{rosi ~ igv`lijdo rjidoox{nsnndom xjovdi{om {ix~ kiln bo{oasib`li di vj`f` 1$99$ Bo{oasib`li ln div{iji gio sn|~j{i{xs`mlndn ngvxns`mnd{ijdn bo{onjiv{`f`mn{s`lvgn mn{okn* nv{o gos`{ndn ~ idij`|` godfnd{sif`lndixsn|idli ox{nsnnd`e godv{s~gf`lvge njnmndi{i$ Or`vdov{ gonb`f`lnd{i godfnd{sif`lndixsn|idli o rnj``d` vsnk`dlna gs~doa o{rosi ~ {ix~* ki{i ln di vj`f` 1$93$

    Oxnd`{o rs`lnk`< godfn d{sif`li dixsn|idli ln rni {o ln xs`lnji| diaj`l`* |isn| ` ~{os o{s`l`*i xo j~m lns o{rosi midl`$

    Godfnd{sif`li dixsn|idli diso`{o ln oxivdi gok v{i{`g` ox{nsnnd`e godv{s~gf`lvg`e

    njnmndi{i `|sind`e ok gsegoa mi{ns`liji* lns mon c`{` ~|sog xolirn x~go{`di ` `|i|ri{` jom$Xovncdo rijli `v{igd~{` ki xsrosi|snkd~ ridov{ godfnd{sif`li dixsn|idli koc`ri gokk`dim`goa ox{nsnndli cn| oc|`si ki j` ln mi{ns`lij gseig `j` siv{n|jl`r* lns ln ~{rsndo ki vn`|ksjl`rov{ godv{s~gf`lvgoa njnmndi{i ovjicjlndoa xsnvlngi c`{do vmidl~ln$ Vj`gi 1$96*xs`gi|~ln k`dim`g` jom %{|r$ |imosd` jom) gojlndiv{n ovor`dn gj`xdoa mo{osi di s~girf~jnili `|i|rid godfnd{sif`lom dixsn|idli$

    Vj`gi 1$96

  • 7/23/2019 vrstoa materijala

    31/104

    RSV[OI MI[NS@LIJI 69

    5$ V[IDLI DIXSN\IDLI

    5$9 LNKDOOVDO V[IDLN DIXSN\IDLI

    Idij`|i dixsn|idli igv`lijdo ox{nsnndoa {ixi xsornkndi ln ~ dlnaorom xoxsndomxsnvlng~ %Xoajirjln 1$9)$ Mn~{`m* ngvxns`mnd{` xogi|~l~ ki vjom {ixi div{iln dn vimo xoorom xsnvlng~* rn ` xo xsnvlnf`mi gol` v ov` {ixi |i{risil~ oksnnd` g~{$ @| {oai vj`lnk` ki lnxo{sncdo xo|diri{` v{idln dixsn|idli ~ vr`m {ogimi ` vr`m xsnvlnf`mi %xoxsnd`m ` gov`m){ixi* gigo c` vn idij`|om {oai v{idli ~{rsk`j` dnoxeokd` ~rln{` |i dlnaor `vxsirid xsosi~d$

    Idij`|~ dixsn|idli di xso`|rojldom govom xsnvlng~ xsornv{ nmo di xs`mlns~xs`|mi{`doa {ixi ox{nsnndoa igv`lijd`m v`jimi B di rjig$ \im`vj`mo ki vmo {ix

    xsnvlngj` dngom go vom sird`dom `li dosmiji d |i{risi g~{ %x v ov` {ixi | * vj`gi 5 $ ji $

    Vj`gi 5$9

    G~{ %x ln xo|`{`rid igo siv{n ~ vm`vj~ v~xso{dom a`cidl~ gi|ijlgn di vi{~$ Xors`dixoxsndoa xsnvlngi ln I * ixors`di govoa xsnvlngi ln Id$ Di vj`f` 5$9c* xs`gi|idln j`lnr` k`o

    {ixi okrolnd gov`mxsnvlngom di gomn klnj~ln rng{os dixsn|idli x d ~ xsirf~ ov` {ixi$ @|

    ~rln{i sirdo{nn {oai k`lnji {ixi* vj`lnk`

  • 7/23/2019 vrstoa materijala

    35/104

    RSV[OI MI[NS@LIJI 6>

    * j[,p{id 3:x8 = ------ %5$5)

