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R 2a
W ih W2 h 1a d2
R 1a d1 a W2 g/a.
W1 F ih h2
h 1a h3
R fr l 1 R rr F R sr
L 1 L2
W f W r Ws
ludoM edoK
.KGM OTO 2 62 - 20
YNU kinkeT satlukaF fitomotO kinkeT nakididneP nasuruJ
KAJEJ AYAG NAARADNEK
: nusuyneP
.T.M ,.dP.M ,ibutraM
fitomotO kinkeT nakididneP nasuruJ KINKET SATLUKAF
ATRAKAYGOY IREGEN SATISREVINU 4002
2
RATNAGNEP ATAK
luduj nagned ludoM kajeJ ayaG naaradneK naudnap iagabes nakanugid ini
aigek malad :utiay ,isnetepmok utas halas kutnebmem kutnu hailuk nat
“ nad imahameM tapad malad naaradnek kareg naamasrep pesnok nakanuggnem
.”naaradnek mumiskam kajej ayag nakutnenem kutnu nakanugid tapad ini ludoM
M hailuk atresep aumes naaradneK kareG akinake es id I retsem V margorP adap
.atrakaygoY iregeN satisrevinU kinkeT satlukaF fitomotO kinkeT idutS
nakijasid ini ludom adaP pesnok - rasad pesnok nad kareg naamasreP gnatnet
ayag - mumiskam kajej ayag nakutnenem arac iapmas naaradnek adap raul ayag
naaradnek iatresid gnay hotnoc - aynnaiaseleynep atreseb laos hotnoc nahital nad -
nahital .aynulrepes sata iridret ini ludoM aud .rajaleb nataigek 1 rajaleb nataigeK
nataigeK ,gnapmunep naaradnek mumiskam kajej ayaG :gnatnet sahabmem
yaG :gnatnet sahabmem 2 rajaleb mumiskam kajej a rotcart - relliartimes .
awsisaham makparahid ,hadum nagned ini ludom irajalepmem asib kutnU
ihunemem gnay lawa isnetepmok ikilimem halet sisilana pesnok gnatnet amaturet ,
iroet aguj nad nemom pesnok ,nanabebmep gnatnet sitametam nagnabmitesek
.adneb
,atrakaygoY iluJ 4002
nusuyneP
.T.M ,.dP.M ,ibutraM
3
LUDOM ISI RATFAD
namalaH
LUPMAS NAMALAH ........................ ...... .................................................... 1
TNAGNEP ATAK RA ................................ ....... ............................................. 2
ISI RATFAD ..................................................... ......... ..... ............................... 3
YRASSOLG / NAHALITSIREP ......................... ....... ....... ............................. 5
NAULUHADNEP . I ........................................................... ....... ...................... 6
.................................................................... luduJ ispirkseD .A .......... ........... 6
..................................................................................... taraysarP .B ............... 6
....................................................... ludoM naanuggneP kujnuteP .C .......... ... 7
nuteP .1 ........................................................ awsisaham igab kuj ........... .. 7
.................................................. ............ nesod igab kujnuteP .2 ........... ... 7
.......................... rihkA naujuT .D .................................................... ......... .... 8
.................................................................................. isnetepmoK .E ............ 8
................................................. naupmameK keC .F ........................ .......... .. . . 01
NARAJALEBMEP .II ........................................................................... ...... .. 11
...................................................... awsisahaM rajaleB anacneR .A ........... .. 11
.......................................................................... rajaleB nataigeK .B .......... .. 11 1 rajaleB nataigeK . 1 : naaradneK mumiskaM kajeJ ayaG
.. gnapmuneP .......... .................................. ............ . 11
rajaleb nataigek naujuT .a 1 ................................................. .......... ... . 11
iretam naiarU .b 1 .................................................................. ......... .... . 21
.c namukgnaR 1 ................................................................... ......... ..... . 17
saguT .d 1 ............................................................................ .......... ...... 18
fitamrof seT .e 1 ................................ ...................................... .......... .. 18
fitamrof set bawaj icnuK .f 1 ............................................. ... ........ .... 18
4
namalaH
2 rajaleB nataigeK . 2 : mumiskaM kajeJ ayaG
rotcarT - reliartimeS ... .. ........... ......................... ........ 19
rajaleb nataigek naujuT .a 2 ............................. ........... ....................... 19
iretam naiarU .b 2 ........................................ .................. .......... ............ 19
namukgnaR .c 2 .................................................................... ........... .... 25
saguT .d 2 ........................................................................ ........... ......... 26
.e fitamrof seT 2 ................................................................. .......... ....... 26
fitamrof set bawaj icnuK .f 2 .............................................. ... ........ ... 27
ISAULAVE .III ............................... ................................................... ....... ... 28
.......................................................................... naaynatreP .A ............ ...... 28
................................................. nabawaJ icnuK .B . .......... ......................... 29
....................................................... nasululeK airetirK .C ........... ............... 29
PUTUNEP .VI ................................................................................. ..... ... ...... 03
AKATSUP RATFAD ........................................................................ ....... ... 13
5
/ NAHALITSIREP YRASSOLG
simanidoreA natabmaH naped naigab adap ajrekeb gnay nigna natabmah halada :
( libom .)naaradnek
rab ward natabmaH gnakaleb naigab adap ajrekeb gnay nigna natabmah halada :
.)naaradnek( libom
tniop hctiH aratna nagnubmas tapmet kitit halada : rotcart nagned reliartimes .
