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QO w OwW|t ?Q[ xR=U sHL OL=w |xv} Ry QO |}=QH= C=}rta sHL TBUx@ xHwD =@ w |R=UxO=U Qw_vtx@ "O};|t CUOx@ Ov@hm CN=U |xv} Ry 'C}=yvuOw@ Z} Qa |iQ] R= w dwO |xv=NOwQ QO xOW=QH= |=yOv@hm =@ pOt |xU}=kt|xOWKqY= |xR=@ '�CU= 10 R= QDnQR@ u=} QH jta x@ ZQa C@Uv� xv=NOwQ<=RH= '2 pmW "CU= xOW ZQi |r}]DUt w Z} Qa 'xv=NOwQ `]kt w s}kDUtpmW QO "OyO|t u=Wv =Q QDU@|rw] p}iwQB QO|m}rwQO}y|L=Q] |xOvyOp}mWDQDU@ |xOWp}OaD `=iDQ= yt 'QDU@ |rO=aD ?}W Se 'QDU@ \UwDt ?}W S0 'QwmPthb 'Ov@hm |xHvB QO |oDUW?; jta ys 'xR=@ Qy QO Ov@hm `=iDQ= yd 'xv=NOwQ'|W}=UQi |xR=@ |ki= |xrY=i Lp '|oDUW?; jta uDiQo Q_vQO =@ Ov@hm `=iDQ=|x} w=R xb w Ov@hm ZQa wb 'Ov@hm G=D ZQa tb '=yOv@hm u}@ |xrY=i LQ@ '2 pmW QO xOWQmP |=yQDt=Q=B OL=w "CU= s�=k |=DU=Q =@ Ov@hm |@v=H xHw|r= 1 \@=wQ T=U=Q@ QwmPt |=yQDt=Q=B u}vJty "Ov=xOW x@U=Lt (m) QDt ?UL

"OvwW|t x@U=Lt 14

n = ytyd

= (S0 � Se) � Lp(S0 � Se) � L = Lp

L(1)

(Se)Sh = (0 056 � (Gs � 1) �D50)10 7

(ns)6 7 (2)

(Se)sch = 0 000293(D50 �Wc

Qf)3 4 (3)

(Se)MPM = 0 058(ns=D901 6)3 2D50df

(4)

df = (qf � nspS0

)0 6 (5)

wb = 2 � hb � tan xb + tb (6)

yg = 0 5 � di � (qfqi

)0 85 (7)

ysHs

= 3( ydHs

)0 6SI�0 19(1� e�0 25 LHs ) (8)

Hs = 1 53sq2f

g(9)

135

"""pQDvm

|=yxR=U

|L=Q]

|R=Uxv

}y@pOt"Ov@hm Q@ OQ=w |=yQ=@ "1 pwOH

fw1 = w � h1 � wb � wc

?; uRw

s�=k

fw2 = 0 5 � w � wc � h2b � tan(xb) � (1 + se � tan(xb))

fw3 = 0 5 � w � wc � hb2 � tan(xb)

fw4 = 0 5 � w � wc � hb � tan(xb) � se � (2 � wb � hb � tan(xb))

fs2 = 0 5 � sat � wc � ys2 � tan(xb) � (1� se � tan(xb)) l =N uRwfs1 = 0 5 � sat � wc � hb2 � tan(xb) � (1 + se � tan(xb))

(fds)v = 0 5 � sub � wc � ys2 � (1� se � tan(xb))2 � kp � sin(atan(se)) |Owta |=yxirwt(fus)v = 0 5 � sub � wc � hb2 � (1 + se � tan(xb))2 � ka � sin(atan(se)) l =N |@v=H Q=Wi

fbed sill = satg � wc � hb � (wb � hb � tan(xb)) Ov@hm uRw

fu = 0 5 � w � wb � wc � (hb + ys + h1 + y + hb � se � tan(xb)� ys � se � tan(xb)) Q=WiQ} R

fdw = 0 5 � w � wc � (2 � (y � yd � ys � se � tan(xb) + hb) � hb � (cos(a tan(se)))2

