22
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ELEKTRIČNE INSTALACIJE I RASVJETA Laborat. vezbi BL !!!!!!!!!!!!!!!!!!!! (2)

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1

>;>;>;>; 5J@KLMNOP+QRARNRM+SJ@K+==:=BC<5J@KLMNOP+QRARNRM+SJ@K+==:=BC<5J@KLMNOP+QRARNRM+SJ@K+==:=BC<5J@KLMNOP+QRARNRM+SJ@K+==:=BC<Potrebno je izraditi kompletan projekat električne instalacije i osvetljenja stana čija je

građevinska osnova data na priloženom crtežu. Projekat mora da obuhvati:1. Proračun osvetljenja za prostoriju sa najvećim i srednjim potrebnim nivoom

osvetljenosti i procenu instalisane snage osvetljenja ostalih prostorija,2. Planove instalacije osvetljenja i utičnica kao i jednopolnu šemu razvodne table u

stanu,3. Kompletan proračun vodova: za napajanje zgrade (od TS do KPO), mernog

razvodnog ormana (KPO – MRO), razvodne table stana (MRO – RT) i svihstrujnih kola u stanu,

4. Proveru vrednosti pada napona i zaštite od strujnog udara,5. Pregled instalisane snage osvetljenja, usvojenih preseka i osigurača za sva strujna

kola u stanu kao i pregleda opterećenja po fazama,6. Specifikaciju materijala.

Projekat uskladiti sa svim važećim propisima i standardima. Strogo se pridržavati ipredvideti sve mere zaštite. Posebni zahtevi sa kojima treba uskladiti projekat su:

• Zgrada se napaja iz distributivne transformatorske stanice u koju je ograđentransformator od 630 kVA, 10/0.42 kV/kV, PCun=6.5 kW, PFe0=1.3 kW, spregeDyn5.

• Distributivna mreža je kablovska. Preko odcepa (kabla) koji je potrebnodimenzionisati napajaju se 3 slične zgrade. Prva se nalazi na 25 m od TS, ameđusobno su udaljene po 12 m. U projektu smatrati da se stan nalazi unajudaljenijoj zgradi.

• Zgrada ima 7 spratova sa po 3 slična stana. Zajednička potrošnja se možeposmatrati kao potrošnja dodatnog stana.

• U svakom stanu se predviđa ugradnja trofaznih utičnica za napajanje trofaznogštednjaka. Simetriranje opterećenja je potrebno izvesti za svaki stan ponaosob.

• MRO su raspoređeni po spratovima, a najveće rastojanje od MRO do RT iznosi12 m.

• Zaštita od previsokog napona dodira se izvodi sistemom TN-C/S, pri čemu se PE iN provodnik odvajaju u KPO gde je izvršeno i glavno izjednačenje potencijalanjihovim vezivanjem na uzemljivač.

• Merama zaštite treba predvideti pojačane mere zaštite u kupatilu i izjednačenjepotencijala metalnih delova.

• Objekat se zagreva daljinski, a hladi se i dogreva električnom energijom (klimauređaji).

• Za zagrevanje tople vode u kupatilu i kuhinji predvideti akumulacioni i protočnibojler, respektivno.

• Može se smatrati da je srednja snaga po utičnici oko 500 W, a da je snagaelektričnog štednjaka oko 7000 W. Snaga ugrađenih klima uređaja iznosi 2200 W(4 uređaja). Snaga protočnog bojlera iznosi oko 2500 W, a akumulacionog oko2000 W. Za dogrevanje kupatila koristi se grejalica snage 1200 W.

• Predviđeno je da zidovi i tavanica objekta budu izrađeni u svetloj boji.Projektni zadatak izdat:

U Banjaluci, 21. Maja 2001.

Predmetni asistent:

Dejan Raca, dipl. ing.

Student – projektant:

Borislav Marić, 0030/95

2

9;$LTOPUMP+@VPW+XWY@KLOPT+JKLZLOKR+WR+WYP[+V@NJLSOP[+VJ@JRUXOP[R9;$LTOPUMP+@VPW+XWY@KLOPT+JKLZLOKR+WR+WYP[+V@NJLSOP[+VJ@JRUXOP[R9;$LTOPUMP+@VPW+XWY@KLOPT+JKLZLOKR+WR+WYP[+V@NJLSOP[+VJ@JRUXOP[R9;$LTOPUMP+@VPW+XWY@KLOPT+JKLZLOKR+WR+WYP[+V@NJLSOP[+VJ@JRUXOP[R

++++++++++++++++++++++++++++9;>;$LTOPUMP+@VPW++++++++++++++++++++++++++++9;>;$LTOPUMP+@VPW++++++++++++++++++++++++++++9;>;$LTOPUMP+@VPW++++++++++++++++++++++++++++9;>;$LTOPUMP+@VPW

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`VRJR\L\O@+WR+QPA@[;6%RQY@AOL+MXNPKL+X?JRAPNP+X+QPA+VJL+[R\NLJPWROKR+;2YL+JRQY@AOL+MXNPKL+WX+VJ@[KLJR+G=[[`@WP[+JRQY@AOR+MXNPKR+M@A+MXVRNP\R+M@KR+KL+MYRARNOR+>==a>==[[;6.NPUOP]L+X+MXTPOKP+[@ONPJRNP+OR+>9=][+@A+V@AR;6.NP_OP]R+X+MXVRNP\X+NJLSR+AR+P[R+QRZNPNOP+V@M\@VR]+P+AR+KL+[@ONPJROR+OR+>9=][+@A+V@AR;6&WNR\L+XNPUOP]L+[@ONPJRNP+OR+YPWPOP+H=+][+@A+V@AR;65JLMPARUL+QR+@WYKLN\KLOKL+[@ONPJRNP+OR+><=][+@A+V@AR+P+OR+JRWN@KROKX+><][+@A+A@YJRNMR;64JLKR\P]X+X+MXVRNP\X+V@WNRYPNP+PQORA+YJRNR;6.+MXVRNP\X+PQYJZPNP+PQKLAORURYROKL+V@NLO]PKR\R+V@YLQPYOKL[+WYPT+[LNR\OPT+VJLA[LNRVJ@Y@AOPM@[+VJLWKLMR+F[[+bMYRAJRNOPTc+WR+PQ@\R]PK@[+_XN@6QL\LOL+S@KL;$RK+VJ@Y@AOPMYLQRNP+QR++QRZNPNOX+WRSPJOP]X+WNROR;

3

2.2 Proracun osvjetljenja

Proracun osvjetljenja je uradjen po metodi stepena korisnog djelovanja za dnevnu sobu ikuhinju,a za ostale prostorije po Watt-noj metodi.1OLYOP+S@JRYRM+KL+AP[LOQPKR+9`Ha9`<[9`YPWPOL+Td9`F[;5@YJWPOR+S@JRYMR+WL+JR]XOR+MR@

