�1394

R}}=B�'h

}QWu=Qt

a|UOvyt

103�9

3"X

'3/1|

xQ=tW'

31�2

|xQwO

Ori

gina

lArt

icleOw@y@ |=Q@ O=yvW}B |x�=Q= w |}xU}=kt |UQQ@

|}xRQr |Q}PB?}U; `} QU |@=} RQ= CkO|}=v@ |=yu=tDN=U

�Q=}Wv=O� �Qis=vy@ O=yQi�OWQ= T=vWQ� � u=}rky=W pwUQ

u=yiY= |DavY x=oWv=O 'u=Qta |UOvyt |xOmWv=O

R= |O=} R O=OaD |=Q@ ,qwtat 'OvDUy hwQat R}v `} QU |@=} RQ= x@ xm '|i}m |=y|@=} RQ=|Qw;`tH =yVwQ u}= QO |O=} R C=aq]= O}=@ xm =Hv; R= "OvwW|t h} QaD =yu=tDN=U

p}tmD O}=@ |UQQ@ OQwt |=yu=tDN=U |=Q@ xm CU= |}=yCU}rlJ w =ysQi x@ R=}v 'OwWpw=ODt |=yha[ w |}=v@ |=yu=tDN=U |xOQDUo sHL x@ xHwD =@ Q=DWwv u}= QO "OwW

hrDNt VwQ wO "OvQ}o|t Q=Qk |UQQ@ OQwt =yu=tDN=U wv u}= '=yu; QO OwHwtw `} QU |@=} RQ= |=Q@ QwWm |R} Qxt=vQ@ w C} Q}Ot u=tR=U 376 |x} QWv w FEMA154

w xO=iDU= 376 |x} QWv Q@ O}m -=D =@ TQ=Ot |}=v@ |=yu=tDN=U |O=} R O=OaD |r}YiDu}@ |@U=vt |ovy=ty xm CU= xO=O u=Wv G}=Dv "CU= xOW p}rLD w x} RHD l} Qy u=mQ=|}=yO=yvW}B u}vJty "OQ=O OwHw 376 |x} QWv QO |r}YiD w `} QU |=y|@=} RQ= G}=Dv

x@ xm 'CU= xOW x�=Q= 376 |x} QWv QO `} QU |@=} RQ= |U=U= |x]@=Q KqY= |=Q@"CU= xO}t=Hv= FEMA154 w 376 |x} QWv wO G}=Dv u}@ |rt=m Cy@=Wt

farhad@cc.iut.ac.irrasol.shahgholian@yahoo.com

'FEMA356 'FEMA154 '|}=v@ u=tDN=U '`} QU |@=} RQ= %|O}rm u=oS=w"376 |x} QWv

xtOkt "1VwQ R= xO=iDU= =@ |Qo}O QoWywSB [5]"CU= xOW x�=Q= R=wy= QyW QO u; OQ@ Q=m R=|=yu=tDN=U '=yu=tDN=U `=wv= x@ u; s}taD w |}=v@ |=yu=tDN=U |=Q@ =} Q; |@=} RQ=|v=tDN=U xwQo Qy |Q}PB?}U; u=R}t w xO=O Q=Qk `} QU |@=} RQ= OQwt =Q u} wRk QyWu} QD|t}Ok QwWm R= GQ=N QO [6]"CU= xOQm XNWt QyW u}= hrDNt j]=vt QO =Q|=ypOt xm |v=tR 'OOQo|t Q@ |Oq}t O=Diy |xyO p�=w= x@ xv}tR u}= QO =yC}r=ai|=Q@ VywSB u}rw= "CU= xOW O=yvW}B =yu=tDN=U Q=DiQ |}=U=vW CyH |]NQ}eu}}aD |=Q@ =yu=tDN=U `} QU |@=} RQ= "Ow@ 1972 p=U QO |}xRQr CQ=UN OQw;Q@QWDvt 1988 p=U QO Q=@ u}rw= FEMA154 VQ=Ro u=wva =@ |}xRQr |Q}PB?}U;u=tDN=U u=UOvyt |=Q@ xO=U w xOQDUo |xO=iDU= |=Q@ ptar=QwDUO u}= "CU= xOWOQwt 2002 p=U QO x} QWv u}= "Ow@ xOW x}yD xO}OVRwt; XYNDtQ}e O=Qi= =D|rw@k p@=k G}=Dv CUv=wD u; O}OH V}=Q} w xm |}xvwo x@ 'CiQo Q=Qk OOHt |@=} RQ=

[3]"Ovm =O}B =yu=tDN=U `=wv= |=Q@ |QDW}@ OQ@ Q=m C}r@=k w x�=Q= =QR= |yHwD p@=k O=OaD OQwt QO xm CU= xOW xOy=Wt Q}N= C=}@ QHD T=U=Q@s=Hv= R= TB 'Ov=xDiQo Q=Qk |R=Usw=kt |r}YiD C=ar=]t OQwt xm |}=yu=tDN=U|}xR=U CqmWt OwHw Cra x@ CU= xOW XNWt |Q}PB?}U; p}rLD |xrLQtR}v OQ=wt R= |Q=}U@ QO "CU}v xiQY x@ Q_vOQwt u=tDN=U |R=Usw=kt 'OOaDtxOW |R=Uy@ KQ] |=QH= QO |DqmWt O=H}= Ea=@ |}=QH= `v=wt p}@k R= |r�=Ut

[1]'�360 |x} QWv� OwHwt |=yu=tDN=U |}xRQr |R=Uy@ ptar=QwDUO Q=WDv= =@QwWm QO 1381 p=U R= |OH Qw] x@ OwHwt |=yu=tDN=U |R=Usw=kt C=ar=]txO=iDU= =yu=tDN=U |r}YiD w `t=H |@=} RQ= |=Q@ x} QWv u}= R= "CU= xOW wQWQ=}DN= QO xv}tR u}= QO |OvtWRQ= C=}@ QHD 'p=U 9 CWPo R= TB RwQt= w OwW|t|=yu=tDN=U|}xRQr |R=Uy@ptar=QwDUO 'u; R=TB "CU= xDiQo Q=Qk QwWm u=UOvytxm &CU= xOW QWDvt 1386 p=U QO [2]'�376 |x} QWv� OwHwt KrUtQ}e |}=v@x�=Q= |}=v@ |=yu=tDN=U |r}YiD R}v w `} QU |@=} RQ= |=Q@ l}miD x@ =Q |]@=w[|=yQwWm w =m} Qt; QO [3]'FEMA154 |x} QWv xm CU= |r=L QO u}= "CU= xOQm"CiQo|t Q=Qk xO=iDU= OQwt =yu=tDN=U `} QU |@=} RQ= |=Q@ p@k |=yp=U R= Qo}O|=yp=U QO =yu=tDN=U |}xRQr OQmrta |UQQ@ |=Q@ `} QU |@=} RQ= |=yVwQ OQ@ Q=mp=U QO |WywSB QO 'u=Q}= QO xrtH R= "CU= xOw@ |OOaDt C=ar=]t w[wt Q}N=|Ov@s}UkD\rDNt w KrUtQ}e|}=v@ '|vD@ '|Oqwi |xDUO 4 x@ =yu=tDN=U 1997'|r}YiD |=ysQi p}tmD w |v}a |=yO}OR=@ R= xO=iDU= =@ s=Om Qy |=Q@ w Ov=xOW|=Q@ |rOt |x�=Q= x@ |Qo}O VywSB QO u}vJty [4]"Ov=xOW |UQQ@ |}xRQr OQmrta|}xvwtv w xDN=OQB u=Q}= hrDNt j]=vt QO =yu=tDN=U |}xRQr |Q}PB?}U; |@=} RQ=

pw�Ut xOvU} wv �"1392 10 9 VQ}PB '1392 8 12 x}LqY= '1392 5 27 Ci=} QO %M} Q=D

"""Ow@y@

|=Q@O=yv

W}B|x�

=Q=w|}x

U}=kt|

UQQ@x@ |Q}PB?}U; C=Qtv w |}=v@ |=yu=tDN=U `} QU |@=} RQ= |=yXN=W "1 pwOH

[2]"376 |x} QWv VwQ

CQ=UN ?} Q[ QDt=Q=B C}a[w =} Q=Okt Q_vOQwt QDt=Q=B h}OQ(Li)