?; |@v=H Q=Wi

|ki=

fuw = 0 5 � w � wc � (2 � h1 + hb � (1 + se � tan(xb)) � hb�(1 + se � tan(xb)) � (cos(a tan(se)))2

(fds)h = 0 5 � wc � sub � ys2 � (1� se � tan(xb))2 � kp � cos(a tan(se)) Q=Wi |ki= |=yxirwt(fus)h = 0 5 � wc � sub � hb2 � (1 + se � tan(xb))2 � ka � cos(a tan(se)) l =N |@v=H

hb = 1 3 � (yd + yl + yg)

C=L}[wDh1 = ( qf�nsp

Se)0 6

hds = ys = 1 3 � (yg + yl)

sat = s � (1� n) + n � w; satg = s � (1� ng) + ng � w; sub = ( s � w) � (1� n)

Hs = y +q2f

2�g�y2 � (yd + ys � se � tan(xb)) + hb � se � tan(xb); Hs = 1 5 � (q2fg )1 3

XwYNt uRw ( satg) 'l =N jQeDUt XwYNt uRw ( sub) "O};|t CUOx@Ot=H XwYNt uRw w �ng� uw}@=o |mwB |xHQO T=U=Q@ xm |vw}@=o Ov@hm `=@W=

"OwW|t x@U=Lt l =NSs = tan��fv

�fh

Sr = �mr

�mo(15)

S:T: :

Ss � 1 3Sr � 1 3 (16)

xm OyO|t MQ |t=ovy �Sr� |vwoS=w p@=kt QO |Q=O}=B '15 |x]@=Q j@=]tQO o |x]kv� Ov@hm |xHvB x@ C@Uv (�mr) sw=kt |=yQovr wtHt C@Uvx]kv u=ty x@ C@Uv (�mo) xOvvmuwoS=w |=yQovr wtHt Q@=Q@ 1 3 '�3 pmW

|W=v s�=k |wQ}v �fs2� 'Ov@hm CUOq=@ QO l =N uRw R= |W=v s�=k |wQ}v'Ov@hm uRw R= |W=v s�=k |wQ}v �fbed sill� 'Ov@hm CUOu}}=B QO l =N uRw R=�fdw� 'Ov@hm CUOq=@ QO ?; |@v=H Q=Wi �fuw� 'Q=WiQ} R |wQ}v �fu�QO l =N lQLt |@v=H Q=Wi �fus� 'Ov@hm CUOu}}=B QO ?; |@v=H Q=Wi�h1� 'Ov@hm CUOu}}=B QO l =N sw=kt |@v=H Q=Wi �fds� 'Ov@hm CUOq=@�hds� w Ov@hm CUOu}}=B QO ?; `=iDQ= (y) 'Ov@hm CUOq=@ QO ?; `=iDQ=CN=U Kr=Yt 'QwmPt pOtQ} R QO "CU= Ov@hm CUOu}}=B QO l =N `=iDQ=xOW ZQi `=@W= w xOv@UJQ}e 'xv=NOwQ QDU@ Kr=Yt w `=@W= '|vw}@=o Ov@hm

"CU=w kp 'QwmPt pwOH QO "CU= xOW x�=Q= 1 pwOH QO Ov@hm Q@ OQ=w |=yQ=@|x} w=R x@ xHwD =@ xm OvDUy l =N lQLt w sw=kt |@v=H Q=Wi ?}=Q[ ?}DQDx@ ka|oOv@UJ R= Q_vhQY =@ w \@DQt |=ypwOH R= w ��� l =N |rN=O l =m]Y=`=@W= XwYNt uRw ( sat) '?; XwYNt uRw ( w) [20]"Ov};|tCUOx@ l =N( s) l =N Ot=H XwYNt uRw w (n)l =N |mwB |xHQO T=U=Q@ xm l =N