isehda neisifeoK ah aynada nakkujnunem gnay naraseb haubes halada : natabm
.nalaj naakumrep nagned libom nab ratatna iranem kirat ayag tabika
epolS .tual ria naakumrep nakgnidnabid nalaj nagnirimek tudus halada :
rotcarT - reliartimes aratna isanibmok nakapurem gnay naaradnek sinej halada :
haubes rotcart kareggnep iagabes nad reliartimes .nataum tapmet iagabes
esab leehW gnakaleb ador ubmus nagned naped ador ubmus aratna karaj halada :
.surul isisop adap libom haubes
6
BAB I
NAULUHADNEP
ispirkseD .A
ludujreb gnay ludoM naaradneK kajeJ ayaG mem ini aparebeb sahab
kareggnep aganet naanacnerep metsis nagned tiakret gnay rasad pesnok
: itupilem ini ludom malad irajalepid gnay iretam napukac nupadA .naaradnek
kajej ayaG )2( nad ,gnapmunep naaradnek mumiskam kajej ayaG )1(
mumiskam rotcart - reliartimes ,
1 rajaleb nataigeK : utiay ,rajaleb nataigek aud sata iridret ini ludoM
nad ,gnapmunep naaradnek mumiskam kajej ayaG :gnatnet sahabmem
mumiskam kajej ayaG :gnatnet sahabmem 2 rajaleb nataigeK rotcart -
relliartimes leb nataigek paites adaP . hotnoc nagned ipakgnelid ulales raja
nahital atreseb aynnasahabmep nad laos - nad fitamrof set ,sagut/nahital
isnetepmok iapacnem malad awsisaham utnabmem kutnu aynulrepes isaulave
.nakparahid gnay
k araces ini ludom irajalepmem iaseles haleteS awsisaham nahurulese
“ nakparahid nad imahameM tapad kareg naamasrep pesnok nakanuggnem
.”naaradnek mumiskam kajej ayag nakutnenem malad naaradnek
taraysarP .B
kinkeT nakididneP nasuruJ awsisaham igab ludom nakapurem ini ludoM
fitomotO iretam isireb gnay ,3D nupuam 1S gnajneJ - uata namaladnep iretam
hailukatam irad naayagnep - gnay fitomoto gnadib id nailhaek hailukatam
hailukatam ipatet ,aynmulebes irajalepid hadus aynsurahes - hailukatam
lepmem kutnu taraysarp iagabes itrareb kadit tubesret nagneD .ini ludom iraja
iretam naikimed - nakapurem naka ini ludom isi nagned tiakret gnay iretam
gnay isnetepmok iapacnem akgnar malad gnitnep tagnas gnay gnajnunep
.nakparahid
7
ludoM naanuggneP kujnuteP .C
awsisahaM igab kujnuteP .1
gA malad akam ,lamiskam gnay rajaleb lisah helorepid ra
nad ,nakitahrepid ulrep gnay rudesorp aparebeb ada ini ludom nakanuggnem
: nial aratna nakanaskalid
pesnok naiaru amaskes nagned imahaf nad halacaB .a - gnay sitiroet pesnok
mek ,ini ludom adap nakijasid pesnok naparenep alup imahaf naidu -
hotnoc malad tubesret pesnok - .aynnaiaseleynep arac atreseb laos hotnoc
asib muleb nad salej gnaruk gnay iretam ada hisam askapret aliB
nesod adapek nakaynanem tapad awsisaham arap kiab nagned imahafid
aigek upmagnem gnay .nahailukrep nat
ini lah ,iridnam araces )nahital laos( sagut paites nakajrek aboC .b
halet gnay namahamep raseb aparebes iuhategnem kutnu nakduskamid
iretam padahret awsisaham paites ikilimid - adap sahabid gnay iretam
.rajaleb nataigek paites
ad alibapA .c adap iretam iasaugnem muleb awsisaham aynnaataynek mal
igal nakajregnem nad acabmem igal ignalu aboc ,nakparahid gnay level
nahital - gnay nesod adapek halaynatreb ulrep ualak nad aynnahital
gnay iretam ualaK .natukgnasreb gnay nahailukrep nataigek upmagnem
naknikay akam )taraysarp( lawa namahamep nakulremem natukgnasreb
raneb duskamid gnay taraysarp awhab - .ihunepid hadus raneb
nesoD igab kujnuteP .2
: kutnu narep nad sagut iaynupmem nesod ,nahailukrep paites malaD
a. m malad awsisaham utnabmeM .rajaleb sesorp nakanacnere
b. sagut iulalem awsisaham gnibmibmeM - nahital uata sagut - gnay nahital
.rajaleb bahat malad naksalejid
c. bawajnem nad urab pesnok imahamem malad awsisaham utnabmeM
.nakulrepid alibapa awsisaham naaynatrep
8
d. gnem kutnu awsisaham utnabmeM gnay nial rajaleb rebmus seska
.nakulrepid
e. .nakulrepid akij kopmolek rajaleb nataigek risinagrogneM
f. .nakulrepid akij gnipmadnep nesod/ilha gnaroes nakanacnereM
g. gnay awsisaham isnetepmok naiapacnep padahret isaulave nakadagneM
.nakutnetid halet
naujuT .D rihkA
ini ludom malad rajaleb nataigek iretam hurules irajalepmem haleteS
: nakparahid awsisaham
1 nabeb naruta nad tafis ,pesnok nakanuggnem tapad nad imahameM .
nahacemep malad gnapmunep naaradnek mumiskam kajej ayag / nalaj
.gnapmunep naaradnek kareggnep metsis naanacnerep halasam
tapad nad imahameM .2 / nalaj nabeb naruta nad tafis ,pesnok nakanuggnem
mumiskam kajej ayag rotcart - reliartimes halasam nahacemep malad
naaradnek kareggnep metsis naanacnerep rotcart - iartimes .rel
.
