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A=>2=0 ?>E81:0 28<V@N20;L=>3> :>;0 ( <>65 1CB8 7=0G=> <5=H>N V 7C<>2;5=0 2 >A=>2=><C AB01V;L=VABN 9 B>G=VABN =0?@C38 682;5==O (B B0 5;5<5=BV2 28<V@N20;L=>3> :>;0 (:. $>@<C;C 4;O @>7@0EC=:C >A=>2=>W ?>E81:8 " <>6=0 ?>40B8 C 283;O4V  EMBED Equation.3 . 09206;82VHV E0@0:B5@8AB8:8 "  GCB;82VABL, >A=>2=0 ?>E81:0, =0?@C30 682;5==O, >?V@. !?>A>18 22V<:=5==O " "5=7><5B@8G=V ?5@5B2>@N20GV 2<8:0NBLAO 70 <>AB>2>N AE5<>N 2 >4=5, 420 01> G>B8@8 ?;5G0. @8 FL><C 2 420 ?@>B8;56=8E ?;5G0 2<8:0NBLAO ?5@5B2>@N20GV, I> @503CNBL =0 >4=C 9 BC 6 A0<C 45D>@<0FVN (=0?@8:;04, @>7<VI5=V ?>@CG), 0 2 420 V=H8E ?;5G0  BV, I> @503CNBL =0 BC 6 A0<C 45D>@<0FVN, 0;5 ?@>B8;56=>3> 7=0:0 (=0?@8:;04, @>7<VI5=V 7 V=H>3> 1>:C ?;0AB8=8, I> 738=0TBLAO). VAB 7 42><0, G>B8@<0 " <0T GCB;82VABL 2V4?>2V4=> C 2 V 4 @078 1V;LHC, =V6 <VAB 7 >4=8< ". ;O :><?5=A0FVW B5<?5@0BC@=>W ?>E81:8 " 28:>@8AB>2CNBL, =0?@8:;04, B0:89 A?>AV1. 20 >4=0:>28E ?5@5B2>@N20GV @>7<VICNBL =0 <VAFV 28<V@N20==O (>48=  =0 45B0;V, I> 45D>@<CTBLAO, 4@C389  =0 45B0;V, O:0 =5 707=0T 45D>@<0FVW) V 2<8:0NBL WE O: 420 AC<V6=V ?;5G0 <>AB>2>W AE5<8. ">4V ?@8@>AB8 >?>@V2 " 70 @0EC=>: B5<?5@0BC@8 >4=0:>2V 2 >1>E ?;5G0E <>ABC V =5 2?;820NBL =0 @57C;LB0B 28<V@N20==O. >AB>2C AE5<C 22V<:=5==O " 7>1@065=> =0 @8A. 13. 7 G>B8@L>E 2V4V1@0=8E B5=7>?5@5B2>@N20GV2 C ?;5GV r1 B0 r3 2<8:0NBLAO ?5@5B2>@N20GV 7 =091V;LH8< >?>@><. ">4V 70 4>?><>3>N 7<V==>3> @578AB>@0, O:89 22V<:=5=> 2 ?;5G5 r4, V O:89 <0T >?V@ >4=>3> ?>@O4:C 7 @>7:84>< 7=0G5=L ?5@5B2>@N20GV2 r1, r2, r3 B0 r4, <>6=0 2AB0=>28B8 <VAB C AB0= @V2=>2038 70 2V4ACB=>ABV 45D>@<0FVW. 0 =0O2=>ABV 45D>@<0FVW =0 28E>4V C @568<V E>;>AB>3> E>4C 1C45 =0?@C30  EMBED Equation.3 .  EMBED Visio.Drawing.11  8A. 13. >AB>20 AE5<0 22V<:=5==O B5=7>?5@5B2>@N20GV2 # @07V >4=>3> 0:B82=>3> ", C2V<:=5=>3> 2 ?;5G5 r1,  EMBED Equation.3  V  EMBED Equation.3   EMBED Equation.3 . # @07V 42>E 0:B82=8E ", 22V<:=5=8E 2 ?;5GV r1 V r3,  EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 . # @07V G>B8@L>E 0:B82=8E " r1=r3=r41 B0 r2=r4=r42 (O:I> =0:;5NT<> 420 " 73>@8, 0 420 V=H8E " 7=87C V 15@5<> 2 =8E ?