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yt R= "CU= xOW xO=iDU= hrDNt |=yxv}tR QO xiOyOvJ |R=Uxv}y@ p�=Ut R= xDUO|vD@t xiOyOvJ |R=Uxv}y@ |=yVwQ u=wD|t =yu; u} QDjiwt w u} QDhwQat xrtHxOW ?@U |U=U= swyit l} QwmPt |=yVwQ QO "OQ@ s=v =Q 8wDQ=B |R=Uxv}y@ Q@w CU= uOw@xQ}J swyit xm Ovm =O}B CUO xv}y@ MU=B x@ Ov=wD@ sD} Qwor= =D CU=R= x ?=wH x=oQy 'CU= ?r=e y ?=wH Q@ x ?=wH %OwW|t u=}@ CQwY u}= x@R= |m} QO smCUO x ?=wH w OW=@v QDO@ y ?=wH R= hOy `@=wD R= l}I}y O}OwDQ=B swyit R= xO=iDU= =@ 'Q[=L |xar=]t QO [23]"OW=@ QDy@ y ?=wH R= hOy `@=wDhOy `@=D l} x@ hOy `@=D wO 'O@=}|t X=YDN= hOy `@=wD x@ xm |vRw ?}=Q[ w?=wH xawtHt '|R=Uxv}y@ |xr�Ut pL w |vRw ?}=Q[ Q}}eD =@ w Ov=xOW p}O@D

"CU= xOt; CUOx@ wDQ=B

G}=Dv p}rLD w |O=yvW}B pOt OQ@ Q=m "3xar=]t OQwt |xk]vt |iQat "1"3

4 pmW j@=]t xm CU= OwQu=oQo xv=NOwQ |=yxN=W R= wUQO=t =} dwO |xv=NOwQ=@ Qwri xwm R= w OQ=O u=} QH �xrqm QyW jQW� CWOwv}t u=DUQyW RmQt p=tW R=OQ}o|t xtWJQU CWOwv}t u=DUQyW jQW |QDtwr}m 20 QO `k=w QDt 1632 `=iDQ=QDU@ ?}W 'QDtwr}m 50 xv=NOwQ pw] "OR} Q|t OwQu=oQo |xv=NOwQ x@ C}=yvQO w"CU= �1 u; QDU@ \UwDt ?}W w �0 6 |}xorH QDU@ ?}W '�2 u; |v=DUywmp=U R= w CU= |r}tmD wv R= x=QovD QO dwO |xv=NOwQ |QDtwQO}y x=oDU}=%R= CQ=@a QwmPt x=oDU}= |}=}i=QeH C=YDNt u}vJty "Ovm|t |Q=OQ@ Q=t; 1345`@ QtQDtwr}m 1791 CL=Ut w QDt 330 `=iDQ= '370270 ZQa '550440 pw]?=NDv= QDt 866 pw] x@ |}xR=@ pOt '|HvU=w CyH Q[=L VywSB QO [24]"CU=|vw}@=o 'QwmPt |xR=@ QO xOWE=OL= |=yOv@hm xm CU= QmP x@ sRq "CU= xOW

"CU=

pOt |HvU=w "2"3|m}vmDw�S w |m}rwQO}y C=aq]= R= xO=iDU= =@ Ov@hm |R=Uxv}y@ pOt |HvU=w|=y?=wH xawtHt Qo}O CQ=@a x@ =} wDQ=B |xy@H "OW s=Hv= '2 pwOH QO OwHwt

"u; QO dwO |xv=NOwQ w OwQu=oQo R} Q@; |x[wL C}akwt "4 pmW

wtHt C@Uv xm OyO|t MQ |t=ovy �Ss� VRer Q@=Q@ QO |Q=O}=B u}vJty "OW=@|=ywQ}v wtHt x@ l =N |rN=O l =m]Y= |x} w=R Cv=Sv=D QO (�fv)s�=k |=ywQ}v