    Vj`gi 5$> Vj`gi 5 $2

    O`{o ln ki `|si| %5 $5 ) kiln kri slnndli ` {o :x!8 ` %x#i * goli vn mn~voc do si|j`g~l~ |i l{/ 3 $

    Rs`lnk` xsir`jo< rnn ajirdo dixsn|idln i* `d` g~{ midl` ok 1s/ ; v rn`m dosmijd`m

    dixsn|idlnm % fs{ `j` fsp)$

    Di ovdor` `|si|i %5$1) ` %5 $5 )* vj`lnkn rnj``dn ajird`e di xsn|idli )$

    Oril `|si| xsnkv{irjliEoogn or |igod vm`fidli `lnkdigln `|si|~ %>$>)$

    0$3 XSOSI^D GODV[S^GF@LVG@E NJNMNDI[I DI VM@FIDLN

    ^ {ned`gol xsigv` xov{ol` d`| xs`mlnsi gok gol`e ln vm`fidln kom`did{do dik ks~a`mrsv{imi ox{nsnndli godv{s~gf`lvg`e njnmndi{i* {l$ giki {idandf`lijdo dixsn|idln s `mixs`misd~ ~joa~$ [`x`d` v~ xs`mlns` vxolnr` k`lnjori godv{s~gf`li ov{risnd` |igor`fimi*|iris`ridlnm* gj`dor`mi* vromlif`mi* `{k$

    Si|mo{s`mo |i gor` d` vxol kri j`mi gol` ln ox{nsnnd v`jimi B gio di vj`f` 0$>$ Gigo lnkncjl`di j`mi e miji* dosmijdo dixsn|idli ~ |igor`f` xsomlnsi k|coa vir`lidli vxsnaom v`ji

    M = B- e * |idnmisjl`ro ln ~ okdov~ di {idandf~lijdo dixsn|idln goln vn xolirjl~ln ~vj`lnkvm`fidli xoxsndom v`jom B ~ dlndom fs{gidom xsnvlng~$ Igo ln v`ji B korojldo rnj`gi*{s~x |igor`fn c`{ n xsnsn|id ~ {om xsnvlng~* vj`gi 0$2$

    k

    Vj`gi 0$>

  • 7/23/2019 vrstoa materijala

    47/104

    RSV[OI MI[NS@LIJI ;1

    ^rln{ rsv{on di vm`fidln |igor`fn ln)

    j!up - @up ' cI

    @|si|` %98$>) xsnkv{irjlil~ {|r$ V{n`dnsoro xsir`jo$ jidor` @ u * 9p ` 9 up nv{o vn di|`ril~ `rjiv{`{` momnd{` {somov{`* i jidor` i 3 I * c3I ` icI xojoild` mom nd{` {somov{ $

  • 7/23/2019 vrstoa materijala

    52/104

    >3 \ji{id G~jndor`

    O`ajnkdo ln ki ok vr`e momndi{i {somov{` |i vg~x xisijnjd`e ov`* dilmidl~ rs`lnkdov{ `miodil ~ okdov~ di {n`d~ ov$

    So{if `li go osk`di{doa v~v{iri$ Dngi v~

    xo|di{` momnd{` {somov{` @u* @ ` @ v

    oc|`som di g$ v~v{irup $ Oksnk`mo momnd{n{somov{` |i g$ v~v{ir u p * gol` ln |igsnd~{

    ogo {n`{i xsnvlngi [ |i g~{ nx* vj`gi 98$>$

    Rn|i `|mn~ v{is`e ` dor`e goosk`di{i ~orom vj~il~ ajiv`

    Igv`lijd` momnd{ {somov{` |i |igsnd~{~ ov u xsnmi knb`d`f`l` ln8 Dm $

    K`liasim momndi{i ~r`lidli {ixi

    `mi `|ajnk gio di vj`f $

    i) Migv`mijdi dixsn|idlixolirjl~l~ vn di ridlvg`ms~cor `mi k`lnjori {ixi ` `|dovn 8 9 8

    d Z 3 -3> -@O 6 ) 6

    = 5 s miu = ;5*5 MXi

    = 2*9 MXi

    @R

    C

    ~

    ` ) CI

    M$

    `:miu3

    j

    :X*FI

    ^/x

    Xsnmi {omn* k`o 3 `mi ovim x~{i rnn migv`mijdo dixsn|idlnok k`lnji 9$ K`liasim xsomlndn s dixsn|idli ~|k~ {ixi ki{ lndi aosdlol vj`f`$ D`ln ~|n{i ~ oc|`s godfnd{sif`li dixsn|idli golivn xolirjl~ln ~ xsnvlng~ C %mlnv{o diajn xsomlndn xsnvlngi{ixi)$ Migv`m ijdi rs`lnkdov{ dixsn|id li di {om mlnv{~