1 0 � � � 15(�) u}tR ?}W 11 1 15 � � � 30

1 2 � > 301 I

l =N wv 21 05 II

1 1 III

1 15 IV

5 ?U=vt |B 320 ?U=vt=v15 s}=k w |ki= hqm =@

|}xR=U Q=w}O 425 |ki= hqm =@35 hqm uwO@5 KrUt uD@ p=O

hkU 515 lwr@ xJQ}D20 |@ Q[ j=D25 |@ wJ Q}D0 2800 OQ=Ov=DU= =@ j@=]D |oOt=W}B 610 2800 OQ=Ov=DU= =@ j@=]D sOa0 uQ=kDt u=tDN=U uqB 710 uQ=kDt=v1 2800 OQ=Ov=DU= =@ j@=]D =ywWR=@ 8

1 2 2800 OQ=Ov=DU= =@ j@=]D sOa1 xk@] l}

C=k@] O=OaD 91 1 xk@] wO1 2 QDW}@ w xk@] xU1 ?wN

Kr=Yt C}i}m 101 2 \UwDt1 3 O@

|NQ@ QO "OwW|t u}}aD u=tDN=U |rm R=}Dt= 'u=tDN=U u; |=y|oS} w x@ \w@ Qt=[a= u}= C}a[w |=Q@ |YN=W "CU= xOW xHwD |}xR=UQ}e <=RH= x@ R}v =ysQiR=}Dt= '|}xR=UQ}e w |}xR=U |=yR=}Dt= ?}mQD =@ C}=yv QO xm 'OwW|t pY=L R}vw |Ov@xk@] |=Q@ xOt;CUOx@ R=}Dt= u}= "OwW|t u}}aD X=N u=tDN=U u; |}xRQr|}xk]vt |=Q@ =Q =ysQi u}= R= |}xvwtv '1 pmW "CU= ?U=vt u=tDN=U |Ov@xOQ

"OyO|t u=Wv O=} R |xrRrR Q]N u=R}t =@

|Q}PB?}U; C=ar=]t s=Hv= hQY |O=} R Q=}U@ |xv} Ry xmCU=|r=L QO u}= "CU=|@=} RQ= VwQ l} R= xO=iDU= "CU= xOW |R=Uy@ KQ] |x}yD u}vJty w |}xRQr=Q |R=Usw=kt u=mt= w VRQ= QDx=Dwm u=tR QO pw@k p@=k CkO =@ xm '`} QU w |D=tOktpwkat=v |=yxv} Ry R= |Q=}U@ Ov=wD|t 'Ovm uWwQ xar=]t OQwt |=yu=tDN=U |=Q@|@=} RQ= l} |xH}Dv R= u=v}t]= ?Um OvtR=}v Qt= u}= "OyO Vy=m =Q |R=Usw=kt

"CU= `} QUj@] xv=o =OH Qw] x@ |ak=w |}=v@ |=yu=tDN=U R= |O=} R O=OaD 'Q=DWwv u}= QOR= |@NDvt O=OaD "Ov=xDiQo Q=Qk `} QU |@=} RQ= OQwt 376 |x} QWv w FEMA154Q=Qk |r}YiD |@=} RQ= OQwt FEMA356 w 376 |x} QWv j@] R}v =yu=tDN=U u}=p=wQ KqY= |=Q@ |O=yvW}B 'pY=L G}=Dv p}rLD w x} RHD w xU}=kt =@ "Ov=xOW xO=Ow u; G}=Dv u}@ |rt=m Cy@=Wt xm 'CU= xOW x�=Q= 376 |x} QWv QO `} QU |@=} RQ=

"Ovm|t Q=QkQ@ FEMA154 G}=Dv

|}=v@ |=yu=tDN=U `} QU |@=} RQ= |=yVwQ "2376 |x} QWv QO `} QU |@=} RQ= VwQ "1"2

R= l} Qy C}i}m 'u; hrDNt <=RH= |UQQ@ w u=tDN=U R= O}OR=@ =@ 'VwQ u}= QO|Q}PB?}U; u=R}t QO |rm XN=W 10 '\=@DQ= u}= QO "OwW|t XNWt =RH= u}=C=YNWtCW=OQ@ w u=tDN=U R= O}OR=@ R=TB "OwW|t xDiQo Q_v QO QF-wt 'u=tDN=Ux@ |Q=Okt 'VwQ u}= |=yQDt=Q=B R= l} Qy x@ \w@ Qt pwOH R= 'u; |=y|oS} w wXN=W '1 |x]@=Q j@] Q}O=kt u}= ?}mQD R= "OwW|t xO=O C@Uv XN=W u;

%O};|t CUOx@ (LR) u=tDN=U Qy |Q}PB?}U;LR = 0 45� [L3 + L4 + L5 + L6 + L7]

�L1 � L2 � L8 � L9 � L10 � (7 5A� 1) � 100 (1)

1 pwOH j@] xv=o 10 |=yXN=W R=l} Qy Q=OktLi (i = 1; :::; 10) 'u; QO xmOQwt |xk]vt |=Q@ 2800 OQ=Ov=DU= \UwD xOWx�=Q= KQ] |=v@t ?=DW C@Uv A w

"CU= u=tDN=U |Q}PB?}U; XN=W LR w xar=]tKQW u}= x@ 1 |x]@=Q R= xO=iDU= =@ 'u=tDN=U |Q}PB?}U; |rm C}a[w

%OwW|t XNWt&�25 > LR %sm |Q}PB?}U; �

&�50 > LR � �25 %\UwDt |Q}PB?}U; �&�75 > LR � �50 %O=} R |Q}PB?}U; �"�75 � LR %u=tDN=U VR} QwQi p=tDL= �

FEMA154 |x} QWv QO |tWJ `} QU |@=} RQ= "2"2xk]vt 3 |=Q@|YwYNt |=ysQiltm =@ FEMA154 |x} QWv QO `} QU|@=} RQ=%Q}_v |rt=wa x@ QwmPt |=ysQi QO "OwW|t s=Hv= O=} R w \UwDt 'sm |R}NxRQr =@w u=tDN=U wv w A}D 'pLt l =N \}=QW 'u=tDN=U x=oCN=U QO xrRrR Q]N u=R}txOW xHwD u=tDN=UC}ty= w `=iDQ= w uqB QO OwHwt |=y|t_vt=v `=wv= 'u; |xR=Uxm 'CU= xOW xDiQo Q_v QO u=tDN=U Qy |=Q@ |R=}Dt= 'u=tDN=U wv T=U=Q@ "CU=|LqY= R=}Dt= u=tDN=U |oS} w Qy x@ |rw=OH ltm =@ TBU "OQ=O s=v x}=B R=}Dt=|LqY= |=yR=}Dt= w x}=B R=}Dt= `tH R= "OwW|t xO=O|ivt =}C@Ft |OOa CQwYx@

94

u=}rky=W

pwUQw

Qis=vy@

O=yQi

"FEMA154 j@] u=tDN=U l} |=Q@ |tWJ `} QU |@=} RQ= sQi R= |}xvwtv "1 pmW

95

"""Ow@y@

|=Q@O=yv

W}B|x�

=Q=w|}x

U}=kt|

UQQ@

'|@ Q[ j=D hkU �=yu=tDN=U pm �47� u=tDN=U 33 %=yu=tDN=U hkU �G|@ wJ Q}D hkU ��13� u=tDN=U 10 'lwr@ xJQ}D hkU ��37� u=tDN=U 26

"OvDW=O KrUt uD@ p=O hkU 'Qo}O OQwt 2 w��56� Qo}O u=tDN=U 40 w uQ=kDt=v uqB ��44� u=tDN=U 31 %u=tDN=U uqB �I

"OvDW=O uQ=kDt uqBxm OvDW=O |}=ywWR=@ ��87� xUQOt 62 %=yu=tDN=U QO OwHwt |=ywWR=@ �K|}=ywWR=@ ��13� u=tDN=U 9 w OvOQm|tv xOQw;Q@ =Q 2800 OQ=Ov=DU= \@=w[

"OvOw@ xOQm u}t-=D =Q 2800 OQ=Ov=DU= \@=w[ xm OvDW=O��20� u=tDN=U 14 'xk@] 1 ��78� u=tDN=U 56 %=yu=tDN=U C=k@] O=OaD �M

"CW=O OwHw R}v xk@] 3 u=tDN=U l} w xk@] 2xUQOt 19 '\UwDt C}i}m =@ |Lr=Yt ��66� u=tDN=U 46 %Kr=Yt C}i}m �O?wN C}i}m =@ |Lr=Yt Qo}O |xUQOt 6 w h}a[ C}i}m =@ |Lr=Yt ��27�

"OvDW=O'O=} R |R}NxrRrR Q]N =@ |k]=vt QO ��44� u=tDN=U 31 %KQ] |=v@t ?=DW �PQo}O u=tDN=U 5 w \UwDt |R}NxrRrR Q]N =@ |k]=vt QO ��47� u=tDN=U 35