[21]"OW=@ 1 3 R= QDnQR@ (�fh) |ki=

|R=Uxv}y@ pOt "3"2"CU= xR=U E=OL= |xv} Ry |R=Uxv}tm '=yxR=U |L=Q] QO ?wr]t h=Oy= R= |m}x@ 1"2 VN@ QO xm '|m}rwQO}y \@=w[ R= xO=iDU= =@ xv} Ry `@=D 'Q[=L VywSB QO(Wb = tb; xb = 0) u; pw] QO Ov@hm O=a@= uOQmZQi C@=F =@ w 'OW xQ=W= u;17 |x]@=Q ?r=k QO |L=Q] Q}eDt u=wvax@ =yOv@hm u}@ xrY=i uDiQo Q_vQO =@ w

%OwW|t h} QaD

Cost(x) =nXi=1

n(UPRC)b(Vi +m1V 0i +m2V 00i ) (17)

|=ysHL ?}DQD x@ V 00i 'V 0i 'Vi 'xR=U sHL OL=w |xv} Ry (UPRCb) 'u; QO xmw |Q=OQ@l =N |xv} Ry p}O@D ?}=Q[m2 wm1 w |R} Ql =N w |Q=OQ@l =N 'xR=Uxv}W}@ 'xv} Ry |R=Uxv}tm Q@ xwqa [22]"OvDUy xR=U E=OL= |xv} Ry x@ |R} Ql =N|Qw]x@ "CU= |L=Q] Qo}O hOy R}v u; Q@ OQ=w |=yQ=@ CLD xR=U |Q=O}=B uDN=Uxv}tm u=R}t x@ xR=U |@=QN R= |W=v |r=tDL= |=yxv} Ry 'xOWQmP hOy u}t-=D =@ xmVN@ QO xm Ov@hm Q@ OQ=w |=yQ=@ p}rLD R= |Q=O}=B `@=D 'Q[=L VywSB QO "OUQ|t18 |x]@=Q j@=]t l =N |Q@ Q=@ C}iQ_ uOw@|i=m ZQi =@ w OW x@U=Lt �2"2�

%O};|t CUOx@Stability(x) = tan��fv

�fh+ �mr

�mo(18)

ZQa w =yxR=U u}@ |xrY=i '?}W pQDvm |=yxR=U QO xm CU= QmP x@ sRqO=OaD '|oDUW?; jta %Q}_v '|L=Q] |=yQDt=Q=B Qo}O QO =Q QF= u} QDW}@ xR=UQO wQ u}= R= "OvQ=O xR=U |xv} Ry w VRer w |vwoS=w Q@=Q@ QO xR=U |Q=O}=B '=yxR=U|=yQ}eDt u=wvax@ =yxR=U u}@ |xrY=i w xR=U ZQa QDt=Q=B wO 'Q[=L |xar=]t

"Ov=xOW xDiQo Q_v QO |L=Q]hOy `@=D "1"3"2

x@ 'Ovm|t wHwCUH =Q |L=Q] |=yQ}eDt |xv}y@ Q}O=kt 'Ov@hm |R=Uxv}y@ pOt|xv} Ry |R=Uxv}tm � xOWxDU=wN h=Oy= x@ xHwD =@ =Q |HwQN u} QDy@ xm |}xvwoQ=Qk sy Q=vm =@ u}=Q@=v@ "OQ=O xr�Ut |=yO}k w �Ov@hm |Q=O}=B |R=Uxv}W}@ w E=OL=19 |x]@=Q j@=]t |R=Uxv}y@ hOy `@=D '3"2 VN@ R= xOt; CUOx@ `@=D wO uDiQo

%OwW|t u=}@

Minimze :W� � nP

i=1n(UPRC)b(m1Vi +m2Vi +m3Vi)

Costmax

+W� � (1=( tan��fv�fh

+ �mr

�mo))

S:T: :

Ss � 1 3; Sr � 1 3; yd � yt; L�Wb � 15 �Hs;0 07 � yd

Hs� 1 87 (19)

w OvDUy hOy `@=wD x@ xDi=}X=YDN= |vRw ?}=Q[ W� w W� 'u; QO xmu}= pL |=Q@ |irDNt |=ysD} Qwor= 'Q}N= p=U OvJ QO "CU= 1 Q@=Q@ u=W wtHt