A=axb=6 m2.Potreban srednji nivo osvjetljenosti iznosi Es=250 lx.Indeks prostorije se racuna premaizrazu:

( )bahAk

k +=

-hk korisna visina prostorije racuna se kaohk=h-hr-hs

-hr visina radne povrsine koja iznosi 0,85m-hs visina vjesanja svjetiljke koja iznosi 0,2m

hk=2,6-0,85-0,2=1,55mUvrstavanjem brojnih vrijednosti za k dobijemo

k=0,8Koeficijenti refleksije su:

-pod rp=0,1-strop rs=0,7-zidovi rz=0,5

Osvjetljenje je rijeseno kao indirektno sa svjetiljkom S-1-200 sa sijalicom 200W sauzarenim vlaknom.Iz tablica za ovu svjetiljku se pronalazi 27,0=η .Faktor zaprljanosti prostorije fz=0,9 .Faktor starenja sijalice fs=0,9 .Ukupan svjetlosni fluksse racuna po izrazu:

zs

suk ff

AEη

Uvrstavanjem brojnih vrijednosti dobija se:lmuk 9250=Φ

Fluks jedne sijalice od 200W iznosi:lms 31001 =Φ

Racunski dobijen potreban broj sijalica je:

9,21

=ΦΦ

=s

ukrn

Konacan usvojen potreban broj sijalica je n=3 sa ukupnom snagom osvjetljenja 600W.#XTPOKR+KL+AP[LOQPKR+9a>`<+[9`YPWPOL+Td9`F[;5@YJWPOR+S@JRYMR+WL+JR]XOR+MR@

A=axb=2,3 m2.Potreban srednji nivo osvjetljenosti iznosi Es=250 lx.Indeks prostorije se racuna premaizrazu:

( )bahAk

k +=

-hk korisna visina prostorije racuna se kaohk=h-hr-hs

-hr visina radne povrsine koja iznosi 0,85m

4

-hs visina vjesanja svjetiljke koja iznosi 0,2m

hk=2,6-0,85-0,2=1,55mUvrstavanjem brojnih vrijednosti za k dobijemo

k=1,28Koeficijenti refleksije su:

-pod rp=0,1-strop rs=0,7-zidovi rz=0,5

Osvjetljenje je rijeseno kao indirektno sa svjetiljkom S-1-200 sa sijalicom 200W sauzarenim vlaknom.Iz tablica za ovu svjetiljku se pronalazi 47,0=η .Faktor zaprljanosti prostorije fz=0,9 .Faktor starenja sijalice fs=0,9 .Ukupan svjetlosni fluksse racuna po izrazu:

zs

suk ff

AEη

Uvrstavanjem brojnih vrijednosti dobija se:lmuk 4107=Φ

Fluks jedne sijalice od 200W iznosi:lms 31001 =Φ

Racunski dobijen potreban broj sijalica je:

32,11

=ΦΦ

=s

ukrn

Konacan usvojen potreban broj sijalica je n=2 sa ukupnom snagom osvjetljenja 400W.Ostale prostorije se rjesavaju po Watt-noj metodi,gdje se potrebna snaga osvjetljenjaracuna na osnovu povrsine prostorije i usvojene specificne snage od 30 W/m2.Rezultati su prikazani u tablici.

Prostorija A Porebnasnaga W

RealizacijaW

Hodnik 3,5 105 2x60S. soba 4 120 2x100D. soba 5 150 2x100Balkon 2,5 75 1x100Trpezarija 3,625 108 2x60Ostava k. 0,8 24 1x60Ostava b. 0,75 23 1x60Kupatilo 3,5 105 2x60Kuhinja 2x200Dnevni boravak 3x200Total 1980

Ukupna instalisana snaga osvjetljenja je 1980 W.

5

9;:+1P[LOQ9;:+1P[LOQ9;:+1P[LOQ9;:+1P[LOQP@OPWROKL+MRS\@YRP@OPWROKL+MRS\@YRP@OPWROKL+MRS\@YRP@OPWROKL+MRS\@YR

)OWNR\PWROR+WROR?R+KLAO@?+WNROR+PQO@WP3WP 306801 =

0LAO@YJL[LOR+WOR?R+WNROR+WL+JR]XOR+V@+@SJRW]X3

1PkP jj =?AKL+KL+ jk +M@L^P]PKLON+KLAO@YJL[LO@WNP+P+PQO@WP3

4,0=jk +bQS@?+YL\PML+POWNR\PWROL+WOR?Lc

5@W\PKL+XO@WLOKR+YJPKLAO@WNP+A@SPKR+WLWPj 12272=

9;:;>+1P[LOQP@OPWROKL+MRS\@YR+@A+8%&+A@+%&9;:;>+1P[LOQP@OPWROKL+MRS\@YR+@A+8%&+A@+%&9;:;>+1P[LOQP@OPWROKL+MRS\@YR+@A+8%&+A@+%&9;:;>+1P[LOQP@OPWROKL+MRS\@YR+@A+8%&+A@+%&

0LAO@YJL[LOL+WNJXKR+WNROR+WL+JR]XOR+VJL[R+PQJRQX3

ϕcos3 n

jj U

PI =

.WYRKR+WL+^RMN@J+WOR?L+ 1cos =ϕ +QR+A@[RePOWNYR;

.O@ZLOKL[+ VU n 380= +P+@WNR\PT+SJ@KOPT+YJPKLAO@WNP+A@SPKR+WL3

AI j 6,18=2NJXKR+QR+M@KX+VJ@Y@AOPM+[@JR+SPNP+VJLAYPfLO+@AJLfXKL+WL+PQ+PQJRQR3

θKKI

Ip

jj =/

?AKL+KL pK +^RMN@J+V@\R?ROKR+MRS\R`R θK NL[VLJRNXJOP+M@L^P]PKLON;

#RM@+WL+JRAP+@+96H+YPWLQP\OPT+MRS\@YR+JRQY@AR+NPVR+*+M@KP+WX+QRNY@JLOP+P+YXMX+WLVRJR\L\O@`+XWYRKR+WL3

8,0=pK ++++ 1=θK

2\PKLAP+ AI j 25,23/ =)Q+NRS\P]L+WL+SPJR+@A?@YRJRKX]P++Y@A+P+VJLWKLM+OKL?@YPT+VJ@Y@AOPMR+VJL[R3

/jtd II >

?AKL+KL+ tdI NJRKO@+A@QY@\KLOR+WNJXKR;