@8@VAB 4>268=8 7 @V7=8<8 7=0:0<8)  EMBED Equation.3 . @8:;04 @>7@0EC=:C " ?V@ =020=B065==O r==3000<; :V;L:VABL " C AE5<V <>ABC  1; 1070 l1=20<<; H8@8=0 b=10<<; " :;5WBLAO =0 <5B0;; ?8B><0 4>?CAB8<0 ?;>I0 ?>25@E=V >E>;>465==O (4>?=2(102<<2/B. >B@V1=> @>7@0EC20B8 ". >72'O70==O 818@0T<> 4@VB 7 :>=AB0=B0=C. V0<5B@ 4@>BC d=0,025<<. 8B><89 >?V@ <0B5@V0;C 4@>BC (=0,45(10-3<(<<. 1G8A;8<> :@>: t(2d=0,05<<. 815@5<> t=0,07<<. 87=0G8<> G8A;> ?5B5;L " 70 D>@<C;>N 2W  1=b/t=10/0,07=143, 72V4:8 W=72. =0945<> 28EV4=89 2=CB@VH=V9 >?V@ r <>ABC 70 D>@<C;>N r=r0+r? 27O2H8 4> C2038, I>  EMBED Equation.3 ,  EMBED Equation.3 , 45  EMBED Equation.3 . ">4V r=r0+r?=2890<. >7@0E>20=5 7=0G5==O r<r==3000<, B>1B> @>7@0EC=>: 28:>=0=> =5 70 >?B8<0;L=8< 20@V0=B><, 0;5 1;87L:8< 4> =L>3>. 0?@C30 =0 2E>4V "  EMBED Equation.3 . >BC6=VABL, A?>6820=0 2 ",  EMBED Equation.3 B. >7@0EC=>: T<=VA=>3> ?5@5B2>@N20G0 ! ! [2], AB>@.99-100. A=>2=V AE5<8 22V<:=5==O  ;O ?5@5B2>@5==O 7<V=8 T<=>ABV C 2V4?>2V4=V 7<V=8 A8;8 AB@C<C, =0?@C38 01> G0AB>B8 =09G0ABVH5 70AB>A>2CNBL <>AB>2C AE5<C 2<8:0==O . >AB>2C AE5<C 22V<:=5==O 7>1@065=> =0 @8A. 14. 0 A5@54=L>3> ?>;>65==O @CE><>W ?;0AB8=8, :>;8 !12=!13, B>1B> ?@8@VAB (=0, <VAB 710;0=A>20=89 V =0?@C30 =0 9>3> 28E>4V 4>@V2=NT =C;N.  EMBED Visio.Drawing.11  8A. 14. >AB>20 AE5<0 22V<:=5==O  ?V@  7 T<=VABN !=100?$=100(10-12$ =0 ?@><8A;>2V9 G0AB>BV f=50F 287=0G0TBLAO O:  EMBED Equation.3 <. "0:5 25;8:5 7=0G5==O >?>@C  28:;NG0T <>6;82VABL 9>3> ?@0:B8G=>3> 70AB>AC20==O 4;O 28<V@N20;L=8E FV;59 G5@57 A8;L=89 2?;82 ?0@078B=8E ?0@0<5B@V2 (28BV:0==O B>I>). >BC6=VABL, I> A?>6820TBLAO ?@8 FL><C ,  EMBED Equation.3 B. 45 U  =0?@C30 682;5==O, 27OB0 B0:>N, I> 4>@V2=NT 100. 5;8G8=0 72>@>B=>3> 2?;82C  287=0G0TBLAO A8;>N 5;5:B@>AB0B8G=>3> ?@8BO30==O <V6 ?;0AB8=0<8,  01> =,  EMBED Equation.3 , 45 W5  5=5@3VO 5;5:B@>AB0B8G=>3> ?>;O, 6; (  707>@, <; !  T<=VABL, $; U0  =0?@C30 465@5;0 682;5==O, . @8 !, (=const Fe=U2/2(C/(. @8:;04 @>7@0EC=:C  >B@V1=> @>7@0EC20B8  70 B0:8E 40=8E: G0AB>B0 465@5;0 682;5==O f=4000F; =0?@C30 465@5;0 682;5==O U=115; ?;>I0 ?>25@E=V ?;0AB8=8 S=20(10-4<2; 2V4AB0=L <V6 ?;0AB8=0<8 (=0,5(10-3<; A5@54>28I5 <V6 >1:;04:0<8   20:CC<. >72'O70==O 1. 