isnetepmoK .E
622 OTO.KGM ludoM - isnetepmok kutnebmem akgnar malad nususid ini 20
“ nad imahameM tapad naaradnek kareg naamasrep pesnok nakanuggnem
.”naaradnek mumiskam kajej ayag nakutnenem malad
lret ,tubesret isnetepmok iapacnem kutnU bus iapacid tapad surah uluhad hibe -
nagned rajaleb pukgnil iulalem aynajrek kujnu airetirk atreseb isnetepmok bus
: tukireb iagabes narajalebmep kokop iretam
9
buSisnetepmoK
airetirK ajreK kujnU
pukgniLrajaleB
narajalebmeP kokoP iretaM
pakiS egneP nauhat nalipmarteK
imahameM
gnem nad - nakanug
pesnok naamasrep
kareg naaradnek
maladutnenem - nak
kajej ayag mumiskam. naaradnek
rep pesnoK .1 -
kareg naamasayag nad - ayag
naaradnek raul gnapmunep
nagned imahafid iauses raneb
iroet lamron nabeB .2
paites adaparadnek sorop -
gnapmunep na nagned gnutihid
iauses raneb.iroet
kajej ayaG .3 mumiskam
naaradnek gnapmunep
nagned gnutihid iauses raneb
.iroet pesnoK .4
kareg naamasrepayag nad - ayag
naaradnek raul isanibmok
rotcart - imesreliart imahafid
d raneb nagne.iroet iauses
lamron nabeB .5 sorop adap
reliartimes nagned gnutihid
iauses raneb.iroet
adap ayaG .6 hctihtniop gnutihid
raneb nagned.iroet iauses
adap nabeB .7 hctihtniop gnutihid
raneb nagned.iroet iauses
lamron nabeB .8 sorop adap
gnakaleb rotcart nagned gnutihid
iauses raneb.iroet
kajej ayaG .9 mumiskam
naaradnek isanibmok
rotcart - imes reliart gnutihid
raneb nagned.iroet iauses
pesnoK .1
naamasrep nad kareg
raul ayag naaradnek
.gnapmunep
lamron nabeB .2 sorop adap
aradnek nagnapmunep
kajej ayaG .3
mumiskam naaradnekgnapmunep
pesnoK .4
naamasrep nad kareg
raul ayag naaradnek
.gnapmunep
lamron nabeB .5 sorop adap
reliartimes adap ayaG .6
tniop hctih adap nabeB .7
tniop hctih lamron nabeB .8
sorop adapb gnakale
rotcart kajej ayaG .9
mumiskamrotcart - imesreliart
itilet ,sitirK
tamrec nad malad
silunem gnabmal
alem nad -rep nakuk -.nagnutih
pesnoK .1
naamasrep kareg
naaradnek.gnapmunep
lamron nabeB .2
sorop adap naaradnekgnapmunep
.3 kajej ayaG
mumiskam naaradnekgnapmunep
pesnoK .4
naamasrep nad kareg
raul ayag naaradnek
.gnapmunep
lamron nabeB .5 sorop adap
reliartimes adap ayaG .6
tniop hctih adap nabeB .7
tniop hctih lamron nabeB .8
sorop adap gnakaleb
rotcart kajej ayaG .9
mumiskamrotcart - imesreliart
gnutihgneM
nagned nad rudesorp
gnay lisahraneb
01
naupmameK keC .F
622 OTO.KGM ludoM irajalepmem mulebeS – adnat nagned halisi ,ini 20
( kec id halet gnay isnetepmok nakkujnunem gnay naaynatrep ) helo ikilim
: nakbawajgnuggnatrepid tapad nad rujuj nagned awsisaham paites
buS
isnetepmoK naaynatreP
nabawaJ “aY“ nabawaJ aliB
nakajreK aY kadiT
imahameM
nad tapad anuggnem - nak
pesnok naamasrep
kareg naaradnek
malad nakutnenem
kajej ayagumiskam m
.naaradnek
.1 imahamem ayaS naamasrep pesnok
ayag nad kareg - gnay raul ayag .gnapmunep naaradnek adap ajrekeb
1 fitamroF seT
.3 gnutihgnem tapad ayaS lamron nabeb
gnapmunep naaradnek sorop paites adap
1 fitamroF seT
.4 gnutihgnem tapad ayaS kajej ayag
napmunep naaradnek mumiskam g
1 fitamroF seT
.5 k imahamem ayaS naamasrep pesno
ayag kareg - gnay raul ayag isanibmok naaradnek adap ajrekeb
rotcart - reliart mes
2 fitamroF seT
6 . gnutihgnem tapad ayaS lamron nabeb
sorop adap reliartimes
2 fitamroF seT
.7 gnutihgnem tapad ayaS adap ayag hctih
tniop rotcart - reliartimes
2 fitamroF seT
.8 gnutihgnem tapad ayaS adap nabeb hctih
tniop rotcart - reliartimes
2 fitamroF seT
.9 gnutihgnem tapad ayaS lamron nabeb
gnakaleb sorop adap rotcart
2 fitamroF seT
.01 gnutihgnem tapad ayaS kajej ayag
adap mumiskam rotcart - .reliart imes
2 fitamroF seT
bawajnem awsisaham alibapA kadiT akam ini ludom irajalep
bawajid gnay iretam iauses kadiT .tubesret
11
BAB II
NARAJALEBMEP
awsisahaM rajaleB anacneR .A
nad ini hawab id lebat isignem nagned rajaleb nataigek anacner haltauB
jaleb nataigek haletes nesod adapek itkub halatnim .iaseles ra
nataigeK sineJ laggnaT utkaW tapmeTrajaleB
nasalAnahabureP
faraPnesoD
nad kareg naamasrep pesnoK .1 ajrekeb gnay raul ayag
gnapmunep naaradnek adap
sorop adap lamron nabeB .2 .gnapmunep naaradnek
.3 adap mumiskam kajej ayaGgnapmunep naaradnek
.4 nad kareg naamasrep pesnoK raul ayag adap rotcart -
reliart imes .
adap lamron nabeB .5 rotcart - reliartimes .
adap ayaG .6 .tniop hctih
.7 ap lamron nabeB sorop ad gnakaleb .rotcart
8 . mumiskam kajej ayaG rotcart - reliartimes
.rajaleB nataigeK .B
: 1 rajaleB nataigeK .1 mumiskaM kajeJ ayaG gnapmuneP naaradneK
: 1 rajaleB nataigeK naujuT .a
)1 . naaradnek adap ajrekeb gnay raul ayag isakifitnedigneM
gnapmunep .