"OvDW=O Q=Qk sm |R}NxrRrR Q]N =@ |k]=vt QO|=yu=tDN=U QO xOWQmP|=yQDt=Q=B R=l} Qy x@?U=vt Q}O=ktX=YDN= R= Oa@"CU= xOt; CUOx@ u=tDN=U Qy |rm |Q}PB?}U; '1 pwOH j@] |UQQ@ OQwt|x} QWv j@] |UQQ@ OQwt |=yu=tDN=U |Q}PB?}U; |@=} RQ= |xH}Dv |xYqN

"CU= xOW xO=O u=Wv 2 pmW QO 376

376 |x} QWv \UwD `} QU |@=} RQ= G}=Dv p}rLD w x} RHD "2"4|xH}Dv QO '1 |x]@=Q |xOvyOp}mWD pt=wa R= l} Qy |vRw Q}F-=D VN@ u}= QOl} Qy |vRw Q}F-=D "CU= xOW x@U=Lt |UQQ@ OQwt |=yu=tDN=U |Q}PB?}U; u}}aD

%OwW|t u}}aD 7 |r= 2 \@=wQ CQwYx@ u; Q=Okt QO 1 |x]@=Q <=RH= R=

LR = 0 45L0R (2)

L0R = L1 L2 L3�7 L8 L9 L10(7 5A� 1) (3)

L3�7 = L3 +L4 +L5 +L6 +L7 (4)

"376 |x} QWv j@] |}=v@ u=tDN=U 71 |Q}PB?}U; u=R}t "2 pmW

"OwW s=Hv= 1xv} Ry � OwU R}r=v; O}=@ 'pw@k p@=k R=}Dt= |xv}tm |x@U=Lt |=Q@|@=QN |q=@ O=OaD uDiQ}PB |xOvyOu=Wv '|rw@k |xQtv u=wvax@ u}}=B R=}Dt= u}}aDuDiQoQ_vQO =@ 'Qo}O |wU R= w CU= |R=Uy@ QDtm |=yxv} Ry s=Hv= w xrRrR R= TBR=}Dt= xJv=vJ "O@=}|t Vy=m CQ=UN u=R}t w V}=Ri= |R=Uy@ |=yxv} Ry 'q=@ OOaQDj}kO |@=} RQ= x@ |R=}v xR=U 'OW=@ QDW}@ pw@k p@=k R=}Dt= |xv}tm R= u=tDN=U |rmQ=Qk j}kO |@=} RQ= OQwt O}=@ CQwY u}= Q}e QO 'OQ=Ov |}xRQr u=wD |UQQ@ CyH|=Q@ C=}[Qi u}= 'FEMA154 VwQ x@ |i}m |@=} RQ= R= xO=iDU= s=ovy QO "OQ}o

%OwW|t Q=}DN= |@=QN u=R}t u}}aD Qw_vtx@ u=tDN=U Qy |Q}PB?}U; wv u}}aDOwHwx@ |}xR=U |=[a= QO ?}U;� sm |Q}PB?}U; %3 � u=tDN=U R=}Dt= ��

&�CU= |WwBsWJ p@=k |}xR=UQ}e |=[a= QO w O};|tv|}xR=U |=[a= QO ?}U;� \UwDt |Q}PB?}U; %2 � u=tDN=U R=}Dt= < 3 ��

&�\UwDt |}xR=UQ}e |=[a= QO w |WwBsWJ p@=k|}xR=U |=[a= QO ?}U;� O=} R |Q}PB?}U; %1 � u=tDN=U R=}Dt= < 2 ��

&�O=} R |}xR=U Q}e |=[a= QO w \UwDt|}xR=U |=[a= QO?}U;� O=} R|r}N |Q}PB?}U; %0 � u=tDN=U R=}Dt=< 1 ��

"�O=} R |r}N |}xR=UQ}e |=[a= QO w O=} R

xar=]t OQwt |=yu=tDN=U |iQat "3|}=yQyW QO xm 'OvOw@ xUQOt u=tDN=U 71 xar=]t u}= QO|UQQ@ OQwt |=yu=tDN=Uu=tDN=U Qy |=Q@ `} QU |i}m |@=} RQ= sQi uOQmQ)B =@ "OvDW=O Q=Qk u=DURwN u=DU= R=Qy |Q}PB?}U; u=R}t 'FEMA154 j@] Q=@ l} w 376 |x} QWv j@] Q=@ l}|UQQ@ u}= G}=Dv "CU= xOW XNWt QwmPt |x} QWv wO R= l} Qy j@] u=tDN=U

"CU= xOW x�=Q= Oa@ VN@ QO

xar=]t OQwt |=yu=tDN=U `} QU |@=} RQ= "4376 |x} QWv j@] `} QU |@=} RQ= "1"4

376 |x} QWv j@] =yu=tDN=U u}= |Q}PB?}U; QO QF-wt |=yXN=W |=y|oS} w%CU= CQwY u}= x@

?}W =@ |k]=vt QO =yu=tDN=U u}= pm xm CU= xOW xOy=Wt %u}tR ?}W �hr="OvOw@ xOW `k=w (0 � � � 15) sm

w III wv l =N |wQ =yu=tDN=U pm �96 pO=at u=tDN=U 68 %l =N wv �?"OvOw@ `k=w II wv l =N |wQ Qo}O u=tDN=U 3

u=tDN=U 4 w?U=vt|B �=yu=tDN=U pm �94� u=tDN=U 67 %=yu=tDN=U|B �A"OvOw@ sm ZQa =@ =} |v=mrB |va} 'OvDW=O ?U=vt=v |B Qo}O

xUQOt 11 '=yvD |ki= hqm �=yu=tDN=U pm �61� u=tDN=U 43 %=yQ=w}O wv �C=} u=tDN=U 17� =yu=tDN=U |x}k@ w s�=k w |ki= hqm �=yu=tDN=U �16�

"OvDW=O s�=k hqm xv w |ki= hqm xv '��23=@ �=yu=tDN=U pm �55� u=tDN=U 40 |oOt=W}B %=yu=tDN=U |oOt=W}B �Eu}= \@=w[ =@ Qo}O u=tDN=U 31 w CW=O Ck@=]t 2800 OQ=Ov=DU= \@=w[

"OvOw@ Q=oR=U=v OQ=Ov=DU=

96

u=}rky=W

pwUQw

Qis=vy@

O=yQi "376 |x} QWv j@] |UQQ@ OQwt u=tDN=U 71 |=Q@ |Q}PB?}U; |xR=@ Qy QO |Q}PB?}U; u=R}t QO QDt=Q=B Qy CmQ=Wt OYQO "2 pwOH

75 � LR 75 > LR � 50 50 > LR � 25 25 > LR |Q}PB?}U; QDt=Q=B37 3 33 8 39 1 49 0 |}xR=U Q=w}O21 3 26 8 27 3 33 1 hkU10 7 7 3 7 0 0 0 u=tDN=U uqB10 7 7 3 7 3 0 0 |oOt=W}B5 3 9 9 8 3 9 8 |B5 1 4 6 4 2 2 9 Kr=Yt C}i}m4 3 4 2 0 7 0 0 |R}NxRQr |xk]vt3 5 3 7 3 4 2 9 =ywWR=@1 8 2 0 2 1 2 1 l =N wv0 0 0 4 0 7 0 20 C=k@] O=OaD0 0 0 0 0 0 0 0 u}tR ?}W

j@] |Q}PB?}U; `=wv= QO |UQQ@ OQwt |=yu=tDN=U |=Q@ |}=yv R=}Dt= "3 pmW"FEMA154

R=}Dt= 'u=tDN=U Qy |=Q@ QwmPt |=yXN=W R= l} Qy uOWXNWt R= Oa@R= |LqY= |=yR=}Dt= uOQm xi=[= =} w QUm R= '|Q}PB?}U; |xOwOLt Qy QO |}=yv|Q}PB?}U; |xOwOLt Qy QO =y u=tDN=U|}=yv R=}Dt= "CU= xOt;CUOx@ =v@t R=}Dt=

"CU= xOW XNWt 3 pmW j@=]t

|:tm |@=} RQ= w |r}rLD |R=UpOt "5p}rLD w |R=UpOt R= CU= sRq `} QU |i}m |@=} RQ= G}=Dv CkO u=R}t |UQQ@ |=Q@xOW|UQQ@ |=yu=tDN=U R= |O=OaDCtUku}= QO "OwW xO=iDU= �|:tm|@=} RQ=�j}kO|aU =yu=tDN=U u}= ?=NDv= QO "Ov=xDiQo Q=Qk |tm |@=} RQ= OQwt u}W}B pL=Qt QOpt=wa w OW=@ xDW=O OwHw |}=yxvwtv Q}PB?}U; |=yu=tDN=U `=wv= R= CU= xOWR= xm xvwou; "OvW=@ xDW=O Qo}Oty =@ |}=yCw=iD R}v =yu; QO |Q}PB?}U; -=Wvt|Q}PB?}U; QO Q=PoQ}F-=D|vRw |=yXN=W u} QDsyt 'OWXNWt sy|i}m|@=} RQ=wtHt QO xm OvOw@ u=tDN=UhkU w|}xR=U |=yQ=w}OC}a[w '|}=v@ |=yu=tDN=Uj@] "OvO=O|t X=YDN= OwN x@ =Q u=tDN=U Qy |Q}PB?}U; u=R}t �70 R= V}@\w@ Qt =yu; uOw@v =} uOw@ Q=Ohqm x@ ,=DOta =yQ=w}O |Q}PB?}U; '376 |x} QWv