    mon vn oksnk`{` xom o~ gonb`f`lnd{i godfnd{sif`ln

    dixsn|idli * gol` or`v` ok ocj`gi |iocjlndli ~ xs`lnji|domxoks~l~$ Vj`gi xogi|~ln xs`cj`d~ sivxoklnj~ dixsn|idli ~ |od`godfnd{sif`ln dixsn|idli$

    -

  • 7/23/2019 vrstoa materijala

    62/104

    23 \ji{id G~jndor`

    c) ^g~xd` g~{ |ig sn{i xsnvlngi F ~ okdov~ di xsnvlng I* lnkd ig ln |c sol~ g~{nri |igsn{i ocik`lnji {ixi %mn{ok v~xnsxo|`f`ln)$ M onmo x`vi{`8 -9

    7s-58- 98 j %3-3> -98 ) %3>-98 )= >*3-@O 6 sik

    `j`958 958

    :X#f i = -----:Xfi=------ >*3-98 6_------ d d

    K`liasim xsomlndn g~{i | i g sn {i T ~|k~ {ixi* ki{ ln di xsn{eokdol v{sid`f`$

    99$3 K@MND\@OD@SIDLN [IXORI OX[NSNND@E DI ^R@LIDLN

    K`mnd|`od`sidln okdovdo oksn`ridln xsomlnsi {ixori ox{nsnnd`e di ~r`lidlnxsorok` vn di ovdor` ~rln{i rsv{on ` ~rln{i gs~{ov{`$

    ^rln{ rsv{on , 98

  • 7/23/2019 vrstoa materijala

    65/104

    RSV[OI MI[NS@LIJI 2>

    9 8 3 6

    b c -$ M ** b I / ! * / )

    B-

    / ` _

    R

    b x Z

    `

    x9 $ $ N $ $ $ $ @ 8

    x 9miu ` /

    $ $ $ $ B[#

    $$$$$$$$$mx*

    x 6

    ^rln{ gs~{ov{`< *0miu = : 0k$ Xs` {omn ln T = T - 3 = 8 * 8 6 > T $X

    Xo{sncd` ridlvg` x somlns rsi{`ji gol` |ikorojliri oril ~rln{ ln * 9 , 8*8618 m$] 1 %Z- p/; )A 0k ] lu %9 - 8*2;) 5> 980 8*86>

    ^vrilimo rn~ rs`lnkdov{ ridlvgoa xsomlnsi rsi{`ji %xsnmi ~rln{~ rsv{on) ` |iogs~~lnmo

    ln di v{i dkiskd~ rs`lnkdov {K = ;8 mm$^d~{sidl` xsomlns rsi{`ji ~ {om ln vj~il~ k =p/ K = 8*2 ;8 = 3; m m $

    99$6 V[I[@G@ DNOKSNND@ \IKIF@

    Gok slniridli xsocjnmi ~r`lidli ~ xsigv` vn xolirjl~l~ v{i{`g` dnoksnnd` |ikif`*gok gol`e sivxojo`r` csol v{i{`g`e lnkdikc` sirdo{nn d`ln korojlid |i oksn`ridln vr`ednxo|di{`e rnj``di$ Xs` slniridl~ {igr`e |iki{igi xs`m`lndl~ln vn `v{` xs`df`x gio ` ~ vj~il~

    v{i{`g` dnoksnnd`e |iki{igi xs` igv`lijdom ox{nsnndl~ %Xoajirjln 1$6)$^| v{i{`g` ~rln{ sirdo{nn* ~ origr`m vn vj~ilnr`mi gos`v{` ` koki{d` ~rln{

    knbosm`sidli gol` vn ovd`ri di okaorisil~`m g~{or`mi ~r`lidli$ Xodor`mo* g~{ ~r`lidlixsnkv{irjli |igsn{ lnkd oa xsnvlngi {ixi ~ okdov~ di ks~a`$