)2 . .gnapmunep naaradnek sorop adap lamron nabeb nakutneneM
.)3 mumiskam kajej ayag nakutneneM gnapmunep naaradnek adap
21
: 1 iretaM naiarU .b
.)1 nauluhadneP
kareG akinakeM gnatnet huaj hibel irajalepmem kutnU
naupmamek kitsiretkarak iuhategnem nigni akij amaturet ,naaradneK
iuhatekid ulrep amatrep gnay akam ,naaradnek anug ayad uata
aaradnek naupmamek anamiagab halada nakukalem tubesret n
iagabreb isatagnem aynnaupmamek nad ) natapecrep( isareleska
.aynkajej ayag atres isairavreb gnay nalaj id nakareg natabmah
nataigek adap akam ,tubesret nagnitnepek nagned nagnubuheS
ab salej araces nakiaruid naka ini rajaleb gnutihgnem anamiag
naaradnek aynsusuhk naaradnek adap mumiskam kajej ayag aynraseb
naijak iatresid ajas utnet ,) gnapmunep naradnek( sorop aud – naijak
.tubesret kajej ayag nagnutihrep irasadnem gnay
2) . kareG namasreP
ayaG - naaradnek adap ajrekeb gnay amatu raul ayag
kapmat 1 rabmag iraD . 1 rabmaG adap tahilid tapad gnapmunep
ayag naaradnek )lanidutignol( gnajnamem hara adap awhab - ayag
t :itupilam tubesret R( akimanidorea nanaha a ador gnidnileg nanahat ,)
Y
R a X
a h a nisW R d
g/a.W h
R fr B F f h d l1 l2 Rrr A Fr
socW
Wf L W Wr 1 rabmaG
31
R( naped fr R ( gnakaleb ador gnidnileg nanahat ,) rr nabeb ,) rabward
R( d R nakajnat nanahat , ) g nis W uata ( ayag nad ,) - adap kajej ayag
F( naped ador f F( gnakaleb ador nad ) r .)
F agrah naped ador kareggnep nagned naaradnek kutnU r lon halada
F gnakaleb ador kareggnep kutnu aynkilabes f . lon agrahreb
adap ukalreb gnay kareg naamasrep nupadA gnajnamem ubmus
: halada ) X ( naaradnek
d2 a.W x m ------ = ------ F = f F + r – R a – R rf – R rr – R d – R g
td 2 g
d2 x ini lah malad ------ ,naaradnek reinil natapecrep halada a uata
td 2
isatifarg natapecrep halada g nakgnades gnisam W nad m ,imub -
.naaradnek tareb nad assam halada gnisam
id naamasrep akam aisreni ayag pesnok nakkusamem nagneD
: idajnem silutid tapad sata
Ff F + r – R( a R + rf R + rr R + d R + g 0 = ) g/a.W +
F akiJ f F + r = R nad F rf R + rr R = r akam : helorepid
R = F a R + r + R d R + g g/a.W +
adap mumiskam kajej ayag nakutnenem kutnu aynranebeS
utiay ,uajnitid ulrep gnay rotkaf aud ada gnapmunep naaradnek
gned nab isehda neisifeok: amatrep adap lamron nabeb/ayag ,nalaj na
sorop - kitsiretkarak : halada audek nad ,naaradnek sorop
audek rotkaf numan naaradnek isimsnart nad aganet naanacnerep
.aynnasahabmep ulud nakhuggnatid
3 gnapmuneP naaradneK soroP adap lamroN nabeB .)
kutnU kutnu nakulrepid gnay mumiskam kajej ayag iskiderpmem
iuhatekid hadus surah uluhad hibelret akam naaradnek naknalajnem
ayag - sorop paites helo nahatid gnay lamron nabeb uata ayag
gnutihid tapad naaradnek sorop adap lamron nabeB .naaradnek
41
kitahrepmem nagned audek katnok kitit adap ajrekeb gnay nemom na
.) B nad A kitit ( nalaj nagned nab
( A kitit id nemoM ∑ MA ) 0 =
Wf L. – l.W 2 soc. R + a h . a R + h.)g/a.W( + d h. d + nis.h.W 0 =
l.W 2 soc. – Ra h . a – h.)g/a.W( – Rd h. d + nis.h.WWf = --------------------------- ------------------------- ------------
L
aT ( adn – nis h.W adap nakirebid ) ,kajnanem naaradnek akitek
.nurunem akij ) + ( adnat aynkilabes
B kitit id nemom kutnu amas gnay arac nagned ayntujnaleS
W aynraseb nakutnenem kutnu naamasrep helorepid r :
B kitit id nemoM ( ∑ MB ) 0 =
Wr L. – l.W 1 soc. – Ra h . a – h.)g/a.W( – Rd h. d + nis.h.W 0 =
l.W 1 soc. R + a h . a R + h.)g/a.W( + d h. d + nis.h.WWr = ---------------- ----------- ------------------------- ------------
L
nis.h.W adap nakirebid )+( adnat ini sumur adaP naaradnek akitek
( adnat aynkilabes ,kajnanem – .nurunem akij )
libom akiJ ( ratadnem nalaj adap nalajreb agrah akam ) 0 =
soc nis nad 1 = agrah aynasaib gnapmunep naaradnek kutnU .0 =
h irad a h nad d h( h itakednem a h ≈ d sata id naamasrep akam ,) h ≈
: idajnem nakanahredesid tapad
l .W 2 h a.w W f = -- --- -- – ---- R ( a + ---- R + d )
g L L
l .W 1 a.w h W r = -- -- -- + ---- R ( a + ---- R + d )
g L L
R = F awhab aynmulebes iuhatekid haleT a R + r + R d R + g g/a.W +
R ratadnem nalaj kutnU g R = F akam 0 = a R + r + R d g/a.W +
W adap F isutitsbus nagneD f W nad r nabeb aynraseb tapadid akam
kutnu( gnapmunep naaradnek sorop paites adap lamron nalaj
: halada ) ratadnem
51
l .W 2 h W f = ------- – ---- F ( – Rr )
L L
l .W 1 h W r = ------ + ---- F ( – Rr )
L L
4 kajeJ ayaG .) M :naaradneK mumiska
nagned ador aynkatnok tabika helorepid tapad gnay kajej ayaG
( hanat dnuorg )hanat( nalaj irad isehda neisifeok helo nakutnetid )
:akam ,naaradnek nab nagned
ed naaradnek kutnU :)BRP( gnakaleb ador karegnep metsis nagn W l1 h
F am sk = W. r = ---- + ---- ( F skam – Rr )
L L
R aneraK r f = r : helorep id akam W.