"OwW|txOW C}=aQ OQwt u}= QO wvD '|:tm |@=} RQ= |=Q@ =yu=tDN=U ?=NDv= QO u}=Q@=v@xJQ}D '|@ Q[ j=D hkU =@ |}=yu=tDN=U 'hkU sDU}U Q_v R= u}vJty "CU=

Ln(L0R) = Ln(L1) + Ln (L2) + Ln(L3�7) + Ln(L8)

+Ln(L9) + Ln(L10) + Ln(7 5A� 1) (5)

ai =Ln (Li)Ln(L0R)

; for i = 1; 2; 3� 7; 8; 9; 10 (6)

ai = LiL3�7

� Ln(L3�7)Ln(L0R)

; for i = 3; 4; 5; 6; 7 (7)

|rm |Q}PB?}U; QO \w@ Qt |Q}PB?}U; QDt=Q=B CmQ=Wt OYQO ai '=yu; QO xmOQwt u=tDN=U 71 |=Q@ =Q QDt=Q=B Qy CmQ=Wt OYQO '2 pwOH [7]"CU= u=tDN=U

"OyO|t u=Wv 376 |x} QWv j@] xar=]t|Q}PB?}U;u=R}t|x@U=Lt s=ovy QO 'OwW|t xOy=Wt2pwOHQO xm Qw]u=ty=OD@= |Q}PB?}U;Crau} QDsyt 'xar=]t OQwt |=yu=tDN=U |=Q@ 376 |x} QWvj@]'|t_vt=v� uqB pmW Ovv=t |rt=wa TBU w =yhkU w |}xR=U |=yQ=w}O C}a[w

"CU= xOw@ =y|B C}a[w w �|oOt=W}B

FEMA154 T=U=Q@ `} QU |@=} RQ= G}=Dv "3"4FEMA154j@]QwmPt|=yu=tDN=U|Q}PB?}U;QO QF-wt|=yXN=W|=y|oS} w

%CU= CQwY u}= x@u=tDN=U 31 '4 6 |=v@t R=}Dt= �=yu=tDN=U pm �7� u=tDN=U 5 %=v@t R=}Dt= �hr="OvDW=O 1 8 |=v@t R=}Dt= ��52� Qo}O u=tDN=U 35 w 3 4 |=v@t R=}Dt= ��44�40 w �=yu=tDN=U pm �44� s_vt=v uqB u=tDN=U 31 %u=tDN=U uqB �?

"OvDW=O ��56� s_vt uqB u=tDN=U"CW=Ov OwHw C=k@] O=OaD u}= =@ |v=tDN=U %xk@] 7 =D 4 u}@ |=y u=tDN=U �A"CW=Ov OwHw C=k@] O=OaD u}= =@ |v=tDN=U %xk@] 7 R= V}@ |=yu=tDN=U �C|v=tDN=U '|UQQ@ OQwt |=yu=tDN=U u}@ %u=tDN=U `=iDQ= QO |t]vt=v �E

"CW=Ov OwHw `=iDQ= QO s_vt=vu}= CN=U |=Q@ |}xt=vu}}; I}y R= CU= xOW ZQi %|r@k |=yxt=vu}}; �G

"CU= xOWv xO=iDU= =yu=tDN=U"OQ=Ov j=OYt =yu=tDN=U u}= |=Q@ %=v@t |xt=vu}}; �I

3 w E wv l =N |wQ =yu=tDN=U pm �96 pO=at u=tDN=U 68 %l =N wv �K"OvOw@ `k=w D wv l =N |wQ Qo}O u=tDN=U

97

"""Ow@y@

|=Q@O=yv

W}B|x�

=Q=w|}x

U}=kt|

UQQ@"|:tm |@=} RQ= |=Q@ xOW?=NDv= |=yu=tDN=U "3 pwOH

XN=W |xQ=tWXN=W |=v@t ?=DW C}i}m O=OaD =ywWR=@ wv |oOt=W}B hkU Q=w}O wv wv ?}W u=tDN=U|Q}PB?}U; KQ] Kr=Yt C=k@] uqB |}xR=U |B l =N u}tR77 0 30 O@ 1 j@=]D sOa uQ=kDt =v j@=]D sOa |@ Q[ j=D |ki= hqm ?U=vt 3 sm 162 0 30 \UwDt 1 j@=]D sOa uQ=kDt j@=]D lwr@ xJQ}D hqm uwO@ ?U=vt 3 sm 260 0 25 \UwDt 1 j@=]D sOa uQ=kDt =v j@=]D sOa |@ Q[ j=D |ki= hqm ?U=vt 3 sm 358 0 30 \UwDt 1 j@=]D sOa uQ=kDt =v j@=]D sOa |@ Q[ j=D hqm uwO@ ?U=vt 3 sm 458 0 30 \UwDt 1 j@=]D sOa uQ=kDt =v j@=]D sOa lwr@ xJQ}D |ki= hqm ?U=vt 3 sm 5

53 5 0 30 \UwDt 1 j@=]D sOa uQ=kDt =v j@=]D sOa |@ Q[ j=D hqm uwO@ ?U=vt 3 sm 645 0 25 \UwDt 2 j@=]D sOa uQ=kDt =v j@=]D lwr@ xJQ}D |ki= hqm ?U=vt 3 sm 745 0 30 \UwDt 1 j@=]D sOa uQ=kDt j@=]D sOa |@ Q[ j=D |Owta w |ki= hqm ?U=vt 3 sm 844 0 25 \UwDt 1 j@=]D sOa uQ=kDt j@=]D sOa |@ Q[ j=D hqm uwO@ ?U=vt 3 sm 941 0 25 \UwDt 2 j@=]D sOa uQ=kDt j@=]D sOa lwr@ xJQ}D |Owta w |ki= hqm ?U=vt 3 sm 10

40 5 0 25 \UwDt 1 j@=]D uQ=kDt j@=]D sOa |@ Q[ j=D |ki= hqm ?U=vt 3 sm 1138 0 25 \UwDt 1 j@=]D sOa uQ=kDt =v j@=]D sOa lwr@ xJQ}D |ki= hqm ?U=vt 3 sm 1218 0 25 \UwDt 1 j@=]D sOa uQ=kDt j@=]D sOa p=O |ki= hqm ?U=vt 3 sm 13

"SAP 2000 Q=Ri=sQv QO xOWpOt |@ Q[ j=D hkU R= |}xvwtv "4 pmW

QDt|Dv=U 15 Q@=Q@ hkU Ct=N[ 'KrUt uD@ p=O hkU =@ |=yu=tDN=U QOQDt|Dv=U 30� 30 |vD@ Q}D CQwYx@ |ki= hqm '=yQ=w}O |t=tD pLt QO w CU=|QDt|Dv=U 150�150 u=tr= 4 x@ |Q=vm |=yQ=w}O pw] QOhkU "CU= xDiQo Q=Qk'510 daN/cm2 |@ Q[ j=D |=yhkU QO '=yhkU |xOQt Q=@ "CU= xOW s}UkDQ_v QO 560 daN/cm2 KrUt uD@ p=O hkU w 630 daN/cm2 lwr@ xJQ}DdaN/cm2 s=@ |wQ QO w 200 daN/cm2 C=k@] QO xOvR Q=@ "CU= xOW xDiQoCUOx@ 8 |x]@=Q R= hkU Qy Q@ OQ=w |@v=H |wQ}v "CU= xOW xDiQo Q_v QO 150

[2]%O};|t

Fi = wihinPj=1

WjhjC1 SaW (8)

Sa = A(1 +S) w x}=B R=QD R= xk@] hkU `=iDQ= hi 'xk@] Qy uRw wi 'u; QO xm2800 OQ=Ov=DU= j@] |R}NxRQr QDt=Q=B w KQ] |=v@t ?=DW ?}DQD x@ S w A xm

"CU=|x]@=Q R= wCU= sDU}U |a=HDQ=Q}e |=yu=mtQ}}eD |=Q@ K}LYD?} Q[ C1

[1]%O};|t CUOx@ 9C1 = 1 + TS �T

2TS �0 2 (9)