87=0G8<> T<=VABL:  EMBED Equation.3 , 45 (  4V5;5:B@8G=0 ?@>=8:=VABL 20:CC<C;  EMBED Equation.3 $/< ">4V  EMBED Equation.3 ?$. 2. =0945<> :CB>2C G0AB>BC =0?@C38 682;5==O:  EMBED Equation.3 A-1. 3. 1G8A;8<> 0:B82=89 >?V@, I> 70157?5GCT <0:A8<0;L=C GCB;82VABL AE5<8:  EMBED Equation.3 <. 4. 87=0G8<> ?>BC6=VABL, I> @>7AVNTBLAO =0 0:B82=><C >?>@V:  EMBED Equation.3 B. 5. 1G8A;8<> A8;C 72>@>B=>3> 2?;82C:  EMBED Equation.3 . >7@0EC=>: ?'T7>5;5:B@8G=>3> ?5@5B2>@N20G0 ! ! [2], AB>@.140-141. V;L:VABL 5;5:B@8:8, I> 28=8:;0 =0 ?;>I8=0E ?;0AB8=8 ?@8 ?@8:;045==V >4=>@V4=>W @>7BO3CNG>W (AB8A:0NG>W) A8;8, 7=0E>4OBL 70 B0:8E C<>2. !8;0 F =0?@02;5=0 274>26 5;5:B@8G=>W >AV:  EMBED Equation.3 (5.1)!8;0 Fx =0?@02;5=0 274>26 <5E0=VG=>W >AV:  EMBED Equation.3 (5.2)45 Q  5;5:B@8G=89 70@O4, ;; Fx, Fy  A8;8, I> 4VNBL ?5@?5=48:C;O@=> 4> >?B8G=>W >AV ?;0AB8=8, ; Sx, Sy  ?;>IV ?>25@E>=L, ?5@?5=48:C;O@=8E 4> 2V4?>2V4=8E >A59; k1  ?'T7>5;5:B@8G=0 AB0;0 (4;O :20@FC 2,14(10-12 ;/).  ?'T7>5;5:B@8G=8E ?@8;040E 728G09=> 28<V@NNBL =5 70@O4 Q, 0 =0?@C3C U, O:0 @>72820TBLAO =0 T<=>ABV, I> CB2>@5=0 >1:;04:0<8 ?;0AB8=8:  EMBED Equation.3 (5.4)45 !  2;0A=0 T<=VABL ?'T7>?;0AB8=8;  EMBED Equation.3 (5.5)(=(k(0, 45 (k =3,5  4V5;5:B@8G=0 AB0;0 4;O :20@FC; Sx, d  2V4?>2V4=> ?;>I0 B0 B>2I8=0-?>25@E=V ?;0AB8=8; (0  4V5;5:B@8G=0 AB0;0 20:CC<C (8,85(10-12 $/<). V4AB0282H8 2 D>@<C;C (5.4) 7=0G5==O ! V Q (7 D>@<C; (5.1) V (5.5)), 4VAB0=5<> 7=0G5==O =0?@C38, O:0 28=8:0T 2 ?;0AB8=V 2 <><5=B ?@8:;045==O A8;8:  EMBED Equation.3 (5.6) @50;L=8E C<>20E ?5@5B2>@N20G 2<8:0NBL 2 A?5FV0;L=V 28<V@N20;L=V AE5<8, 0 B><C ?0@0;5;L=> 9>3> 2;0A=V9 T<=>ABV ! 1C4CBL 22V<:=5=V T<=>ABV, =0?@8:;04, 2EV4=>3> :>;0 ?V4A8;N20G0 !2E, 7 T4=C20;L=>3> :015;N !:.  FL><C @07V =0?@C30, O:C @>72820T ?5@5B2>@N20G, 7<5=H8BLAO V 73V4=> 7 D>@<C;>N (8.4) AB0=>28B8<5  EMBED Equation.3 (5.7) (5.7) 28?;820T: I>1 >B@8<0B8 <0:A8<0;L=C =0?@C3C V =091V;LHC GCB;82VABL, A;V4 ?@03=CB8 4> B>3>, I>1 :>6=0 7 A:;04>28E AC<0@=>W T<=>ABV 1C;0 O:><>30 <5=H>N. A=>2=0 B@C4=VABL ?@8 28<V@N20==V =0?@C38  WW 157?5@5@2=89 A?04 C G0AV G5@57 28BV:0==O 70@O4C 7 ?;0AB8=. >73;O=5<> F5 O28I5, 4>A;V482H8 ?