: ini lah malaD
.nalaj nagned nab isehda neisifeok =
f r .naaradnek ador gnidnileg nanahat neisifeok =
: )DRP( naped ador kareggnep nagned naaradnek kutnU
W l 2 h F am sk = W. f = ---- – ---- ( F skam – Rr )
L L
: helorep id aynrihkA
l : kajnanem nalaj kutnU 2 l2 soc θ
1( W. 1 – fr ) h. Fr-m ska = --------- ------------- ---- -
L – h
1( W. 2 f + r ) h. Ff- skam = -----------------------
L + h
61
laos hotnoC :
k haubeS iaynupmem )sorop aud( gnapmunep naaradne esab leehw =
nad naped sorop gnakaleb id mc 001 adareb ayntareb tasup ,mc 062
Nk 51= naaradnek tareB .ratad nalaj naakumrep sataid mc 06
nalaj isehda neisifeok nad 8,0 = gnidnileg nanahat neisifeok nagned
nagned metsis nakanuggnem tubesret naaradneK .7,0 = nab
:halnakutneT .naped ador kareggnep
.naaradnek mumiskam kajej ayaG .)a
.naaradnek sorop audek helo atiredid gnay lamron nabeB .)b
ador kareggnep metsis nagned tubesret naaradnek lasiM .)c
algnutih ,gnakaleb .aynmumiskam kajej ayag h
naiaseleyneP :
iuhatekiD adoR kareggneP nagned gnapmunep naaradnek haubeS :
.ratad nalaj sata id nalajreb )DRP( napeD
= L mc 062 Nk 51 = W
l1 l mc 001 = 2 L = – l1 062 = – mc 061 = 001
f mc 06 = h r nad 8,0 = 7,0 =
iD nakaynat skam F .)a :
b .) W f nad Wr
F .)c skam BRP nagned akij
bawaJ : W 1( 2 + fr. ) h 51.7,0 ( 06.8,0 + 061 )
F .)a skam = ------------------- = ------------------------- = 7, 32 Nk 2 + L + 062 h 06
F skam 7, 32 2 W .)b f = --------- = ------- = 01 , 33 1 Nk
W = rW – Wf 51 = – = 133,01 k 966,4 N
: gnakaleB adoR kareggneP nakanuggnem libom akiJ .)c
W. 1( 1 – fr. ) h 51.7,0 ( 001 – 06.8,0 )
F skam = -------------------- = ------------------------- = 505,2 Nk L – 062 h – 06
71
.c namukgnaR : 1
yaG .)1 a- : itupilem gnapmunep naaradnek adap ajrekeb gnay raul ayag
R( akimanidorea nanahat a R( naped ador gnidnileg nanahat ,) fr ,)
R ( gnakaleb ador gnidnileg nanahat rr nabeb ,) rabward R( d ,)
R nakajnat nanahat g nis W uata ( ayag nad ,) - adap kajej ayag ador
F( naped f F( gnakaleb ador uata ) r .)
: sumur nagned gnutihid tapad naped sorop adap lamron nabeB .)2
: nurunem/ikadnem nalaj kutnU .)a
l.W 2 soc. – Ra h . a – h.)g/a.W( – Rd h. d + nis.h.WWf = --------------------------------- -- ------------------------------
L
: ratadnem nalaj kutnU .)b l .W 2 a.w h
W f = ------- – ---- R ( a + ---- R + d ) g L L
: sumur nagned gnutihid tapd gnakaleb sorop adap lamron nabeB .)3
: nurunem/ikadnem nalaj kutnU .)a
l.W 1 soc. R + a h . a R + h.)g/a.W( + d h. d + nis.h.WWr = -------------------------------------------------- ---- ------------
L
adnem nalaj kutnU .)b : rat
l .W 1 h W a. W r = ------ + ---- R ( a + ---- R + d )
g L L : sumur nagned gnutihid tapad mumiskam kajej ayaG .)4
F skam = W .
: napeD adoR kareggneP nagned naaradnek kutnU .)a
1( W. 2 f + r ) h. F skam = -----------------------
+ L h
: gnakaleB adoR kareggneP nagned naaradnek kutnU .)b
1( W. 1 – fr ) h. F skam = -----------------------
L – h
81
.d saguT 1 :
iaynupmem )sorop aud( gnapmunep libom haubes iuhatekiD leehw
esab gnakaleb sorop naped id mc 59 adareb ayntareb tasup ,mc 012 =
nad nalaj naakumrep sataid mc 56 51 tudus nagned kajnanem 0 tareB .
nad 5,0 = gnidnileg nanahat neisifeok nagned Nk 61= naaradnek
tubesret naaradneK .6,0 = nab nagned nalaj isehda neisifeok
:halnakutneT .gnakaleB ador kareggnep metsis nakanuggnem
jej ayaG .)1 .naaradnek mumiskam ka
.naaradnek sorop audek helo atiredid gnay lamron nabeB .)2
.e fitamrof seT : 1
iaynupmem )sorop aud( gnapmunep naaradnek haubeS esab leehw =
06 nad naped sorop gnakaleb id mc 011 adareb ayntareb tasup ,mc 091
mc nagned Nk 52= naaradnek tareB .ratad nalaj naakumrep sataid
nab nagned nalaj isehda neisifeok nad 3,0 = gnidnileg nanahat neisifeok
.gnakaleb ador kareggnep metsis nakanuggnem tubesret naaradneK .7,0 =
:halnakutneT
.naaradnek mumiskam kajej ayaG .)1
.)2 .naaradnek sorop audek helo atiredid gnay lamron nabeB
kareggnep nakanuggnem akij tubesret libom kajej ayag nakgnidnaB .)3
! anam gnay tauk hibeL ! naped ador
.f icnuK J bawa F seT fitamro : 1
F .)1 skam = 88,01 Nk
W .)2 f = 45,51 Nk
Wr = 64,9 Nk
)DRP( napeD adoR kareggneP nagned akiJ .)3 F skam = 7, 3 9 Nk F aneraK skam F > DRP kutnu skam BRP kutnu
itrareB tauk hibel nakanuggnem akij naped ador kareggnep .
91
: 2 rajaleB nataigeK .2 mumiskaM kajeJ ayaG rotcarT - iartimeS l re
: 2 rajaleB nataigeK naujuT .a
1 .) isakifitnedigneM adap ajrekeb gnay raul ayag rotcart - reliartimes .
2 .) sorop adap lamron nabeb nakutneneM .reliartimes
3 .) adap ayag/nabeb nakutneneM .tniop hctih
4 .) gnakaleb sorop adap lamron nabeb nakutneneM .rotcart
5 .) adap mumiskam kajej ayag nakutneneM rotcart - reliartimes .