CUOx@ T = 0 05H3 4 |x]@=Q R= w CU= xR=U |rY= ?w=vD u=tR T 'u; QO xmh}] QO C@=F ?=DW w C@=F CaQU |x}L=v wO u}@ lQDWt ?w=vD u=tR Ts "O};|t

|=yu=tDN=U 'xOWQmP OQ=wt x@ xHwD =@ "Ov=xOW ?=NDv= KrUt uD@ p=O w lwr@x@ |R=UpOt |=Q@ "Ov=xOW XNWt 3 pwOH QO |:tm |@=} RQ= |=Q@ |UQQ@ OQwt|rw 'CU= xOW pOt pt=m C=}�RH =@ u=tDN=U |=yhkU '|:tm |@=} RQ= Qw_vt|ki= |=yQvi CQwYx@ =yQ=w}O 'pOt Qy OL R= V}@ uOWnQR@ R= R}yQB Qw_vt x@xOW QmP |Oa@ |=yOv@ QO Qt= C=}�RH "Ov=xOW pOt =yhkU CmQL |xOvvmOwOLt

"CU=

=yhkU |R=UpOt "1"5R= xO=iDU= =@ SAP2000 Ver.11.0.8 Q=Ri=sQv QO |Oa)@ wO CQwYx@ =yhkU'|@ Q[ j=D hkU =@ |=yu=tDN=U QO "Ov=xOW |R=UpOt |]N OwOLt <=RH=R= =yxJQ}D u}@ w xOW pOt OwN pLt QO 'OvDUy IPE wv R= xm hkU |=yxJQ}D

"CU= QDt|Dv=U 11 Q@=Q@ u; Ct=N[ xm 'CU= xOW xO=iDU= xDUwB u=tr=daN/cm2 Q@=Q@ xOWs=Hv= |=yV}=tR; R= xDUwB u=tr= |a=HDQ= ?} Q[

"CU= 0 25 |w=Ut u; uwU=wB ?} Q[ w 22000daN/cm2 Q@=Q@?}DQD x@hkU |}=v@Kr=Yt|}=yv |WWm w|Q=Wi |=yVvD1550 daN/cm3 hkU Kr=Yt |tHL uRw [2]"CU= 0 7 daN/cm2 w 40"OyO|t u=Wv =Q xOWpOt |@ Q[ j=D hkU xvwtv l} '4 pmW "CU= xOW ZQi|xDUwB lJwm |=yu=tr= O=a@= "CU= xOW s}UkD u=tr= 2 x@ OwN pw] QO xJQ}D QypLt� QDnQR@ |=yu=tr= w QDt|Dv=U 150�80 �|OwQw |=ywQy=Q pLt QO� hkU|xOvyOu=Wv =yp}rLD G}=Dv "CU= QDt|Dv=U 250 � 80 �xUQOt QDiO w Tqmw O};|tv OwHwx@ |tyt |WWm VvD |@v=H Q=@ CLD =yhkU u}= QO xm CU= u;u=tDN=U QO "OvDUy Kr=Yt|}=yv |Q=WiVvD R= |QUm |xv}W}@ |Q=Wi |=yVvDQDt|Dv=U 10� 30 |vD@ |=yQ}D CQwYx@ hkU |=yxJQ}D 'lwr@ xJQ}D hkU =@|tHL uRw "CU= xOW xO=iDU= QDt|Dv=U 10Ct=N[ =@ uD@ R= =yu; |wQ wh} QaD"CU= xOW ZQi 0 25 Q@=Q@ u; uwU=wB ?} Q[ w 2500 daN/cm3 KrUt uD@|=yu=tr= O=a@= w xOW s}UkD u=tr= 2 x@ OwN pw] QO xJQ}D Qy R}v =yhkU u}= QO

"CU= |@ Q[ j=D Cr=L x@=Wt hkU |xDUwB

98

u=}rky=W

pwUQw

Qis=vy@

O=yQi |vwoS=w QF= QO CUmW �?

%OwW|t xDiQoQ_v QO 13 |x]@=Q CQwYx@ Q=w}O |vwoS=w T=U=Q@ |WQ@ Ctw=ktVr = 0 9�PD+L

Lh

(13)

Q=Okt xm CU= Q=w}O pLt ?} Q[ a 'Q=w}O `=iDQ= h 'Q=w}O pw] Q@=Q@ L 'u; QO xm|vwoS=w T=U=Q@ Q=w}O |WQ@ Ctw=kt Vr w 0 5 Q@=Q@ QN; |xk@] |=yQ=w}O |=Q@ u;

"CU=|Q]k VWm QF= QO CUmW �G

%OwW|t u}}aD 14 |x]@=Q R= Q=w}O QO |Q]k VWm T=U=Q@ |WQ@ Ctw=kt

Vt = �meA�Lh

�r1 + fa

�me(14)

|x}k@ w CU= Q=w}O QO |Q]k VWm T=U=Q@ Q=w}O |WQ@ Ctw=kt Vt 'u; QO xm"Ov=xOW h} QaD ,q@k =yQDt=Q=B

xHvB QO Q=Wi QF= QO CUmW �Ox@U=Lt 15 |x]@=Q R= Q=w}O |xHvB QO Q=Wi w |oOWOQN T=U=Q@ |WQ@ Ctw=kt

%OwW|t

Vc = �PD�Lh

��1� fa0 7 f 0m

�(15)

|xHvB QO |oOWOQN |=Q@ Q=w}O |WQ@ Ctw=kt Q@=Q@ Vc w PD = 0 9D 'u; QO xm"Ov=xOW h} QaD ,q@k =yQDt=Q=B |x}k@ w CU= Q=w}O

CUmW |=yOwt T=U=Q@ Q=w}O Qy |WQ@ C}iQ_ '376 |x} QWv QO =t=CQwYx@ x} QWv u}= "4"4 Ov@ T=U=Q@ KrUtQ}e |}=v@ |=yQ=w}O |xLiYuwQO

%OwW|t x@U=Lt Q=}at wO u}= R= pY=L Q=Okt u} QD|v=QL@Cqt RQO VRer T=U=Q@ |WQ@ Ctw=kt %Cqt RQO VRer QF= QO CUmW �hr=CUOx@ 11 |x]@=Q u=ty R= 376 |x} QWv QO KrUtQ}e |}=v@ |=yQ=w}O QO

%OwW|t x@U=Lt 16 |x]@=Q R= Q=_Dv= OQwt |WQ@ Ctw=kt �me w O};|t�me = 0 56 �te +0 75 fa (16)

'CU= u=tDN=U Cqt|WQ@Ctw=kt R= pY=LG}=Dv\UwDt Q=Okt �te 'u; QO xmfa = PD+L

A w OwW xDiQo Q_v QO QDW}@ 7 daN/cm2 R= O}=@v u; Q=Okt xm|=yQ=@ w (D) xOQt |=yQ=@ R= pY=L |QwLt |wQ}v PD+L 'u; QO xm CU=

"OwW|t x@U=Lt Q=w}O |q=@ R=QD QO w CU= (L) xOvRQO Q=w}O |Q]k VWm T=U=Q@ |WQ@ Ctw=kt %|Q]k VWm QF= QO CUmW �?

"OwW|t u}}aD FEMA356 =@ x@=Wt 14 |x]@=Q u=ty R= 376 |x} QWv

376 |x} QWv w FEMA356 j@] VQ}PB |=yQ=}at "4"5\w@ Qt |x]@=Q CLD Q=_Dv= OQwt |@v=H Ctw=kt xm|DQwY QO '=yQ=w}O |@v=H Q=DiQ|Q]kVWm x@ \w@ QtCtw=kt R= QDtm �11 |x]@=Q� Cqt RQO VRer QF= QO VQ@ x@|SQv= hqD= |va} 'CU= pmWQ}}eD \UwD xOvwWpQDvm CQwYx@ 'OW=@ �14 |x]@=Q�wQ}v \UwD xOvwWpQDvm CQwY x@ Q=w}O Q=DiQ CQwYu}= Q}e QO "CU= xHwD p@=kxO=O |]NQ}e Q=DiQ |xR=H= w CU= R}J=v |SQv= hqD= |va} 'OwW|t xDiQo Q_v QOZQi wQ}v \UwD xOvwWpQDvm CQwY x@ =yQ=w}O QO |QwLt Q=Wi Q=DiQ "OwW|tv

"OwW|t

u}= "OwW|t u}}aD 2800 OQ=Ov=DU= 3 pwOH T=U=Q@ u; Q=Okt w CU= KQ] ?=DR=@"OwW|t `} RwD hkU |x@r Q@ Owta O=ODt= QO CN=wvm} CQwYx@ |@v=H |wQ}v