/PJR+WL+MRS\+WR+57*+PQ@\R]PK@[+P+SRMRJOP[+VJ@Y@AOP]P[R+VJLWKLMR 26mmq = ;1RM\L+NJLSR

OR[+MRS\+556g+ 265 mmx +WR+ AItd 40= ;8RMWP[R\OR+AXQPOR+@A+8%&+A@+%&+KL+>9[;)QS@J+@WP?XJR]R+WL+YJWP+OR+@WO@YX+PQJRQR3

tdpoj IKKII θ<<

AIA o 324,20 <<.+8%&+WL+XWYRKR+@WP?XJR]+WR+N@V\KPYP[+X[LNM@[+NPVR+16NJ@[P+O@[POR\OL+WNJXKL+ AIo 25= ;

6

9;:;9+1P[LOQP@OPWROKL+MRS\@YR+@A+#5&+A@+8%&9;:;9+1P[LOQP@OPWROKL+MRS\@YR+@A+#5&+A@+8%&9;:;9+1P[LOQP@OPWROKL+MRS\@YR+@A+#5&+A@+8%&9;:;9+1P[LOQP@OPWROKL+MRS\@YR+@A+#5&+A@+8%&

0LAO@YJL[LOR+WOR?R+NJP+WNROR+WL+JR]XOR+V@+@SJRW]X3

∑=3

133 PkP jj

?AKL+KL+ 3jk +M@L^P]PKLON+KLAO@YJL[LO@WNP+P+PQO@WP3

33∞

∞ += kkk j

4AKL+KL+ 18,0=∞k5@W\PKL+XO@WLOKR+YJPKLAO@WNP+A@SPKR+WL

WPj 240773 =0LAO@YJL[LOL+WNJXKR+NJP+WNROR+WL+JR]XOR+VJL[R+PQJRQX3

ϕcos33

3n

jj U

PI =

.WYRKR+WL+^RMN@J+WOR?L+ 1cos =ϕ +QR+A@[R]POWNYR;

.O@WLOKL[+ VU n 380= +P+@WNR\PT+SJ@KOPT+YJPKLAO@WNP+A@SPKR+WL3

AI j 6,363 =2NJXKR+QR+M@KX+VJ@Y@AOPM+[@JR+SPNP+VJLAYPfLO+@AJLfXKL+WL+PQ+PQJRQR3

θKKI

Ip

jj

3/3 =

?AKL+KL pK +^RMN@J+V@\R?ROKR+MRS\R`R θK NL[VLJRNXJOP+M@L^P]PKLON;

#RM@+WL+JRAP+@+96H+YPWLQP\OPT+MRS\@YR+JRQY@AR+NPVR+*+M@KP+WX+QRNY@JLOP+P+YXMX+WLVRJR\L\O@`+XWYRKR+WL3

8,0=pK ++++ 1=θK

2\PKLAP+ AI j 7,45/3 =

)Q+NRS\P]L+WL+SPJR+@A?@YRJRKX]P++XWV@OWMP+Y@A+P+VJLWKLM+OKL?@YPT+VJ@Y@AOPMR+VJL[R3/3jtd II >

?AKL+KL+ tdI NJRKO@+A@QY@\KLOR+WNJXKR;

/PJR+WL+MRS\+WR+57*+PQ@\R]PK@[+P+SRMRJOP[+VJ@Y@AOP]P[R+VJLWKLMR 216mmq = ;1RM\L

NJLSR+OR[+MRS\+556g+ 2165 mmx +WR+ AItd 73= ;8RMWP[R\OR+AXQPOR+Y@AR+KL+9=+[;)QS@J+@WP?XJR]R+WL+YJWP+OR+@WO@YX+PQJRQR3

tdpoj IKKII θ<<

AIA o 5,623,50 <<.+#5&+WL+XWYRKR+@WP?XJR]+WR+N@V\KPYP[+X[LNM@[+NPVR+16NJ@[P+O@[POR\OL+WNJXKL+ AIo 60=;

7

9;:;:+1P[LOQP@OPWROKL+MRS\@YR+@A+#5&>+A@+#5&9;:;:+1P[LOQP@OPWROKL+MRS\@YR+@A+#5&>+A@+#5&9;:;:+1P[LOQP@OPWROKL+MRS\@YR+@A+#5&>+A@+#5&9;:;:+1P[LOQP@OPWROKL+MRS\@YR+@A+#5&>+A@+#5&

0LAO@YJL[LOR+WOR?R+Q?JRAL+WR+G+WVJRN@YR+V@+NJP+WNROR+WL+JR]XOR+V@+@SJRW]X3

∑=22

1PkP jzjz

?AKL+KL+ jzk +M@L^P]PKLON+KLAO@YJL[LO@WNP+P+PQO@WP3

121kkk jz +

+= ∞∞

4AKL+KL+ 18,0=∞k5@W\PKL+XO@WLOKR+YJPKLAO@WNP+A@SPKR+WL

WPjz 94494=0LAO@YJL[LOL+WNJXKR+Q?JRAL+WL+JR]XOR+VJL[R+PQJRQX3

ϕcos3 n

jzjz U

PI =

.WYRKR+WL+^RMN@J+WOR?L+ 1cos =ϕ +QR+A@[RePOWNYR;

.O@ZLOKL[+ VU n 380= +P+@WNR\PT+SJ@KOPT+YJPKLAO@WNP+A@SPKR+WL3

AI jz 143=2NJXKR+QR+M@KX+VJ@Y@AOPM+[@JR+SPNP+VJLAYPfLO+@AJLfXKL+WL+PQ+PQJRQR3

θKKI

Ip

jzjz =/

?AKL+KL pK +^RMN@J+V@\R?ROKR+MRS\R`R θK NL[VLJRNXJOP+M@L^P]PKLON;

#RM@+WL+JRAP+@++JRQY@AX+NPVR+1+M@KP+WX+QRNY@JLOP+P+YXMX+WL+VRJR\L\O@`+XWYRKR+WL38,0=pK ++++ 1=θK

+2\PKLAP+ AI jz 178/ =)Q+NRS\P]L+WL+SPJR+@A?@YRJRKX]P+++Y@A+P+VJLWKLM+OKL?@YPT+VJ@Y@AOPMR+VJL[R3

/jztd II >

?AKL+KL+ tdI NJRKO@+A@QY@\KLOR+WNJXKR;/PJR+WL+MRS\+WR+PQ@\R]PK@[+@A+X[JLQLO@?+V@\PLNP\LOR++P+SRMRJOP[+VJ@Y@AOP]P[RVJLWKLMR 2mm300q = ;1RM\L+NJLSR+OR[+MRS\++ 240mm300x3 2 + +WR+ A396Itd = ;8RMWP[R\OR+AXQPOR+Y@AR+KL+>9+[;#RS\+WL+WNPNP+O@QRWNP[+@WP?XJR]L[+X+$2`NPV+(`+ a335Io =