: 2 iretaM naiarU .b
.)1 nauluhadneP
aynah kadit atik nagnapal id awhab nakujnunem naatayneK
,ajas sorop aud naaradnek uata gnapmunep naaradnek nagned umetreb
aynlasim ,nial gnay naaradnek sinej iapmuj atik aguj kaynab ipatet
.gnarab natukgna naaradnek gnarab natukgna naaradnek kusamreT
halada nanimod gnilap gnay rotcart nad reliart aratna isanibmok uata
rotcart nad reliartimes adap nasahabmep takgnisrepmem kutnU .
kutnu nakhutubid gnay kajej ayag nakiaruid naka ini rajaleb nataigek
aaradnek naknalajnem isanibmok n rotcarT - reliartimeS .
2 .) adap rauL ayaG rotcarT - reliartimeS
adap mumiskam kajej ayag nagnutihreP rotcart - reliartimes naka
adap nagned gnidnabid ayag rusnu naktabilem kaynab hibel
gnapmunep naaradnek ayag nupadA . - ajrekeb gnay amatu raul ayag
adap rotcart - reliartimes . 2 rabmag adap tahilid tapad
tapad ) ratadnem nalaj adap paggnaid naaradnek ( 2 rabmag iraD
ayag awhab iuhatekid - adap ajrekeb gnay raul ayag rotcart - reliartimes
upilem adap simanidorea natabmah :it rotcart nad reliartimes R ( a1
R nad a2 R ( naaradnek ador paites gnidnileg nanahat natabmah ,) fr R , rr ,
R nad rs gnisam naaradnek tareb ayag natabmah ,) - nenopmok gnisam
W( 1 W , 2 W nad ih W( naaradnek aisreni tabika natabmah nad ) 1 a. g/
W nad 2 . ) g/a.
02
R 2a
W ih W2 d2
h a2 W a 2 g/a. Ra 1 d1
W1 F ih h2
h 1a h3
h1
R fr A l 1 l2 Rr r B F Rrs C L1
L2 W f W r Ws
.2 rabmaG
awhab paggnagnem nagneD rotcart nad reliartimes iagabes
adap lamron nabeb akam ,hasipret araces sabeb adneb times reliar
W( S adap latnosiroh nupuam lakitrev nabeb nad ,) tniop hctih F( ih nad
W ih .nakutnetid tapad )
3 .) soroP adap lamroN nabeB reliartimeS
eB gnakaleb sorop adap ajrekeb gnay lamron nab reliartimes akij
naid nalaj : sumur nagned gnutihid tapad ratadnem pagg
W2d 2 R + .2a h 2a h + 2 W. 1 g / a. - F ih . h 3 W s = ----------------------------- - -------------------
L2
h agrah akiJ 2a h 3 h2 : idajnem sata id naamasrep akam
W 2 d 2 .h 2 W2 a. W s = -- ---- + ----- R ( 2a + ----- – F ih )
L2 L2 g
4 .) adap ayaG ( tnioP hctiH nagnubmaS rotcarT nad ) reliartimes
m nagneD ayag naamasrep libmagne - gnay latnosiroh ayag
adap ayag aynraseb akam ,reliartimes adap ajrekeb tniop hctih tapad
: sumur nagned nakutnetid
12
W 2 a.
F ih R = 2a + ----- f + r sW. g
sumur iraD F ih sata id nakisutitsbusid akij :helorepid sW sumur ek
W 2 d 2 W s = --------------
L 2 f + r h2
5 .) adap nabeB tnioP hctiH ( nagnubmaS rotcarT nad ) reliartimes
ayag naamasrep libmagnem nagneD - gnay lakitrev ayag
adap ajrekeb reliartimes adap nabeb aynraseb akam , tniop hctih tapad
: utiay ,nakutnetid
W ih W + s W = 2
W ih W = 2 – Ws W naamasrep nakisutitsbusnem nagneD s W naamasrep adap ih naka
:helorepid
d2 1 akiJ – ------------ C = ih : akam W ih C = ih W2 C ih 1 <
L2 f + r h2
6 gnakaleB soroP adap lamroN nabeB .) rotcarT :
awhab paggnagnem nagneD rotcart nad sabeb adneb iagabes
nagned naped ador katnok kitit adap nemom halmuj nakitahrepmem
gnakaleb sorop adap lamron nabeb akam ,nalaj rotcart tapad
: tukireb iagabes nakutnetid
W111 R + 1a . h 1a h + 1 W. 1 a. F + g / ih h 3 L ( + 1 –d1 W ) ih
W r = ------------------------------------------------------------------ L1
d 2 W ih 1 ( = – ---------------- W ) 2
L 2 f + r h 2
22
h agrah akij ayntujnaleS 1a h 3 h1 W naamasrep akam r : idajnem
W111 R( + 1a W + 1 F + g / a. ih h ) 1 L ( + 1 –d1 W ) ih W r = ----------------------------------------------- -----------------
L1
ayaG .)7 J kaje M adap mumiska P soro B gnakale T rotcar
ayag naamasrep nakitahrepmem nagneD - ag gnay latnosiroh ay
adap ajrekeb otcart r gnakaleb sorop adap kajej ayag aynraseb akam ,
rotcat : utiay ,nakutnetid tapad
W1 a. F R = 1a + ----- f + r W( s W + ih F + ) ih g
: halada rotcart gnakaleb sorop adap mumiskam kajej ayaG
F skam = W . r
W nad F naamasrep nakgnubaggnem nagneD r : helorepid sata id
W [. 1 l 1 – h1f r W ( 1 W + ih L( + ) 1 – d1 W ) ih L / ] 1 F skam = ------------------------------------------------------------
1 – h. 1 L / 1
W naamasrep nakisutitsbusnem nagneD ih F ek skam :tapadid
W [. 1 l 1 – h 1 f r W ( 1 C + ih W. 2 L ( + ) 1 – d1 C ) ih W 2 ] F skam = ------------------------------------------- - --------------------
L1 – h. 1
:laoS hotnoC
naaradnek haubeS rotcart - reliartimes tareb : iaynupmem t rotcar
tareb ,Nk 76 reliartimes ,Nk 762 rotcart esableehw ,mc 183 =
sorop reliratimes gnakaleb sorop gnakaleb id mc 117 adareb
rotcart , tniop hctih adareb sorop naped id mc 16 gnakaleb rotcart
nalaj sata id mc 261 nad ratadnem isatifarg tasuP . otcart r adareb
32
naped sorop gnakaleb id mc 302 rotcart ,nalaj sata id mc 79 nad
tareb tasup gnades reliartimes sorop naped id mc 033 adareb
reliartimes R .nalaj naakumrep sataid mc 871 nad 1a nanahat(
adap kimanidorea rotcart 3,1 = ) Nk mc 051 kitit adap ajrekeb
R ,ratadnem nalaj sataid 2a 2,1 = Nk f aynraseb nad r . 7,0 = ; 8,0 =
ted/m 48,2 = a 2 ted/m 01= g ; 2 : halnakutneT .
sorop adap lamron nabeb aynraseB .)a reliartimes sorop nad
gnakaleb .rotcart
aynraseB .)b adap ayag tniop hctih .
gnakaleb sorop adap mumiskam kajej ayag aynraseB .)c rotcart .