=yQ=w}O |R=UpOt "2"5KrUtQ}e|}=v@Kr=Yt =@|=yQ=w}O|xLiYuwQO|@v=H|DNU'|]N|=yp}rLD QOVWwB uDiQoQ_vQO uwO@ 'xOQwNvlQD `]kt K]U |UOvy C=}YwYN =@ ?U=vDtu}}aD 10 |x]@=Q R= Q=w}O Qy |@v=H |DNU T=U= u}= Q@ "OwW|t x@U=Lt =tv

%OwW|t

K = 1h3

3EIg + hGA

(10)

550 f 0m Q@=Q@ w Q=w}O Kr=Yt |a=HDQ= ?} Q[ E 'Q=w}O `=iDQ= h 'u; QO xmf 0m Q=Okt ,qwtat "CU= Q=w}O Kr=Yt |Q=Wi Ctw=kt f 0m u; QO xm [2]'CU=40 daN/cm2 \UwDt Kr=Yt |=Q@ '60 daN/cm2 Q@=Q@ ?wN Kr=Yt |=Q@|Q=Wi Ctw=kt "OwW|t xDiQo Q_v QO 20 daN/cm2 Q@=Q@ O@ Kr=Yt |=Q@ wxOWs=Hv= |Q=Wi Ctw=kt V}=tR; x@ xHwD =@ =yu=tDN=U |x}rm |=Q@ Q=w}O Kr=YtKr=Yt |WQ@ pwOt G u}vJty "CU= xOW xDiQo Q_v QO 40 daN/cm2 Q@=Q@`]kt K]U A R}v w 'CU= 0 4E Q@=Q@ � = 0 25 |=Q@ u; Q=Okt xm CU= Q=w}O

"CU= xOQwNlQD `]kt pm K]U |=Q@ |UQv}= u=tt Ig w Q=w}OQvi l} CQwYx@ 'uqB QO OwN |Q}oQ=Qk pLt x@ xHwD =@ =yQ=w}O R= l} Qy

"Ov=xOW pOt hkU |=yso =Qi=}O x@ OwN p=YD= pLt QO xR=U pOt QO |ki=

|x} QWv w FEMA356 j@] Q=w}O Qy sw=kt |WQ@ |wQ}v "3"5376

`]=kt QO OwHwt |=ywQ}v K]U uOw@pR=v |xOvyOu=Wv =yp}rLD G}=Dv uwJ|WQ@ C}iQ_ |xU}=kt CQwYx@ ,=DOta =yu=tDN=U |:tm |@=} RQ= 'CU=yhkU"Ow@ Oy=wN �|ki= Qvi Qy ptar=Tma |wQ}v |va}� l} Qy |WQ@ |wQ}v =@ =yQ=w}O|}=v@ |=yQ=w}O |xLiYuwQO CUmW |=yOwt T=U=Q@ Q=w}O Qy |WQ@ C}iQ_4 u}= R= pY=L Q=Okt u} QD|v=QL@ CQwYx@ [4]'FEMA356 T=U=Q@ KrUtQ}e

"OwW|t x@U=Lt Q=}atCqt RQO VRer QF= QO CUmW �hr=

CQwYx@ KrUtQ}e |}=v@ |=yQ=w}O QO Cqt RQO VRer T=U=Q@ |WQ@ Ctw=kt%OwW|t xDiQo Q_v QO 11 |x]@=Q

Vs = �meA (11)

|WQ@ Ctw=kt �me w Cqt |xOvQ=O Q@ QO Xr=N `]kt CL=Ut A 'u; QO xm%OwW|t x@U=Lt 12 |x]@=Q j} Q] R= xm 'CU= Q=_Dv= OQwt

�me = 0 375 �te +0 5 fa (12)

'CU= u=tDN=U Cqt |WQ@ Ctw=kt R= pY=L G}=Dv \UwDt Q=Okt �te 'u; QO xm'CU= fa = PD+L

A w OwW xDiQo Q_v QO QDW}@ 7 daN/cm2 R= O}=@v u; Q=Okt xm|=yQ=@ R= pY=L |QwLt |wQ}v T=U=Q@ u; Q=Okt w PD+L = 1 1(D+L) xmCtw=kt R}v VS "OwW|t x@U=Lt Q=w}O |q=@ R=QD QO (L) xOvR |=yQ=@ w (D) xOQt

"CU= Cqt RQO VRer T=U=Q@ Q=w}O |WQ@ Q=_Dv= OQwt

99

"""Ow@y@

|=Q@O=yv

W}B|x�

=Q=w|}x

U}=kt|

UQQ@

Qy OQmrta K]U u}}aD w |@=} RQ= G}=Dv |UQQ@ "6u=tDN=U

u}= =@ [2]'376 |x} QWv VwQ x@ |i}m |@=} RQ= QO u=tDN=U Qy OQmrta K]U%OwW|t u}}aD =yZQi

|xO=iDU= C}r@=k OQmrta K]U u}t-=D =@ pO=at '�25 > LR %sm |Q}PB?}U;&(IO) xikw |@

VR} QwQi |xv=DU; OQmrta K]U u}t-=D =@ pO=at '�75 � LR %O=} R |Q}PB?}U;&(CP )

|vt}= OQmrta K]U u}t-=D =@ pO=at '�75 > LR � �25 %\UwDt |Q}PB?}U;"(LS) |v=H

x@ xHwD =@ [3]'FEMA154 VwQ x@ |i}m |@=} RQ= R= xO=iDU= s=ovy QOQ=}DN= u=tDN=U Qy OQmrta K]U u}}aD |=Q@ C=}[Qi u}= '2�2 Ov@ C=L}[wD

%OwW|t&(IO) OQmrta K]U =@ pO=at %3 � u=tDN=U R=}Dt= ��

&(LS) OQmrta K]U =@ pO=at %2 � u=tDN=U R=}Dt= < 3 ��"(CP ) OQmrta K]U =@ pO=at %0 � u=tDN=U R=}Dt= < 2 ��

u}}aD 3 pwOH w 19 |x]@=Q j@] |:tm |@=} RQ= QO Q=w}O Qy OQmrta K]U|Q}ou}ov=}t R= '|:tm|@=} RQ= R= pY=L u=tDN=U OQmrta K]U u}}aD |=Q@ "OwW|tK]U uOQmXNWt R= Oa@ 'Q=m u}= |=Q@ "OwW|t xO=iDU= =yQ=w}O |Q}PB?}U; |vRw|xOwOLt |=yQ=w}O '1 OOa =@ IO |xOwOLt QO |=yQ=w}O 'Q=w}O Qy |Q}PB?}U;O=OaD "OvwW|t XNWt 3 OOa =@ CP |xOwOLt |=yQ=w}O w 2 OOa =@ LSxOt;CUOx@ OOa s}UkD =@ w OwW|t ?Q[ Q_vOQwt OOa QO xOwOLt Qy |=yQ=w}O=} LS 'IO CQwYx@ u=tDN=U |Q}PB ?}U; u=R}t 'uqB QO =yQ=w}O pm O=OaD x@|Q=QkQ@ CQwY QO 'wQ}v \UwD xOvwWpQDvm Q=w}O OQwt QO "O};|t CUOx@ CP|=Q@ "OwW|t Qw_vt CP CQwYu}= Q}e QO w IO OQmrta K]U ?19 |x]@=Q

%O};|t CUOx@ CQwY u}= x@ |Q}PB?}U; 1 |xQ=tW u=tDN=U |=Q@ p=FtOOa 83 %=yQ=w}O pm O=OaD ��

OOa 24 %IO |xOwOLt |=yQ=w}O O=OaD ��OOa 21 %LS |xOwOLt |=yQ=w}O O=OaD ��OOa 38 %CP |xOwOLt |=yQ=w}O O=OaD ��

%u=tDN=U |rm |Q}PB?}U; u=R}t ��(24� 1) + (21� 2) + (38� 3)

83 = 2 16 ) CP

OQwt |WQ@ Ctw=kt CQwYx@ Q=w}O |v=QL@ |WQ@ Ctw=kt O}=@ '|@=} RQ= |=Q@x@U=Lt \@=wQ u}= j@] (VCL) |WQ@ Ctw=kt u}�=B |xv=Qm =} (VCE) Q=w}O Q=_Dv=

"OwWw hr=17 |=yx]@=Q =@ j@=]t V2 w V1 |WQ@ |=yCtw=kt =OD@= 'Qw_vt u}= x@

%O};|t CUOx@ ?17

V1 = min

( �13 w 11 \@=wQ� |vwoS=w w VRer R= |W=v |WQ@ Ctw=ktFEMA356 j@] |@=} RQ= s=ovy QO