137

"""pQDvm

|=yxR=U

|L=Q]

|R=Uxv

}y@pOt=yu; E=OL= |xv} Ry w |Q=O}=B QO =yOv@hm u}@xrY=i QF= |UQQ@ "1"2"3

Q@=Q@ m xm |Dr=L QO 20 |x]@=Q R= xO=iDU= =@ pOt QO =yxR=U u}@ xv}y@ |xrY=i%CU= xOt; CUOx@ 'CU= 1

m� L�Wb � 15�Hs (20)

�0 5 |vRw ?} Q[ QO xv} Ry |xv}W}@� 0 5 R= xrY=i ?} Q[ m ?} Q[ xJv=vJxR=U |xv}y@ O=a@= 'OwW xO=O pOt x@ �0 5 |vRw ?} Q[ QO xv} Ry |xv}tm � 2 5 =D'0 5 =D 1 R=m?} Q[ Vy=m =@ '6 pmW j@=]t "OwW|t pY=L 5 pwOH j@=]tE=OL= |xv} Ry 'xR=U `=iDQ=V}=Ri= p}rO x@ =t= 'O@=}|tVy=m =yxR=U O=OaD xJ Qo ="OwW|t |O=YDk=Q}e KQ] xH}Dv QO w O@=}|t Vy=m xR=U |Q=O}=B w V}=Ri= u;O@=}|t Vy=m =yxR=U u}@ |xrY=i '2 5 =D 1 R= m ?} Q[ V}=Ri= =@ |iQ] R=u; CUOu}}=B QO |a[wt |oDUW?; jta R= 'xR=U `=iDQ= Vy=m x@ xHwD =@ w"O@=}|t Vy=m u; E=OL= |xv} Ry w V}=Ri= xR=U |Q=O}=B u}=Q@=v@ "OwW|t xDU=m|oDUW?; |rO=aD \}=QW =Q} R 'OwW|tv pY=L ?wr]t \}=QW R}v Cr=L u}= QOw OyO|t MQ 'CU= |v=QL@ XwYNt |SQv= Q@=Q@ 15 xm |}xrY=i QO |a[wt

"dwO |xv=NOwQ |=Q@ pOt R= pY=L |wDQ=B |vLvt "5 pmW

j@=]t hOy `@=wD R= l} Qy �1 =D 0� |vRw VRQ= Q}}eD =@ |R=Uxv}y@ pOt ?wret=v"Ot; CUOx@ 3 pwOH

sy p@=kt QO �|Q=O}=B |xv}W}@ w xv} Ry |xv}tm � hOy `@=D wO Q}O=kt sUQ =@xv}y@ |=yMU=B "Ow@ Oy=wN 5 Q=Owtv pmW x@ �wDQ=B� ?wret=v |=y?=wH xawtHt'u; j@=]t xm CU= xOW xO=O u=Wv 5 pmW QO 0 5 w 1 '0 |vRw ?}=Q[ <=R= x@|=Q@ 0|vRw?} Q[ 'OW=@ xv} Ry |xv}tm =@ xR=U E=OL=|L=Q] R= hOy xm|t=ovyE=OL= hOy '|Q=O}=B `@=D QO 1 |vRw ?} Q[ p=ta= =@ w OwW|t Qw_vt |Q=O}=B `@=D?} Q[ x@ xHwD =@ w 1 =D 0 |vRw?}=Q[ QO "OwW|t jkLt |Q=O}=B |xv}W}@ =@ xR=UO=a@= "O};|t CUOx@ xR=U |Q=O}=B w xv} Ry 'hOy `@=wD x@ xDi=}X=YDN= |vRw"CU= xOW x�=Q= 4 pwOH QO =QH= QO =yu; |L=Q] G}=Dv w dwO xv=NOwQ |=yOv@hmhOy `@=D wO uDiQo Q_vQO =@ xm CU= u; |=} wo 4 w 3 |=ypwOH |xU}=kt|=yxv} Ro x@ |@=}CUO Q@ xwqa '�hOy `@=D wO |R=Uxv}W}@ w xv} Ry |R=Uxv}tm �"Ot; Oy=wN CUOx@ QDW}@ |Q=O}=B w QDtm |xv} Ry =@ |=yOv@hm '|L=Q] hrDNt