@8=F8?>2C AE5<C ?'T7>5;5:B@8G=>3> ?@8;04C 4;O 28<V@N20==O A8; (@8A. 15, 0). '5@57 5;5:B@>48, 70@O465=V 2V4 T<=8< 70@O4><, 3@0=V 7'T4=CNBLAO 7 ?V4A8;N20G5<. <=VABL !( <V6 G0AB8=>N ?5@5B2>@N20G0, I> =5A5 70@O4, V 75<;5N <VAB8BL B0:V A:;04>2V:  T<=VABL <V6 3@0=O<8 :20@F>2>W ?;0AB8=8 !;  T<=VABL 7'T4=C20;L=>3> :015;N !:;  2EV4=0 T<=VABL ?V4A8;N20G0 !2E.  8A. 15. @8=F8?>20 (0) B0 5:2V20;5=B=0 (1) AE5<8 ?'T7>5;5:B@8G=>3> ?@8;04C 4;O 28<V@N20==O A8;8 ?V@ R( A:;040TBLAO 7 B0:8E :><?>=5=BV2:  ?>25@E=5289 B0 >1'T<=89 >?>@8 :20@FC R;  >?V@ V7>;OFVW 7'T4=C20;L=>3> :015;N R:;  2EV4=89 >?V@ ?V4A8;N20G0 R2E. 07=0G5=C AE5<C <>6=0 725AB8 4> 5:2V20;5=B=>W AE5<8 (@8A. 15, 1), I> A:;040TBLAO 7 :>=45=A0B>@0 !(, @>7@O4 O:>3> G5@57 >?V@ R( <>6=0 @>73;O40B8 O: 28BV: 70@O4C ?;0AB8=8 ?'T7>?5@5B2>@N20G0. @8:;04 8.1. 87=0G8B8 =0?@C3C <V6 >1:;04:0<8 :20@F>2>3> ?'T7>5;5:B@8G=>3> ?5@5B2>@N20G0, O:I> 4VT A8;0 F=1 :3A=9,81 , ?;>I0 ?;0AB8=8 Sx=5 A<2=5(10-4 <2, 0 WW B>2I8=0 d=0,5 A<=0,005 <. >72'O70==O. <=VABL ?'T7>5;5:B@8G=>3> ?5@5B2>@N20G0  EMBED Equation.3  5>1EV4=0 =0?@C30  EMBED Equation.3  @>B5 FO =0?@C30 =5 <>65 1CB8 157?>A5@54=L> 28<V@O=0 ?@8;04><, O:89 A?>6820T ?>BC6=VABL, >A:V;L:8 2V= @>7@O460B8<5 ?'T7>5;5<5=B =02VBL 2 ?@>F5AV AB2>@5==O 70@O4V2. "><C =0?@C30, I> 7=V<0TBLAO 7 ?'T7>?5@5B2>@N20G0, 728G09=> ?>40TBLAO =0 A?5FV0;L=C 5;5:B@>==C ;0<?C 7 <0;>N 2EV4=>N T<=VABN V =04728G09=> 25;8:8< 2EV4=8< >?>@><. @8=F8?>2C AE5<C B0:>3> ?V4:;NG5==O ?>:070=> =0 @8A. 16. V AE5<8 10G8<>, I> ?0@0;5;L=> ?;0AB8=V ?'T7>?5@5B2>@N20G0 ?@8T4=0=> T<=VABL 28<V@N20;L=>W AE5<8 !AE, O:0 A:;040TBLAO 7 T<=>ABV 7 T4=C20;L=>3> 4@>BC (2V4=>A=> 7075<;5=>W AE5<8) V 2EV4=>W T<=>ABV ?V4A8;N20G0.  2@0EC20==O< HC=BCNG>3> 2?;82C T<=>ABV !AE =0?@C30, O:0 7=V<0TBLAO 7 ?'T7>?5@5B2>@N20G0, 1C45 4>@V2=N20B8  EMBED Equation.3 (5.11) EMBED Visio.Drawing.11  8A. 16. 'T4=0==O ?'T7>?5@5B2>@N20G0 7 2E>4>< ?V4A8;N20G0 @8:;04 8.2. 87=0G8B8 =0?@C3C, I> 7=V<0TBLAO 7 ?'T7>?5@5B2>@N20G0, 70 40=8<8, =02545=8<8 2 ?@8:;04V 8.1, O:I> T<=VABL AE5<8 !AE = 4(10-12 $. >72'O70==O.  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