8

9;:;H+1P[LOQP@OPWROKL+MRS\@YR+@A+#5&9+A@+#5&>9;:;H+1P[LOQP@OPWROKL+MRS\@YR+@A+#5&9+A@+#5&>9;:;H+1P[LOQP@OPWROKL+MRS\@YR+@A+#5&9+A@+#5&>9;:;H+1P[LOQP@OPWROKL+MRS\@YR+@A+#5&9+A@+#5&>

0LAO@YJL[LOR+WOR?R+AYPKL+Q?JRAL+WR+G+WVJRN@YR+V@+NJP+WNROR+WL+JR]XOR+V@+@SJRW]X3

∑=44

1PkP jzjz

?AKL+KL+ jzk +M@L^P]PKLON+KLAO@YJL[LO@WNP+P+PQO@WP3

222kkk 2j +

+= ∞∞

4AKL+KL+ 18,0=∞k5@W\PKL+XO@WLOKR+YJPKLAO@WNP+A@SPKR+WL

WPjz 163944=0LAO@YJL[LOL+WNJXKR+Q?JRAL+WL+JR]XOR+VJL[R+PQJRQX3

ϕcos3 n

jzjz U

PI =

.WYRKR+WL+^RMN@J+WOR?L+ 1cos =ϕ +QR+A@[RePOWNYR;

.O@ZLOKL[+ VU n 380= +P+@WNR\PT+SJ@KOPT+YJPKLAO@WNP+A@SPKR+WL3

AI jz 249=2NJXKR+QR+M@KX+VJ@Y@AOPM+[@JR+SPNP+VJLAYPfLO+@AJLfXKL+WL+PQ+PQJRQR3

θKKI

Ip

jzjz =/

?AKL+KL pK +^RMN@J+V@\R?ROKR+MRS\R`R θK NL[VLJRNXJOP+M@L^P]PKLON;

#RM@+WL+JRAP+@++JRQY@AX+NPVR+1+M@KP+WX+QRNY@JLOP+P+YXMX+WL+VRJR\L\O@`+XWYRKR+WL38,0=pK ++++ 1=θK

+2\PKLAP+ AI jz 276/ =)Q+NRS\P]L+WL+SPJR+@A?@YRJRKX]P+++Y@A+P+VJLWKLM+OKL?@YPT+VJ@Y@AOPMR+VJL[R3

/jztd II >

?AKL+KL+ tdI NJRKO@+A@QY@\KLOR+WNJXKR;/PJR+WL+MRS\+WR+PQ@\R]PK@[+@A+X[JLQLO@?+V@\PLNP\LOR++P+SRMRJOP[+VJ@Y@AOP]P[RVJLWKLMR 2mm300q = ;1RM\L+NJLSR+OR[+MRS\++ 240mm300x3 2 + +WR+ A396Itd = ;8RMWP[R\OR+AXQPOR+Y@AR+KL+>9+[;#RS\+WL+WNPNP+O@QRWNP[+@WP?XJR]L[+X+$2`NPV+(` A335Io =

9

9;:;<+1P[LOQP@OPWROKL+MRS\@YR+@A+$2+A@+#5&99;:;<+1P[LOQP@OPWROKL+MRS\@YR+@A+$2+A@+#5&99;:;<+1P[LOQP@OPWROKL+MRS\@YR+@A+$2+A@+#5&99;:;<+1P[LOQP@OPWROKL+MRS\@YR+@A+$2+A@+#5&9

0LAO@YJL[LOR+WOR?R+NJP+Q?JRAL+WR+G+WVJRN@YR+V@+NJP+WNROR+WL+JR]XOR+V@+@SJRW]X3

∑=66

1PkP jzjz

?AKL+KL+ jzk +M@L^P]PKLON+KLAO@YJL[LO@WNP+P+PQO@WP3

3633 ++= ∞

∞kkk j

4AKL+KL+ 18,0=∞k5@W\PKL+XO@WLOKR+YJPKLAO@WNP+A@SPKR+WL

WPjz 227543=0LAO@YJL[LOL+WNJXKR+Q?JRAL+WL+JR]XOR+VJL[R+PQJRQX3

ϕcos3 n

jzjz U

PI =

.WYRKR+WL+^RMN@J+WOR?L+ 1cos =ϕ +QR+A@[RePOWNYR;

.O@ZLOKL[+ VU n 380= +P+@WNR\PT+SJ@KOPT+YJPKLAO@WNP+A@SPKR+WL3

AI jz 333=2NJXKR+QR+M@KX+VJ@Y@AOPM+[@JR+SPNP+VJLAYPfLO+@AJLfXKL+WL+PQ+PQJRQR3

θKKI

Ip

jzjz =/

?AKL+KL pK +^RMN@J+V@\R?ROKR+MRS\R`R θK NL[VLJRNXJOP+M@L^P]PKLON;

#RM@+WL+JRAP+@++JRQY@AX+NPVR+1+M@KP+WX+QRNY@JLOP+P+YXMX+WL+VRJR\L\O@`+XWYRKR+WL39,0=pK ++++ 1=θK

+2\PKLAP+ AI jz 370/ =)Q+NRS\P]L+WL+SPJR+@A?@YRJRKX]P+++Y@A+P+VJLWKLM+OKL?@YPT+VJ@Y@AOPMR+VJL[R3

/jztd II >

?AKL+KL+ tdI NJRKO@+A@QY@\KLOR+WNJXKR;/PJR+WL+MRS\+WR+PQ@\R]PK@[+@A+X[JLQLO@?+V@\PLNP\LOR++P+SRMRJOP[+VJ@Y@AOP]P[RVJLWKLMR 2300mmq = ;1RM\L+NJLSR+OR[+MRS\++ 23004 mmx +WR+ AItd 396= ;8RMWP[R\OR+AXQPOR+Y@AR+KL+9<+[;)QS@J+@WP?XJR]R+WL+YJWP+OR+@WO@YX+PQJRQR3

tdpojz IKKII θ<<

AIA o 356333 <<.+$2+WL+XWYRKR+O@QRWNP+@WP?XJR]+WR+N@V\KPYP[+X[LNM@[+NPVR+(+O@[POR\OL+WNJXKL

A335Io = ;