: naiaseleyneP
iuhatekiD isanibmok naaradnek haubeS : rotcart - relirtimes
W 1 l Nk 76 = 1 mc 302 =
W 2 h Nk 762 = 1 mc 79 =
L 1 mc 183 = h 2 mc 871 =
L2 – d1 L mc 117 = 2 – d2 mc 033 =
R 1a R 3,1 = 2a 2,1 =
d1 = h mc 16 3 mc 261 =
h 1a 7,0 = rf mc 051 =
ted/m 48,2 = a 8,0 = 2
ted/m 01 = g 2
nakaynatiD W .)a s W nad r
F .)b ih
F .)c skam
bawaJ :
L2 d + 117 = 1 mc 277 = 16 + 117 =
d 2 L = 2 – 277 = 033 – mc 244 = 033
h paggnaiD 2a h nad 3 h itakednem 2
42
: sW gnutihgneM .)a W2 d2
= sW -------------- L2 f + r h2
244 . 762
= -------------------- 871 . 7,0 + 277
= Nk 26,131
W1 l1 R + 1a ah 1 h + 1 W1 F + g/a ih h3 L( + 1–d1 W ) ih
Wr = ------ -- ------- -------------------------------------- ------- L1
agrah aneraK - F agrah ih W nad ih ep akam iuhatekid muleb ulr
.uluhad hibel gnutihid
W ih W = 2 – Ws
762 = – 26,131
= Nk 83,531
W2 .a F .)b ih = R 2a + ------- f + r Ws
g
48,2 .762 + 2,1 = ----- ----- --- 26,131 . 7,0 +
01 = Nk 61,961
: utiay ,gnutihid tapad urab rW gnarakeS
.3,1 +302.76 + 051 .79 .76 261.61,961 + 01/48,2 183( + – 83,531)16
Wr = ------ -- ------- ---------------------------------- ---------- ------- 183
= Nk 96,622
. W [ 1 l 1 – h 1 f r W ( 1 C + ih W. 2 L ( + ) 1 – d1 C ) ih W 2 ] F .)c skam = ----------------------------------------------------------------
L1 – h. 1
8,0 [ 302.76 – 7,0.79 ( 76 + 83,531 ( + ) 183 – 16 ) 83,531 ] = ---------------------------------- ---- ------------------------------
183 – 79.8,0 = Nk 68,311
52
.c namukgnaR : 2
.)1 rotcarT - reliartimeS halada gnay sorop agit nagned naaradnek sinej
kanugid kaynab .gnarab natukgna kutnu na
ayaG.)2 - adap ajrekeb gnay raul ayag rotcart - reliartimes :itupilem
adap simanidorea natabmah rotcart nad reliartimes R ( a1 R nad a2 ,)
R ( naaradnek ador paites gnidnileg nanahat natabmah fr R , rr R nad , rs ,)
tareb natabmah gnisam naaradnek - W( nenopmok gnisam 1 W , 2 nad
W ih W( naaradnek aisreni tabika natabmah nad ) 1 W nad g/a. 2 .) g/a.
.)3 soroP adap lamroN nabeB reliartimeS :sumur nagned gnutihid tapad
W2 d 2 W s = -----------------
L 2 f + r h2
.)4 adap ayaG tnioP hctiH : sumur nagned gnutihid
W 2 a. F ih R = 2a + - -- --- f + r sW.
g
iop hctih adap nabeB .)5 : sumur nagned gnutihid tn
d 2 W ih 1 ( = – ---------------- W ) 2
L 2 f + r h 2
.)6 gnakaleb sorop adap lamron nabeB rotcart : sumur nagned gnutihid
W111 R( + 1a W + 1 F + g / a. ih h ) 1 L ( + 1 –d1 W ) ih
W r = ---------------------------------------------------------------- L1
7 .) ayaG mumiskam kajej rotcart : sumur nagned gnutihid
W [. 1 l 1 – h 1 f r W ( 1 C + ih W. 2 L ( + ) 1 – d1 C ) ih W 2 ] F skam = ------------------------------------------- - --------------------
L1 – h. 1
62
.d saguT 2 :
isanibmok naaradnek haubeS rotcart - reliartimes tareb iaynupmem
adareb gnay kitit adap tasupret gnay Nk 57 rotcart 21 id mc 5 aleb gnak
sorop naped rotcart tareB .ratadnem nalaj sata id mc 58 nad reliartimes
gnakaleb sorop gnakaleb id mc 021 karaj adap tasupret Nk 052 rotcart
.nalaj sata id mc 571 nad tniop hctiH kitit adap adareb 03 naped id mc
gnakaleb sorop rotcart ta id mc 011 nad .nalaj sa rotcart esab leehW =
gnakaleb sorop karaj ,mc 002 rotcart sorop nagned reliartimes =
; 8,0 = nalaj nagned nab isehda neisifeok nakutnetid akiJ .mc 072
.ted/m 3 = naaradnek natapecrep ;4,0 = ador gnidnileg nahat neisifeok 2
natapecrep nad .ted / m 8,9 = isatifarg 2 :! halgnutih akam
1 sorop adap lamron nabeB .) reliartimes .
2 adap lamron nabeB .) tniop hctih .
3 mumiskam kajej ayaG .) .rotcart
4 gnakaleb sorop adap lamron nabeB .) rotcart .
.