)V1 =

( �16 |x]@=Q� Cqt RQO VRer R= |W=v |WQ@ Ctw=kt376 |x} QWv j@] |@=} RQ= s=ovy QO

)(hr=17)

V2 = min

( w 14 x]@=wQ� |oOWOQN w VWm R= |W=v |WQ@ Ctw=ktFEMA356 j@] |@=} RQ= s=ovy QO �15

)V2 =

( �14 |x]@=Q� |Q]k VWm R= |W=v |WQ@ Ctw=kt376 |x} QWv j@] |@=} RQ= s=ovy QO

)(?17)

%OW=@ Q=QkQ@ ?18 w hr=18 \@=wQ QO xOWQmP \}=QW O}=@ x=ov;

if V1 � V2 ) VCE = V1 (hr=18)

if V1 > V2 ) VCL = V2 (?18)

s=Hv= ?19 w hr=19 \@=wQ j@] Q=w}O |@=} RQ= 'Q=w}O |WQ@ Ctw=kt u}}aD R= TB%OwW|t

VUDVCE

� m (hr=19)

VUFVCL

� 1 (?19)

|@v=H |wQ}v p=ta= R= pY=L �Qvi |wQ}v� Q=w}O |WQ@ |wQ}v VUD '=yu; QO xm20 |x]@=Q R= xm CU= Qvi |xOWKqY= |wQ}v VUF w xR=U Q@ 8 |x]@=Q j@]

%O};|t CUOx@

VUF = VUDC1J

(20)

|a=HDQ= Q}e |=ypmWQ}}eD wkw p=tDL= K]U |xOvyOu=Wv J QDt=Q=B 'u; QO xm'1 Q@=Q@ ?}DQD x@ O=} R Q=}U@ w O=} R '\UwDt 'sm |R}NxRQr =@ j]=vt QO w CU=x@ xDU@=w w Ctw=kt KqY= ?} Q[ 'hr=18 |x]@=Q QO m QDt=Q=B "CU= 2 w 1 5

"CU= xOW x�=Q= 4 pwOH QO QDt=Q=B u}= Q}O=kt "CU= Q=w}O |Q}PBpmW[2]"376 |x} QWv QO |}=v@ |=yQ=w}O (m) Ctw=kt KqY= ?} Q[ "4 pwOH

OQmrta K]UQ=DiQ wv|rY=Q}e |=[a= |rY= |=[a= C}r@=k

|xv=DU; |vt}= |xv=DU; |vt}= |xO=iDU=VR} QwQi |v=H VR} QwQi |v=H xikw |@

8 6 4 3 1 |Ov@hqm =@ u=tDN=U |=Q@ Cqt RQO VRer4 3 2 1 5 1 |Ov@hqm uwO@ u=tDN=U |=Q@ Cqt RQO VRer

100

u=}rky=W

pwUQw

Qis=vy@

O=yQi j@]|@=} RQ= G}=Dv =@ xU}=kt w xOWKqY= |x]@=Q =@ `} QU|@=} RQ= G}=Dv "6 pwOH

"FEMA356|:tm |@=} RQ= 376 |x} QWv QO `} QU |@=} RQ= |xQ=tW

FEMA356 j@] 21 |LqY= |x]@=Q \UwD u=tDN=UCP CP 1CP CP 2CP CP 3CP CP 4CP CP 5CP LS 6LS LS 7LS LS 8LS LS 9LS LS 10LS LS 11LS LS 12LS LS 13

QO |Q}PB?}U; |x]@=Q |OOa ?} Q[ KqY= Q=my=Q "1"7376 |x} QWv

QO 'FEMA356 \UwD |:tm |@=} RQ= 'OwW|t xOy=Wt 4 pwOH QO xm Qw]u=tyu=Wv 376 |x} QWv |i}m |@=} RQ= x@ C@Uv =Q |QDW}@ |Q}PB?}U; 'hqDN= OQ=wt

"CU= xO=O|Q}PB?}U; XN=W R= |Q}ou}ov=}t =@ 'Qo}O pt=wa uOw@C@=F ZQi =@ =PrCUOx@ 21 |x]@=Q CQwYx@ O}OH |OOa ?} Q[ |Q}PB?}U; |xOwOLt l} QO

%O};|tO}OH |OOa ?} Q[ = 0 45� 50

37 5 = 0 60 (21)

|=Q@ |Q}PB?}U; XN=W \UwDt w xv}W}@ Q}O=kt ?}DQD x@ 37 5 w 50 'u; QO xmK]U wO QO O}OH |OOa ?} Q[ Q=Okt "CU= \UwDt |Q}PB?}U; =@ =yu=tDN=U`} QU |@=} RQ= |x]@=Q OwW|t O=yvW}B xH}Dv QO "CU= x@=Wt R}v Qo}O |Q}PB?}U;

%OwW KqY= 22 |x]@=Q CQwYx@ 376 |x} QWv QOLR = 0 60(L3 +L4 +L5 +L6 +L7)

�L1 L2 L8 L9 L10(7 5A� 1) (22)

|UQQ@ OQwt =yu=tDN=U xQ=@ wO '22 |x]@=Q CQwYx@ |@=} RQ= |x]@=Q KqY= R= Oa@QF-wt CU= xDUv=wD OL xJ =D |O=yvW}B Q=my=Q OwW xOy=Wt =D OvwW|t xO=O Q=Qk

"OwW `k=w'6 w 5 |=ypwOH |xU}=kt "CU= xOW x�=Q= 6 pwOH QO xQ=@ wO |UQQ@ G}=DvOQ=wt Q}=U QO 'OQwt l} RH x@ w CU= G}=Dv |x_Lqt p@=k KqY= |xOvyOu=Wv

"OQ=O OwHw pt=m j=@]v=

376 |x} QWv QO |Q}PB?}U; C=Qtv KqY= "2"7KqY= |=Q@ "OwW KqY= �1 pwOH� |Q}PB?}U; C=Qtv pwOH O}=@ Cr=L u}= QO=@ w 2 pwOH QO xOWXNWt |vRw |=yXN=W x@ xHwD =@ '|Q}PB?}U; C=Qtv

"|@=} RQ= OQwt |=yu=tDN=U OQmrta K]U u}}aD G}=Dv |xU}=kt "5 pwOH|tm |@=} RQ= `} QU |@=} RQ= |xQ=tW

FEMA356 376 |x} QWv FEMA154 376 |x} QWv u=tDN=UCP CP CP CP 1CP LS CP LS 2CP LS CP LS 3CP LS CP LS 4CP LS CP LS 5CP LS CP LS 6LS LS LS LS 7LS LS LS LS 8LS LS LS LS 9LS LS LS LS 10LS LS LS LS 11LS LS LS LS 12LS IO IO IO 13

|x} QWv `} QU |@=} RQ=� VwQ 4 R= u=tDN=U Qy OQmrta K]U ?}DQD u}= x@w x@U=Lt �FEMA356 w 376 |x} QWv |:tm |@=} RQ= 'FEMA154 w 376w `} QU |@=} RQ= G}=Dv xm OwW|t xOy=Wt pwOH QO "CU= xOW QmP 5 pwOH QO

"OvDUy u=Um} 376 |x} QWv j@] |:tm`} QU|}xRQr|@=} RQ= OQm} wQ wOu}@?U=vt|ovy=ty|xOvyOu=Wv w[wtu}=FEMA154 C=} QWv QO w[wt u}ty x@=Wt "CU= 376 |x} QWv QO |r}YiD w|}xQ=B QO 376 |x} QWv 'Qo}O |wU R= "OwW|t xOy=Wt R}v FEMA356 ww xOQm pta QDxv=Q=mx_i=LtQ}e FEMA356 =} FEMA154 x@ C@Uv OQ=wtl}t=Om xmv}= "CU= xOQm x@U=Lt \w@ Qt |=yu=tDN=U |=Q@ =Q |QDtm |Q}PB?}U;syt w[wt OwN 'Ov=xO=O CUOx@ |QDxv=v}@`k=w G}=Dv '=yptar=QwDUO xwQo wO u}= R=

"CU= |FL@ p@=k wxm 'FEMA154 w FEMA |=yptar=QwDUO QDW}@ |xk@=U x@ xHwD =@ =t=u; R= TB |=yxrRrR QO |rta ?Q=HD T=U=Q@ w QWDvt 1988 p=U QO Q=@ u}rw=KqY= |Qw] =Q 376 |x} QWv \@=wQ u=wD|t 'CU= xOW V}=Q} w 2002 p=U QOxDW=O FEMA356 =} FEMA154 =@ |QDW}@ j@=]D p}rO Qy x@ u; G}=Dv xm OQm7 VN@ QO 376 |x} QWv |@=} RQ= |x]@=Q KqY= |=Q@ |O=yvW}B |=yVwQ "OW=@