10

9;:;F+1P[LOQP@OPWROKL+MRS\@YR+X+WNROX9;:;F+1P[LOQP@OPWROKL+MRS\@YR+X+WNROX9;:;F+1P[LOQP@OPWROKL+MRS\@YR+X+WNROX9;:;F+1P[LOQP@OPWROKL+MRS\@YR+X+WNROX(RQPYOR+WNJXKR+[@O@^RQO@?+WNJXKO@?+M@\R+WL+JR]XOR+VJL[R+PQJRQX3

nf

in U

PI =

?AKL+KL+ iP +POWNR\PWROR+WOR?R+WNJXKO@?+M@\R`+R+ VU nf 220= ;

(RQPYOR+WNJXKR+NJ@^RQO@?+WNJXKO@?+M@\R+WL+JR]XOR+VJL[R+PQJRQX3

nL

in U

PI

3=

?AKL+KL+ iP +POWNR\PWROR+WOR?R+WNJXKO@?+M@\R`+R+ VU nL 380= ;5JLWKL]P+MRS\@YR+@A+SRMJR+WR+57*+PQ@\R]PK@[+XWY@KLOP+WX+V@+VJLV@JX]P3

6QR+WNJXKOL+MJX?@YL+@WYKLN\KLOKR+ 25.1 mmq =6QR+@WNR\L+WNJXKOL+MJX?@YL++ 25.2 mmq =

5@WN@+WL+@A+%&+Y@AP+>G+VRJR\L\OPT+Y@A@YR`+JRQY@AR+NPVR+*`QR+M@JLM]P@OL+^RMN@JL+WLXQP[RKX+YJPKLAO@WNP3

7,0=pK ++++ 1=θK)QS@J+@WP?XJR]R+WL+YJWP+OR+@WO@YX+MJPNLJPKX[R3

tdpon IKKII θ<<1.1

)Q+NRS\P]R+NJRKO@+A@QYP\KLOR+WNJXKR+QR+VJLWKLM+ 25.1 mmq = PQO@WP+ AItd 5.18= `+R+QR25.2 mmq = PQO@WP+ AItd 23= `

DR+V@KLAPOL+WNJXKOL+MJX?@YL+X+WNROX+JLQX\NRNP+WX+ARNP+NRSL\RJO@+MR@+P+JRWV@JLA+@VNLJL]LOKRV@+^RQR[R;

Br.

Namjena Pi W In A q mm2 Ittd A Io A L m

>; .NP]OP]R+MX; ++++<== +++++9;9G +++9`< ++++9: ++++++>F +++++:;C9; &WYKLN\KLOKL> ++++<I= +++++9`< +++>`< ++++>I`< ++++++>= ++++9C:; 4JPKR\P]R+MX; +++>9== +++++<`H< +++9`< ++++9: ++++++>F +++++9;G<H; .NP]OP]R+MXT; +++><== +++++F`I> +++9`< ++++9: ++++++>F +++++H;F<; .NP]OP]R+NJV; +++>=== +++++H`<H +++9`< ++++9: ++++++>F +++++G;9F; .NP]OP]R

AO;S;+++><== +++++F`I> +++9`< ++++9: ++++++>F ++++>F;C

G; .NP]OP]R+W;W; +++><== +++++F`I> +++9`< ++++9: ++++++>F ++++>F;FI; .NP]OP]R+AK;W; +++><== +++++F`I> +++9`< ++++9: ++++++>F ++++9=C; &WYKLN\KLOKL9 +++>HH= +++++F`< +++>`< ++++>I`< ++++++>= ++++:=>=; 5J@N@]OP+S@K; +++9<== ++++>>`:= +++9`< ++++9: ++++++>F +++++H;<>>; 2NLAOKRM +++G=== ++++>=`FH +++9`< ++++9: ++++++>F +++++I;:>9; -M;S@K\LJ +++99== ++++>= +++9`< ++++9: ++++++>F +++++<>:; DY@O]L +++++6 +++++6 +++>`< ++++>I`< ++++++>= +++++>>H; #\P[R+X; +++99== ++++>= +++9`< ++++9: ++++++>F +++++>9><; #\P[R+X; +++99== ++++>= +++9`< ++++9: ++++++>F +++++>9>F; #\P[R+X; +++99== ++++>= +++9`< ++++9: ++++++>F +++++>9>G; #\P[R+X; +++99== ++++>= +++9`< ++++9: ++++++>F +++++>9

11

/J;/J;/J;/J; +++++">+++++">+++++">+++++"> ++++++"9"9"9"9 ++++"9"9"9"9>; ++++<==9; ++++<I=:; ++++>9==H; ++++><==<; ++++>===F; ++++><==G; ++++><==I; +++><==C; +++>H==>=; ++++9<==>>; +++:=== ++++9=== +++9===>9; +++99==>H; +++99==><; ++++99==>F; +++99==>G; +++99==$@NR\ +++>=H== ++++>=H== +++CFI=

12

9;H5J@YKLJR+VRA@YR+ORV@OR9;H5J@YKLJR+VRA@YR+ORV@OR9;H5J@YKLJR+VRA@YR+ORV@OR9;H5J@YKLJR+VRA@YR+ORV@OR

9;H;>5J@YKLJR+VRA@YR+ORV@OR+@A+$2+A@+#5&99;H;>5J@YKLJR+VRA@YR+ORV@OR+@A+$2+A@+#5&99;H;>5J@YKLJR+VRA@YR+ORV@OR+@A+$2+A@+#5&99;H;>5J@YKLJR+VRA@YR+ORV@OR+@A+$2+A@+#5&9

1XQPOR+MRS\@YWM@?+Y@AR+WR+SRMRJOP[+VJ@Y@AOP]P[R+P+PQ@\R]PK@[+@A+X[JLQLO@?V@\PLNP\LOR+AP[LOQPKR+:a:==h9H= 2mm +@A+$2+A@+#5&9+PQO@WP+9<+[;5@A+VJLNV@WNRYM@[AR+WX+OR+@YRK+MRS\+VJPM\KX]LOL+:+Q?JRAL+WR+KLAO@YJL[LO@[+WOR?@[

WP zj 2275433 =5RA+ORV@OR+PQ[LfX+$2++P+#5&9++WL+JR]XOR+V@+PQJRQX

23

2

)(100

n

zjkpoTS U

lxtgrPu

α+=∆ −

?AKL+WX36+J++V@AXQOP+@[WMP+@NV@J+++ km/Ω6+a++V@AXQOP+POAXMNPYOP+@NV@J+++ km/Ω6\+AXQPOR+Y@AR+++M[)Q+NRS\P]L+QR+VJ@Y@AOPML+VJLWKLMR+:==+ 2mm WL+XQP[R3