.e fitamrof seT : 2
naaradnek haubeS rotcart - reliartimes tareb : iaynupmem rotcart 06
tareb ,Nk reliartimes ,Nk 042 rotcart esableehw sorop ,mc 073 =
reliratimes gnakaleb sorop gnakaleb id mc 007 adareb rotcart , hctih
tniop gnakaleb sorop naped id mc 55 adareb otcart r sata id mc 021 nad
isatifarg tasuP .nalaj rotcart naped sorop gnakaleb id mc 091 adareb
rotcart nad 001 isatifarg tasup gnades ,nalaj sata id mc reliartimes adareb
sorop naped id mc 003 reliartimes nalaj naakumrep sataid mc 561 nad
R .ratad 1a 6,1 = R , nalaj sataid mc 051 kitit adap ajrekeb 2a ; 3,1 =
f aynraseb r . 3,0 = ted/m 65,2 = a ; 7,0 = 2 ted/m 8,9= g nad , 2 :halgnutih ,
sorop adap lamron nabeb aynraseB .)1 reliartimes .
n nabeb aynraseB .)2 adap lamro tniop hctih ..
adap ayag aynraseB .)3 tniop hctih .
gnakaleb sorop adap lamron nabeb aynraseB .)4 rotcart
gnakaleb sorop adap mumiskam kajej ayag aynraseB .)5 rotcart .
72
.f icnuK J bawa F seT fitamro : 2
= sW .)1 31 5, 47 Nk
W .)2 ih = Nk 62,401
F .)3 ih = 15 ,9 01 Nk
W .)4 r = 571 ,9 Nk 9
F .)5 skam = 67 , 04 Nk
82
BAB III
ISAULAVE
.A naaynatreP
gnakaleb ador kareggnep nagned gnapmunep naaradnek haubeS .1
iaynupmem esab leehw adap tasupret Nk 71 = naaradnek tareB .mc 081 =
nalaj naakumrep sataid mc 05 nad gnakaleb sorop naped id mc 08 kitit
nalaj isehda neisifeok nad 52,0 = gnidnileg nanahat neisifeok akiJ .ratad
:halgnutih akam ,56,0 = nab nagned
ajej ayaG .a .naaradnek mumiskam k
.naaradnek sorop audek helo atiredid gnay lamron nabeB .b
2 . naaradnek haubeS rotcart - reliartimes tareb : iaynupmem rotcart ,Nk 07
tareb reliartimes ,Nk 002 rotcart esableehw sorop ,mc 053 = reliratimes
akaleb id mc 007 adareb gnakaleb sorop gn rotcart , hctih tniop adareb
gnakaleb sorop naped id mc 05 rotcart tasuP .nalaj sata id mc 011 nad
tareb rotcart naped sorop gnakaleb id mc 081 adareb rotcart nad 09 id mc
tasup gnades ,nalaj sata tareb reliartimes 82 adareb sorop naped id mc 0
reliartimes R .ratad nalaj naakumrep sataid mc 021 nad 1a 5,1 =
R , nalaj sataid mc 521 kitit adap ajrekeb 2a f ; 1,1 = r ; 2,0 = .6,0 =
ted/m 4,2 = a akiJ 2 ted/m 8,9 = g nad , 2 : halnakutnet akam ,
sorop adap lamron nabeb aynraseB .a reliartimes .
adap lamron nabeb aynraseB .b tniop hctih ..
adap ayag aynraseB .c tniop hctih .
gnakaleb sorop adap lamron nabeb aynraseB .d rotcart
gnakaleb sorop adap mumiskam kajej ayag aynraseB .e rotcart .
92
nabawaJ icnuK .B
F .a .1 skam 6 = 555, Nk
W .b r Nk 580,01 =
W f Nk 519,6 =
W .a .2 s 744,121 = k N
W .b ih = 355,87 Nk
F .c ih = Nk 963,47
W .d r Nk 846,131 =
F .e skam Nk 988,76 =
.C nasululeK airetirK
airetirK rokS 1( – )01 toboB ialiN nagnareteK
1 romon laos ( fitingoK ) 2 nad 5
sulul tarayS laminim ialin
65
isaton silunem naitileteK 1
teK rudesorp natape 2
nabawaj alumrof natapeteK 1
utkaw natapeteK 1
RIHKA IALIN
03
BAB VI
PUTUNEP
622 OTO.KGM ludum halnaikimeD – luduj nagned 20 kajeJ ayaG
naaradneK ital aparebeb ipakgnelid nagned nususid iaseles halet ini set ,sagut/nah
ludom nautnab nagneD .aynnabawaj icnuk atreseb rihka isaulave nupuam fitamrof
nagnabmekrep iridnes uatnamem tapad awsisaham arap nakparahid ini
raneb halet akerem hakapa ,aynisnetepmok - isnetepmok ikilimem raneb
jut adap nimrecret anamiagabes rajaleb nataigek paites adap nakparahid gnay nau
.muleb uata
akam laminim nasululek tarays iapacnem halet gnay awsisaham arap igaB
.ini hailukatam adap aynrajaleb nataigek nakitnehgnem tapad hadus akerem
ululek ihunemem tapad muleb akij aynkilabeS surah akerem akam ,laminim nas
iretam naigab adap amaturet aynrajaleb ilabmek gnalugnem - muleb gnay iretam
huggnus hibel surah akerem aynkiabes nad )sulul muleb( ayniasaukid - huggnus
irad nautnab kusamret ada gnay satilisaf naktaafnamem nagned rajaleb malad
.ini hailukatam rotatilisaf iagabes nesod
13
AKATSUP RATFAD
.0791 .noipmahC & dlonrA ecneicS dna noitaluclaC elciheV rotoM :hciwroN ..dtL ,snoS dna rehctelF yb niatirB taerG
.1791 ..E.D ,eloC .scimanyD elciheV yratnemelE tnemetrapeD lacinahceM fo.I.M ,robrA nnA nagihciM fo ytisrevinU gnireenignE
.7791 .nitraM snoicinhceT selciheV rotoM rof noitaluclaC dna ecneicS : nodnoL .dtL sserP ytisrevinU hsilgnE ehT
.1002 .namojN ,artnatuS aynisakilpA nad iroeT fitomotO igolonkeT aruS . : ayab.aydiW anuG tibreneP
.8791 .Y.J ,gnoW .selciheV dnuorG fo yroehT .snoS & yeliW nhoJ :kroY weN