"CU= xOW x�=Q=

376 |x} QWv QO |@=} RQ= |x]@=Q KqY= "7xDiQo Q_v QO Q=my=Q wO '�1 |x]@=Q� 376 |x} QWv QO |@=} RQ= |x]@=Q KqY= |=Q@

%OwW|txO=O Q}}eD xOt;CUOx@ G}=Dv j@] �0 45� |Q}PB?}U; |x]@=Q |OOa ?} Q[ "1

"OwW=yu; |vRw XN=W x@ xHwD =@ '`} QU |@=} RQ= G}=Dv QO QF-wt |=yQDt=Q=B Vkv "2'OwN |vRw XN=W =@ ?U=vDt pt=a Qy w OQ}o Q=Qk |UQQ@ OQwt �2�4 Ov@�

"Ovm Ci=} QO |O}OH |@=} RQ= |xQtv

101

"""Ow@y@

|=Q@O=yv

W}B|x�

=Q=w|}x

U}=kt|

UQQ@C=Qtv KqY= R= Oa@ |@=} RQ= OQwt |=yu=tDN=U |Q}PB?}U; G}=Dv "8 pwOH

"376 |x} QWv QO |Q}PB?}U;|tm |@=} RQ= xH}Dv C=Qtv =@ `} QU |@=} RQ= xH}Dv |xQ=tWFEMA356 j@] 376 |x} QWvQO xOWKqY= u=tDN=U

CP CP 1CP CP 2CP CP 3CP CP 4CP CP 5CP CP 6LS LS 7LS LS 8LS LS 9LS LS 10LS LS 11LS LS 12LS LS 13

|Q}PB?}U; |xQtv 'xvwtv |=Q@ "CU= xOW x�=Q= 7 pwOH QO G}=Dv "OQ}o|t CQwY%OwW|t ?=UL CQwY u}= x@ |@ Q[ j=D hkU |=Q@ O}OH

%xOW|UQQ@ |=yu=tDN=U |Q}PB?}U; QO hkU |vRw XN=W u}ov=}t33 1 + 27 3 + 26 8 + 21 3

4 = 108 54 = 27

%|@ Q[ j=D hkU |=Q@ O}OH |Q}PB?}U; |xQtv(1 + 0 27)� 20 = 25 4 � 25u}@ |rt=m j=@]v= '|Q}PB?}U; C=Qtv KqY= R= TB 'OwW|t xOy=Wt xm xvwou=tyFEMA356 |x} QWv QO |tm |@=} RQ= w 376 |x} QWv QO `} QU |@=} RQ= G}=DvCU= xDUv=wD swO |O=yvW}B Q=my=Q OUQ|t Q_v x@ ?}DQD u}= x@ "CU= xOW pY=L=} FEMA154 w 376 C=} QWv QO |}xRQr |@=} RQ= G}=Dv u}@ =Q |rt=m Cy@=Wt

"Ovm O=H}= FEMA356|=yu=tDN=U |Q}PB?}U; ,=OOHt xOWKqY= |Q}PB?}U; C=Qtv R= xO=iDU= =@

"OwW|t xOy=Wt 8 pwOH QO u; G}=Dv xm 'CU= xOW x@U=Lt |UQQ@ OQwt

|Q}oxH}Dv "8|}=v@ u=tDN=U 71 OQwt QO |r}YiD |@=} RQ= w `} QU |@=} RQ= s=Hv= =@ 'Q=DWwv u}= QOw `} QU |@=} RQ= G}=Dv u}@ |@ wN Q=}U@ j@=]D xm CU= xOW xOy=Wt QwWm QO OwHwtC=} QWv u}@ |ovy=ty u}ty x@=Wt xJ Qo = "OQ=O OwHw 376 |x} QWv QO |r}YiD376 |x} QWv wtHt QO =t= 'OwW|t xOy=Wt R}v FEMA356 w FEMA154KqY= |=Q@ VwQ wO "OQ=O Q@ QO Qw@ Rt C=} QWv x@ C@Uv |QDtm |Q=mx_i=LtOwHwt |=yXN=W|@Uv uRw T=U=Q@ 376 |x} QWv QO |Q}PB?}U; u}}aD |x]@=Qx@=Wt |H}=Dv x@ u=wD|t =yv; R= l} Qy R= xO=iDU= =@ xm CU= xOW x�=Q= x]@=Q QOQO C=Qtv KqY= Q=my=Q '|O=yvW}B Q=my=Q wO u}@ R= "O}UQ FEMA C=} QWv =@=Q FEMA356 j@] |r}YiD |@=} RQ= =@ |rt=m j=@]v= xar=]t OQwt |=yu=tDN=U"OQ}o Q=Qk xO=iDU= OQwt 376 |x} QWv QO |QF-wt Qw]x@ Ov=wD|t xm 'OyO|t u=Wv

|@=} RQ= |=yXN=W |=Q@ |O=yvW}B |xOWKqY= |Q}PB?}U; C=Qtv "7 pwOH"376 |x} QWv QO `} QU

(Li) CQ=UN ?} Q[ =} Q=Okt QDt=Q=B h}OQ|xQtv |xQtv C}a[w Q_vOQwtO}OH |r@k QDt=Q=B1 1 0 � � � 15

(�) u}tR ?}W 11 1 1 1 15 � � � 301 2 1 2 � > 301 05 1 I

l =N wv 21 10 1 05 II

1 15 1 1 III

1 20 1 15 IV

6 5 ?U=vt |B 322 20 ?U=vt=v20 15 s}=k w |ki= hqm =@

|}xR=U Q=w}O 435 25 |ki= hqm =@50 35 hqm uwO@7 5 KrUt uD@ p=O

hkU 520 15 lwr@ xJQ}D25 20 |@ Q[ j =]32 25 |@ wJ Q}D0 0 2800 OQ=Ov=DU= =@ j@=]D |oOt=W}B 612 10 2800 OQ=Ov=DU= =@ j@=]D sOa0 0 uQ=kDt u=tDN=U uqB 712 10 uQ=kDt=v

1 05 1 2800 OQ=Ov=DU= =@ j@=]D =ywWR=@ 81 25 1 2 2800 OQ=Ov=DU= =@ j@=]D sOa

1 1 xk@] l}C=k@] O=OaD 91 1 1 1 xk@] wO

1 2 1 2 QDW}@ w xk@] xU1 05 1 ?wN

Kr=Yt C}i}m 101 25 1 2 \UwDt1 35 1 3 O@

'�=yhkU C}a[w ,qFt� pt=a Qy OQwt QO |vRw |=yXN=W R= |Q}ou}ov=}t100 Q@ w XNWt Q}PB?}U; |=yxwQo pm QO pt=a Qy |vRw XN=W \UwDt|Q}PB?}U; |xQtv QO '1 OOa =@ pY=L OOa `tHpY=L TBU "OwW|t s}UkDQ_vOQwt |xOWKqY= |xQtv u=ty 'xOt;CUOx@ O}OH |xQtv "OwW|t ?Q[ |r@k|=Q@ \ki "OwW|t s=Hv= |Q}PB?}U; QO QF-wt |=ypt=a lD lD |=Q@ Q=m u}= "CU==v@t ?=DW QO xOW?Q[ OOa Q}}eD CQwYx@ Q=mu}= 'KQ] |=v@t ?=DW QF-wt pt=a

102

u=}rky=W

pwUQw

Qis=vy@

O=yQi

CWwv=B1. cost-bene�t

�References� `@=vt1. Regulations for Seismic Rehabilitation of Existing Build-

ings, Document 360, President Deputy of Planning andStrategic Inspection, 2nd Ed. (2006).

2. Regulations for Seismic Rehabilitation of Existing Un-reinforced Masonry Buildings, Document 376, PresidentDeputy of Planning and Strategic Inspection, 2nd Ed.(2007).

3. FEMA154, Rapid Visual Screening of Buildings for Po-tential Seismic Hazards, A Handbook, Federal Emer-gency Management Agency (May 2002).

4. FEMA356, Seismic Rehabilitation Prestandard, FederalEmergency Management Agency (2000).

5. Shakib, H. and Bayat, H. \Evaluation of buildings", Per-formances in Ghaenaat Earthquake, Iranian Center forMitigation of Natural Hazards (1997).

6. Zahraei, S.M. \Study on the seismic vulnerability ofbuildings in Ghazvin city", Building and Housing Re-search Center (2004).

7. Behnamfar, F. \Common weakpoints of school and hos-pital buildings in Iran", Reduction of Earthquake RiskSeminar, Sharif University of Technology (Spring 2008).

103