"pOt |HvU=w CyH R=}vOQwt C=aq]= "2 pwOHdwO |xv=NOwQ |m}rwQO}y C=aq]= dwO |xv=NOwQ |m}vmDw�S C=aq]=

Lp(km) 866 ng 0 3Wc(m) 70 sat(kg=m3) 2133S0 0 0117 satg(kg=m3) 2155

Q100(m3=s) 613 s(kg=m3) 2650D50(mm) 18 w(kg=m3) 1000D84(mm) 38 sub(kg=m3) 1133D16(mm) 9 �0 40

n 0 195 ns 0 035

"pOt |HvU=w R= pY=L G}=Dv "3 pwOHCost(unit) Stability L(m) Wb(m) hb(m) ys(m) yd(m) w�

8972 991 7 290 59 126 21 4 912 2 868 0 67 08683 271 7 283 56 969 20 738 4 814 2 793 0 645 0 16810 492 6 331 52 950 16 719 4 658 2 673 0 600 0 24977 524 5 259 48 789 12 558 4 491 2 545 0 552 0 33927 045 4 539 46 280 10 049 4 388 2 465 0 524 0 43218 326 3 977 44 528 8 297 4 315 2 409 0 504 0 52681 110 3 486 43 164 6 933 4 257 2 364 0 489 0 62230 673 3 009 41 993 5 762 4 206 2 326 0 476 0 71917 979 2 631 41 166 4 935 4 171 2 298 0 466 0 81917 979 2 631 41 166 4 935 4 171 2 298 0 466 0 91917 979 2 631 41 166 4 935 4 171 2 298 0 466 1

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yt

"Ov@hm E=OL= |xv} Ry QO |rO=aD ?}W QF= "7 pmW

"Ov@hm |Q=O}=B QO |rO=aD ?}W QF= "8 pmW

"|rw] ?}W Q}}eD =@ Ov@hm `=iDQ= w xrY=i Q}}eD "9 pmW

V}=Ri= w xv} Ry Vy=m =@ xR=U E=OL= u}=Q@=v@ &CU= R=}v QDtm `=iDQ= =@ |=yxR=U w"Ow@ Oy=wN x=Qty |Q=O}=B

pOt |HvUC}U=UL "3"3w E=OL= |xv} Ry OQw;Q@ QO pkDUt |=yQ}eDt Q}F-=D u=wD|t =Q |vwvm VN@ R= hOyQO w �50 =D |@O w |rw] ?}W Q}}eD =@ |HvUC}U=UL "OQm u=wva xR=U |Q=O}=B

"CU= xOW s=Hv= 0 5 |vRw ?} Q[|rw] ?}W "1"3"3

|rO=aD ?}W <=R= x@ w |rw] ?}W Q}}eD =@ =yu; `=iDQ= w =yOv@hm u}@ xrY=i Q}}eDEa=@ ?}W V}=Ri= 'pOt G}=Dv j@=]t "CU= xOW xO=O u=Wv 9 pmW QO C@=Fu}= R= "OwW|t |rO=aD ?}W x@ uO}UQ |=Q@ xDi=}V}=UQi C=@ wUQ sHL V}=Ri=

"=yu; E=OL= |xv} Ry w |Q=O}=B QO =yOv@hm u}@ xrY=i QF= "6 pmW"=QH= QO xR=U |L=Q] G}=Dv w =QH= QO Ov@hm O=a@= "4 pwOH

Wb(m) yd(m) yl(m) L(m)

8 2 5 56 173Stability = 2 65; Cost(unit) = 6300

"m ?} Q[ C=Q}}eD =@ xR=U |xv}y@ O=a@= C=Q}}eD "5 pwOHm yd(m) Wb(m) L(m)

0 5 1 003 8 075 88 6110 6 0 837 8 098 73 8820 7 0 718 8 133 63 3760 8 0 629 8 176 55 5090 9 0 559 8 230 49 4011 0 504 8 297 44 528

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