  • 7/23/2019 vrstoa materijala

    66/104

    22 \ji{id G~jndor`

    {ix xsomldjl`roa xsnvlngi ~gj`ln{nd ln di vrol`m gsilnr`mi I ` C* i di vsnk`d` ox{nsnnd lnmom nd{om ~r`lid li M *$ K`o 9 `mi x~d` gs~d` i k`o 3 xsv{ndiv{` xoxsnd` xsnvlng$ Oksnk`{`

    snig{`rdn mom nd{n ~ ~gjln{nd l`mi ` vg`f`si{` k`liasim mom ndi{i ~r`lidli {ixi$\ikido< M* * /* A* @ xj = 3@ x3$

    XS@MLNS 96

    ^ ~gjln{ndl`mi vn xolirjl~l~ snig{`rd`momnd{` M I ` M C $

    ^rln{ sirdo{nnXi

    {id3 :x8 = = - Z T * j34 = -8 *; ;; =, :x8 = -93i $ ;>>5 --------------

  • 7/23/2019 vrstoa materijala

    78/104

    15 \ji{id G~jndor`

    Dixsnad~{` njnmnd{ ~ {og` F v ajird`m dixsn|idl`mi ` Moesori gs~d`fi dixsn|idliB /6akln ln< b CB= ----- xsoa`c ~ {og` C |coa klnjoridli vimo v`jn B

    ;5N@U

    C @6 / Zb CC = --------- %[) - xsoa`c ~ {og` C |coa klnjoridli vimo snigf`ln C6N @U

    Rs`lnkdov{` xsoa`ci b CB ` b CB `|si~di{n v~ idij`{`g` %r`k` Xoajirjln 93$3$6)* ij` vn moa~

    di` ` ~ okaorisil~`m {icj`fimi$ ^rs{iridlnm koc`rnd`e rs`lnkdov{` ~ ~rln{ knbosmif`ln*od ajiv`B j6 C @6 >B 6 $ = 8 * xi d`ln {ngo koc`{` dnxo|di{~ snigf`l~ ~ {og` C< C = $

    ;51 6N @ 92

    r $ $ 9 9B $Dnxo|di{n snigf`ln ~ {og` I vj`lnkn di ovdor` ~rln{i sirdo{nn ` `|dovn< I = `

    _____ 9 2

    6 BjMi =

    I 92

    93$6 GOVO VIR@LIDLN

    Giki sird`di ox {nsnndli govi ` dn xsoji|` gso| ajirdn fnd{sijdn ov` {somov{` u ` p xoxsndoa xsnvlngi {ixi* div{iln govo vir`lidln* vj`gi 93$3;$ Xsnvlng sird`dn ox{nsnndli vxoxsnd`m xsnvlngom ln {sia ox{nsnndli S* gol` v xo|`{`rd`m vmlnsom ov` u |i{risi g~{ :x$

    Govo vir`lidln div{~xi ` ~ vj~il~ ki ln {sia ox{nsnndli rns{`gijid i xsnvlng {ixi |igsnd~{*`j` v~ m~ ajirdn fnd{sijdn ov` {somov{` govn* vj`gi 93$3>$ ^ vr`m {`m vj~ilnr`mi*knbosm`sidln {ixi dn |c`ri vn ~ sird`d` ox{nsnndli$

  • 7/23/2019 vrstoa materijala

    87/104

    RSV[OI MI[NS@LIJI 51

    /ox{nsnndli!

    Z : x

    [%U

    Vj`gi 93$3>

    Si|mo{s`mo god|oj~ xsirog~{doa xoxsndoa xsnvlngi ox{nsnnd~ di vjocokdom gsil~v`jom B* goli v ov` u gio ajirdom fnd{sijdom ov` {somov{` |i{risi g~{ nx* vj`gi 93$32$ ^

    dngom xsnvlng~ | origo ox{nsnndoa {ixi* xolirjl~l~ vn ~d~{sidln v`jn Y ` M $ Xoxsndiv`ji Y `|i|`ri {idandf`lijdo dixsn|idln ~ xsnvlng~* kog ln momnd{ vir`lidli M ~|sog xolirndosmijdoa dixsn|idli$ Mn~{`m* {idandf`lijdo dixsn|idln ln mijndo ~ ~vxosnkc` v

    dosmijd`m* xi vn oc`do |idnmis~ln$ Rng{os momnd{i vir`lidli M ogom`{ ln di {sia

    ox{nsnndli S * i mon vn siv{ir`{` di kr`ln gomxodnd{n M u ` M p * gigo {o xogi|~ln vj`gi

    Rnj``dn or`e rng{osi v~