Jd=`=F ad=`=GC)Q+VJ@VPWRO@?+^RMN@JR+WOR?L+ 95,0cos =ϕ +W\PKLAP+ 32,0=ϕtg.O@WLOKL[+SJ@KOPT+YJPKLAO@WNP+A@SPKR+WL+3

22 380025,0)32,0*079,006,0(227543*100 +=∆ −kpoTSu

%315,02 =∆ −kpoTSu

9;H;95J@YKLJR+VRA@YR+ORV@OR+@A++#5&9+A@+#5&>9;H;95J@YKLJR+VRA@YR+ORV@OR+@A++#5&9+A@+#5&>9;H;95J@YKLJR+VRA@YR+ORV@OR+@A++#5&9+A@+#5&>9;H;95J@YKLJR+VRA@YR+ORV@OR+@A++#5&9+A@+#5&>

1XQPOR+MRS\@YWM@?+Y@AR+WR+SRMRJOP[+VJ@Y@AOP]P[R+P+PQ@\R]PK@[+@A+X[JLQLO@?V@\PLNP\LOR+AP[LOQPKR+:a:== 2mm h9H=+@A+#5&9+A@+#5&>+PQO@WP+>9+[;5@AVJLNV@WNRYM@[+AR+WX+OR+@YRK+MRS\+VJPM\KX]LOL+9+Q?JRAL+WR+KLAO@YJL[LO@[+WOR?@[

WP zj 1639942 =5RA+ORV@OR+PQ[LfX+#5&9++P+#5&>++WL+JR]XOR+V@+PQJRQX

22

12

)(100

n

zjkpokpo U

lxtgrPu

α+=∆ −

?AKL+WX36+J++V@AXQOP+@[WMP+@NV@J+++ km/Ω6+a++V@AXQOP+POAXMNPYOP+@NV@J+++ km/Ω6\+AXQPOR+Y@AR+++M[)Q+NRS\P]L+QR+VJ@Y@AOPML+VJLWKLMR+:==+ 2mm WL+XQP[R3

Jd=`=F ad=`=GC)Q+VJ@VPWRO@?+^RMN@JR+WOR?L+ 95,0cos =ϕ +W\PKLAP+ 32,0=ϕtg.O@WLOKL[+SJ@KOPT+YJPKLAO@WNP+A@SPKR+WL+3

%11,0u 1kpo2kpo =∆ −

13

9;H;:+5J@YKLJR+VRA@YR+ORV@OR+@A++#5&>+A@+#5&9;H;:+5J@YKLJR+VRA@YR+ORV@OR+@A++#5&>+A@+#5&9;H;:+5J@YKLJR+VRA@YR+ORV@OR+@A++#5&>+A@+#5&9;H;:+5J@YKLJR+VRA@YR+ORV@OR+@A++#5&>+A@+#5&

1XQPOR+MRS\@YWM@?+Y@AR+WR+SRMRJOP[+VJ@Y@AOP]P[R+P+PQ@\R]PK@[+@A+X[JLQLO@?V@\PLNP\LOR+AP[LOQPKR+b:a:==h9H=c+ 2mm +@A+#5&>+A@+#5&+PQO@WP+>9+[;5@AVJLNV@WNRYM@[+AR+WX+OR+@YRK+MRS\+VJPM\KX]LOR+>+Q?JRAR+WR+KLAO@YJL[LO@[+WOR?@[

WP zj 944942 =5RA+ORV@OR+PQ[LfX+#5&>++P+#5&++WL+JR]XOR+V@+PQJRQX

22

1

)(100

n

zjkpokpo U

lxtgrPu

α+=∆ −

?AKL+WX36+J++V@AXQOP+@[WMP+@NV@J+++ km/Ω6+a++V@AXQOP+POAXMNPYOP+@NV@J+++ km/Ω6\+AXQPOR+Y@AR+++M[)Q+NRS\P]L+QR+VJ@Y@AOPML+VJLWKLMR+:==+ 2mm WL+XQP[R3

Jd=`=F ad=`=GC)Q+VJ@VPWRO@?+^RMN@JR+WOR?L+ 95,0cos =ϕ +W\PKLAP+ 32,0=ϕtg.O@WLOKL[+SJ@KOPT+YJPKLAO@WNP+A@SPKR+WL+3

%062,0u kpo1kpo =∆ −

9;H;H+5J@YKLJR+VRA@YR+ORV@OR+@A++#5&+A@+8%&9;H;H+5J@YKLJR+VRA@YR+ORV@OR+@A++#5&+A@+8%&9;H;H+5J@YKLJR+VRA@YR+ORV@OR+@A++#5&+A@+8%&9;H;H+5J@YKLJR+VRA@YR+ORV@OR+@A++#5&+A@+8%&

1XQPOR+MRS\@YWM@?+Y@AR+WR+SRMRJOP[+VJ@Y@AOP]P[R+P+57*+PQ@\R]PK@[++AP[LOQPKR+<a>F2mm +@A+#5&+A@+8%&+PQO@WP+9=+[;5@A+VJLNV@WNRYM@[+AR+WX+OR+@YRK+MRS\+VJPM\KX]LOR+:

WNROR+WR+KLAO@YJL[LO@[+WOR?@[W24077P s3j =

5RA+ORV@OR+PQ[LfX+#5&++P+8%&++WL+JR]XOR+V@+PQJRQX

2

)(100

n

jsmrokpo U

lxtgrPu

α+=∆ −

?AKL+WX36+J++V@AXQOP+@[WMP+@NV@J+++ km/Ω6+a++V@AXQOP+POAXMNPYOP+@NV@J+++ km/Ω6\+AXQPOR+Y@AR+++M[)Q+NRS\P]L+QR+VJ@Y@AOPML+VJLWKLMR+>F+ 2mm WL+XQP[R3

Jd>`>H ad=`=C)Q+VJ@VPWRO@?+^RMN@JR+WOR?L+ 95,0cos =ϕ +W\PKLAP+ 32,0=ϕtg.O@WLOKL[+SJ@KOPT+YJPKLAO@WNP+A@SPKR+WL+3

%38,0=∆ −mrokpou

14

9;H;<+5J@YKLJR+VRA@YR+ORV@OR+@A+++8%&+A@+%&9;H;<+5J@YKLJR+VRA@YR+ORV@OR+@A+++8%&+A@+%&9;H;<+5J@YKLJR+VRA@YR+ORV@OR+@A+++8%&+A@+%&9;H;<+5J@YKLJR+VRA@YR+ORV@OR+@A+++8%&+A@+%&

1XQPOR+MRS\@YWM@?+Y@AR+WR+SRMRJOP[+VJ@Y@AOP]P[R+P+57*+PQ@\R]PK@[++AP[LOQPKR+<aF2mm +@A+8%&+A@+%&+PQO@WP+>9[;5@A+VJLNV@WNRYM@[+AR+WX+OR+@YRK+MRS\+VJPM\KX]LO+>+WNRO

WR+KLAO@YJL[LO@[+WOR?@[WP sj 122721 =

5RA+ORV@OR+PQ[LfX++8%&+P+%&+WL+JR]XOR+V@+PQJRQX

2

)(100

n

jsromro U

lxtgrPu

α+=∆ −

?AKL+WX36+J++V@AXQOP+@[WMP+@NV@J+++ km/Ω6+a++V@AXQOP+POAXMNPYOP+@NV@J+++ km/Ω6\+AXQPOR+Y@AR+++M[)Q+NRS\P]L+QR+VJ@Y@AOPML+VJLWKLMR+F+ 2mm WL+XQP[R3

Jd9`CI ad=`>)Q+VJ@VPWRO@?+^RMN@JR+WOR?L+ 95,0cos =ϕ +W\PKLAP+ 32,0=ϕtg.O@WLOKL[+SJ@KOPT+YJPKLAO@WNP+A@SPKR+WL+3

%3,0=∆ −romrou

+ 9;H;<+5J@YKLJR+VRA@YR+ORV@OR+X+WNROX9;H;<+5J@YKLJR+VRA@YR+ORV@OR+X+WNROX9;H;<+5J@YKLJR+VRA@YR+ORV@OR+X+WNROX9;H;<+5J@YKLJR+VRA@YR+ORV@OR+X+WNROX5RA+ORV@OR+QR+[@O@^RQOR+M@\R+WL+JR]XOR+VJL[R+PQJRQX3

2

**100*2

n

i

UlrP

u =∆

DR+NJ@^RQOR+M@\R+WL+JR]XOR+PQ+PQJRQR3

2

**100

n

i

UlrP

u =∆

6 iP +POWNR\PWROR+WOR?R5J@YKLJR+VRAR+ORV@OR++[@QL+WL+PQYLWNP+QR+ORK+OLV@Y@\KOPKP++W\X]RKORKXAR\KLOPKL+XNP]O]L@VNLJL]LOL+WR+5d99==i+M@KX+ORVRKR+Y@A+AXQPOL+9=[+`AP[LOQPKR+:a9`<;

%3,1220

02,0*2,7*2200*100*22 ==∆u

DR+@WYKLN\KLOKL3

%59,0220

02,0*9,11*600*100*22 ==∆u

.MXVRO+VRA+ORV@OR+@A+$2+A@+ORKXAR\KLOPKL?+V@NJ@WR]R+PQO@WP3

proromromrokpokpokpokpokpokpots uuuuuu −−−−−− ∆+∆+∆+∆+∆+∆=∆ 1122

%467,23,13,038,0062,011,0315,0u =+++++=∆ +bQR+XNP]OP]Lc%315,259,03,038,062,011,0315,0u =+++++=∆ +bQR+@WYKLN\KLOKLc

1@QY@\KLOP+VRA+ORV@OR+QR+@WYKLN\KLOKL+KL+:j+`QR+@WNR\@+<j+;1@SPKLOP+VRA@YP+ORV@ORQRA@Y@\KRYRKX+ARNL+QRTNKLYL+KLJ+WX+X+@SR+W\X]RKR+k:j;

15

:;+5J@JR]XO+WNJXKR+MJRNMPT+WV@KLYR+P+VJ@YKLJR+QRWNPNL:;+5J@JR]XO+WNJXKR+MJRNMPT+WV@KLYR+P+VJ@YKLJR+QRWNPNL:;+5J@JR]XO+WNJXKR+MJRNMPT+WV@KLYR+P+VJ@YKLJR+QRWNPNL:;+5J@JR]XO+WNJXKR+MJRNMPT+WV@KLYR+P+VJ@YKLJR+QRWNPNL

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++:;>++++:;>++++:;>++++:;>++++#JRNRM+WV@K+OR+$2#JRNRM+WV@K+OR+$2#JRNRM+WV@K+OR+$2#JRNRM+WV@K+OR+$2

5@ARNR]P+@+NJROW^@J[RN@JX+M@KP+ORVRKR+Q?JRAX+WX3F:=+M7-+l+>=B=;H9+M7BM7+l+ kW5.6PCun = +l+ kW3.1P 0Fe = +l+ %6u k =

%03.1100S

Pu

n

Cunr == +++++++l %91.5uuu 2

r2kx =−

+%LQPWNROWR+NJROW^@J[RN@JR+PQO@WP3

Ω=

= m62.2

US

PR 2

n

n

CunT

%LRMNROWR+NJROW^@J[RN@JR+PQO@WP3

Ω== m15S100

UuXn

2nx

T

)[VLAROWR+MJRNM@?+WV@KR+JR]XOR+WL+VJL[R+PQJRQX3

Ω=+= m2.15XRZ 2T

2T

d

2NJXKR+NJ@V@\O@?+MJRNM@?+WV@KR+WL+JR]XOR+VJL[R+PQJRQX3

dnf

pks3 ZUI =

kA140152.0220I pks3 ==

5@WN@+KL+QR+@WP?XJR]+ A335Io = bNPV+(c+`X+$2`+WNJXKR+VJLMPAR+MJRNM@?+WV@KR

<=+M-m+ kA14I pks3 = QOR]P+AR+@WP?XJR]+QRA@Y@\KRYR+XW\@Y+QR+VJLMPA+MJRNM@?+WV@KR;

:;9:;9:;9:;9++++#JRNRM+WV@K+OR+8%&#JRNRM+WV@K+OR+8%&#JRNRM+WV@K+OR+8%&#JRNRM+WV@K+OR+8%&

%LQPWNROWR+P+JLRMNROWROWR++NJROW^@J[RN@JR+PQO@WL3

Ω= m62.2R T +l++l++l++l+ Ω= m15XT

(X\NR+JLRMNROWR+P+JLQPWNROWR+NJROW^@J[RN@JR+WL+A@SPKX+PQ3

++++ TTO RR = +l++l++l++l+ TTO XX =

1XQPOR+MRS\@YWM@?+Y@AR` 2mm)240300x3( + `+@A+$2+A@+#5&+KL+HC[;

16

%LQPWNROWR+P+JLRMNROWROWR++Y@AR+b$26#5&c+PQO@WL3

Ω= m94.2R 1V +l++l++l++l+ Ω= m871.3X 1V

Ω=⋅⋅+=⋅+= m23.13049.007.0394.2R3RR N1V10V

Ω=⋅= m6,11X3X 1V10V

1XQPOR+MRS\@YWM@?+Y@AR` 2mm)16x5( `+@A+#5&+A@+8%&+KL+9=[;

%LQPWNROWR+P+JLRMNROWROWR++Y@AR+b#5&68%&c+PQO@WL3

Ω= m8.22R 2V +l++l++l++l+ Ω= m8.1X 2V

Ω=⋅= m4.42R86.1R 2V20V +l++l++l++l+ Ω=⋅= m6.30X17X 2V20V

.MXVOL+P[VLAROWL+PQO@WL3d

2Vd1V

dT

d ZZZZ ++=

02V

01V

0T

0 ZZZZ ++=

id ZZ =

Ω=+= m)21j28(Zd

Ω=+= m)31j58(Z0

2NJXKR+KLAO@V@\O@?+MJRNM@?+WV@KR+WL+JR]XOR+V@+PQJRQX3

01

3ZZZ

UI id

nfpks ++

⋅=

AI pks 4880135.02203

1 =⋅=

)Q+APKR?JR[R+b)`Nc+QR+@WP?XJR]+X+#5&bNPV+1+ A60Io = c`WL+YPAP+AR+]L+@WP?XJR]+JLR?@YRNP+QRNdddd=;==9+W+`WN@+KL+[ROKL+@A+VJ@VPWROPT+=;HW;DOR]P+AR+@WP?XJR]+QRA@Y@\KRYR+XW\@YL;

:;:+#JRNRM+WV@K+OR+%&:;:+#JRNRM+WV@K+OR+%&:;:+#JRNRM+WV@K+OR+%&:;:+#JRNRM+WV@K+OR+%&

1XQPOR+MRS\@YWM@?+Y@AR` 2mm)6x5( `+@A+8%&+A@+%&+KL+>9[;

+%LQPWNROWR+P+JLRMNROWROWR++Y@AR+b8%&6%&c+PQO@WL3

Ω= m35R 3V +l++l++l++l+ Ω= m2.1X 3V

17

Ω=⋅=⋅+= m140R4R3RR 3VN3V30V

Ω=⋅= m6.3X3X 3V30V

.MXVOL+P[VLAROWL+PQO@WL3d

3Vd

2Vd1V

dT

d ZZZZZ +++=

03V

02V

01V

0T

0 ZZZZZ +++=

id ZZ =

Ω+= m)22j63(Zd

Ω+= m)34j198(Z0

2NJXKR+KLAO@V@\O@?+MJRNM@?+WV@KR+WL+JR]XOR+V@+PQJRQX3

01

3ZZZ

UI id

nfpks ++

=

AI pks 1980333.02203

1 =⋅=

)Q+APKR?JR[R+b)`Nc+QR+@WP?XJR]+X+8%&bNPV+1+ A25Io = c`WL+YPAP+AR+]L+@WP?XJR]+JLR?@YRNP+QRNd=;==9W+`WN@+KL+[ROKL+@A+VJ@VPWROPT+=;HW;DOR]P+AR+@WP?XJR]+QRA@Y@\KRYR+XW\@YL;

:;H+#JRNRM+WV@K+OR+V@NJ@WR]P[R:;H+#JRNRM+WV@K+OR+V@NJ@WR]P[R:;H+#JRNRM+WV@K+OR+V@NJ@WR]P[R:;H+#JRNRM+WV@K+OR+V@NJ@WR]P[R

5@W[RNJR]L[@+ORKMJPNP]OPKP+W\X]RK`QR+ORKXAR\KLOPKP+V@NJ@WR];

1XQPOR+MRS\@YWM@?+Y@AR` 2)5,13( mmx `ORKXAR\KLOPKL?+V@NJ@WR]R+KL+9=[;

+%LQPWNROWR+P+JLRMNROWROWR++V@NJ@WR]M@?+Y@AR+PQO@WL3

Ω= mRV 2384 +l++l++l++l+ Ω= mX V 34.43

Ω=⋅=⋅+= mRRRR VNVV 95243 4440

Ω=⋅= mXX VV 143 440

.MXVOL+P[VLAROWL+PQO@WL3d

VdV

dV

dV

dT

d ZZZZZZ 4321 ++++=

04

03

02

01

00VVVVT ZZZZZZ ++++=

18

id ZZ =

Ω+= mjZ d )27302(

Ω+= mjZ )48952(0

2NJXKR+KLAO@V@\O@?+MJRNM@?+WV@KR+WL+JR]XOR+V@+PQJRQX3

01

3ZZZ

UI id

nfpks ++

=

AI pks 423558.12203

1 =⋅=

.+%&+WX+X?JRfLOP+RXN@[RNWMP+@WP?XJR]P+NPVR+/;DR+@WP?XJR]+ AI 100 = +PQ+b)`Nc+APKR?JR[R@]PNR[@+YJPKL[L+JLR?@YROKR+Nd=;=9W+WN@+KL+[ROKL+@A+A@QY@\KLOPT+=;HW;DOR]P+AR+@WP?XJR]PQRA@Y@\KRYRKX+XW\@YL+V@+VPNROKX+QRWNPNL;

19

H;25!*),)#-*)0-+8-$!%)0-"-H;25!*),)#-*)0-+8-$!%)0-"-H;25!*),)#-*)0-+8-$!%)0-"-H;25!*),)#-*)0-+8-$!%)0-"-

DR+KLARO+WNRO3DR+KLARO+WNRO3DR+KLARO+WNRO3DR+KLARO+WNRO3++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++M@[;>;JRQY@AOR+NRS\REEEEEEEEEEE;;E+++>9;L\;SJ@KP\@EEEEEEEEEEEEEE;;;+++>:;RXN@[RNWMP+@WP?XJR]P>=-;EEEE;E;;E;;;;;+++:H;RXN@[RNWMP+@WP?XJR]P>F-EEEEEEEE;++><H;[@O@^RQOR+XNP]OP]REEEEEEEEEE;+++>:<;[@O@^RQOR+XNP]OP]R+AXV\RE;EEEEEEE++9F;NJ@^RQOR+XNP]OP]REEEEEEEEEEE;;;+++>G;KLAO@V@\OP+VJLMPAR]EEEEEEEEEE;;+++<I;AY@V@\OP+VJLMPAR]EEEEEEEEEEE;+++<C;VJLMPAR]+QR+MXVRNP\@EEEEEEEEEE;;+++>>=;QRWNPNPOP+XJfRK+AP^LJLO]PKR\OL+QRWNPNLEE;;;E;;++>>>;QY@O]L;EEEEEEEEEEEEEEE;++>>9;NRWNLJ+QY@O]REEEEEEEEEEEEE+++>>:;VJ@Y@AOPM+556g+:a9`<EEEEEEEEE;+9==[>H;VJ@Y@AOPM+556g+:a>`<EEEEEEEEE;++F=[