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8/9/2019 Bridge Planning
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Bridge Engineering-Planning of Bridges-
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Bridge Planning
1. Traffic Studies
2. Hydrotechnical Studies
3. Geotechnical Studies
4. Environental !onsiderations
". #lternatives for Bridge Ty$e
%. Econoic &easi'ility
(. Bridge Selection and )etailed )esign
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1. Traffic Studies
* i v e r
!ity !enter
+e, Bridge
+e, *oad in
E/isting +et,or
P a
s i g*i v er
!ity !enter
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Traffic Studies
0 Traffic studies need to 'e carried out toascertain the aount of traffic that ,illutilie the New or Widened Bridge
0 This is needed to deterine Econoic
&easi'ility of the Bridge0 So for this Services of a Trans$ortation
Planner and or Traffic Engineer are
*euired0 Such Studies are done ,ith hel$ of TrafficSoft,are such as TransCAD, EMME2 etc.
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Traffic Studies
0 Traffic Studies should $rovide follo,ing
inforation 5 Traffic on Bridge iediately after o$ening
5 To no, the aount of traffic at various ties during
life of the Bridge
5 Traffic 6i/ 7i.e. nu'er of otorcars 'uses heavy
trucs and other vehicles8
5 Effect of the ne, lin on e/isting road net,or
5 Predoinant 9rigin and )estination of traffic that ,illuse the Bridge
5 Strategic i$ortance of the ne,:i$roved Bridge
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2. Hydrotechnical Studies
0 # thorough understanding of the river andriver history is crucial to $lanning of Bridgeover a river
0 Hydrotechnical Studies should include:
1.To$ogra$hic Survey 2 u$strea and2 do,nstrea for sall rivers includingongitudinal section and ;-sections
2. &or 'ig rivers "s
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Hydrotechnical Studies
a8 Scale of the to$ogra$hic a$:!onduct
To$o-Survey 5 12=== for sall rivers
5 1"=== for large rivers
'8 The High &lood evels and the 9'served &lood evel should 'e indicated a$
c8 Sufficient +u'er of /-sections should 'e
taen and H& and 9& ared onthe
d8 *iver Bed surveying ,ould reuire
soundings
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Hydrotechnical Studies
e8 !atchent #rea 6a$
Scale recoended 5 1"==== or
5 12"===
f8 #ll *eservoirs *ainGauges Stns. *iverGauge Stns. should 'eared on a$
Catchment of River Indus
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Hydrotechnical Studies
River Catchment Boundaries with Tributaries
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Hydrotechnical Studies
River Catchment Boundaries with Sub-Basin Boundaries
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3. Hydrological )ata
0 The Hydrological )ata to 'e collected are
1. *ainfall )ata fro *ain Gauge Stations
in the !atchent #rea
2. >sohyetal 6a$ of the !atchent #rea
sho,ing contours of #nnual *ainfall
3. Hydrogra$hs of &loods at *iver Gauge
Stations
4. &lo, ?elocities
". Sedient oad in *iver &lo, during
floods
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Hydrologic )ata
!am"le of an IS#H$T%& '%P
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Hydrologic )ata
!am"le of River Hydrogra"h
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Hydrologic )ata
!am"le of a River Hydrogra"h
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)esign &lood evels
0 ##SHT9 Gives &ollo,ing Guidelines for Estiating
)esign &lood evels
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)esign &lood evels
0 %%SHT# (ives )ollowing (uidelines for stimating
*esign )lood &evels
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)esign &lood evels
0 !#+#)>#+ 6>+>ST*@ 9& T*#+SP9*T#T>9+
Gives &ollo,ing Guidelines for Estiating )esign &lood evels
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)esign &lood evels
0 !#+#)>#+ 6>+>ST*@ 9& T*#+SP9*T#T>9+
Gives &ollo,ing Guidelines for Estiating )esign &lood evels
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)esign &lood evels
0 !#+#)>#+ 6>+>ST*@ 9& T*#+SP9*T#T>9+
Gives &ollo,ing Guidelines for Estiating &ree'oard *euireents
)RB#%R* R+,IR'TS
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Estiating )esign &lood
)lood Pea. *ischarge at Stream or River &ocation
*e"ends u"on:1. !atchent #rea !haracteristics
5 Sie and sha$e of catchent area
5 +ature of catchent soil and vegetation
5 Elevation differences in catchent and 'et,een catchentand 'ridge site location
2. *ainfall !liatic !haracteristics
5 *ainfall intensity duration and its s$atial distri'ution
3. Strea:*iver !haracteristics 5 Slo$e of the river
5 *iver 'ed flo, in the river
5 *iver &acilities: )as on the river
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'ethods of stimating *esign )lood
1. E$irical 6ethods
2. &lood &reuency #nalysis
3. *ational 6ethod
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*ational 6ethod of Pea &lood Estiation
0 #tte$ts to give estiate of )esign )ischarge
taing into account 5 The !atchent !haracteristics
5 *ainfall >ntensity
5 )ischarge !haracteristics of the !atchent
A I C Q T =
A )esign )ischarge
>T #verage rainfall intensity 7in:hr8 for soe recurrence interval T
during that $eriod of tie eual to Tc.Tc Tie of !oncentration
# #rea of the catchent in S. iles
! *unoff coefficientC fraction of runoff e/$ressed as a
diensionless decial fraction that a$$ears as surface runoff
fro the contri'uting drainage area.
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*ational 6ethod of Pea &lood Estiation
0 Tie of !oncentration can 'e estiated using
Barns'y Dillias &orula ,hich is ,idely used'y
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*ational &orula 5 *unoff !oefficient
#rea !haracteristic *un-off !oefficient !
Stee$ Bare *oc =.=Stee$ *oc ,ith Doods =.F=
Plateau ,ith light cover =.(=
)ensely 'uilt-u$ areas =.= 5 =.(=
*esidential areas =.(= 5 =."=
Stiff !layey soils =."=
oa =.4= 5 =.3=
Su'ur's ,ith gardens =.3=Sandy soils =.1 5 =.2=
ungle area =.1= 5 =.2"
Pars a,ns &ields =.2" - =."=
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/0 (eotechnical Studies
(eotechnical Studies should "rovide the
following Information:
1.The ty$es of *ocs )i$s &aults and
&issures
2. Su'soil Ground Dater evel Auality
#rtesian !onditions if any
3. ocation and e/tent of soft layers4. >dentification of hard 'earing strata
". Physical $ro$erties of soil layers
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Geotechnical Studies
!am"le: Cross section of the 1ansas River2 west of Silver &a.e2 1ansas
Ty"ical Borehole
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nvironmental Considerations
1. >$act on &ollo,ing &eatures of Environent need toconsidered 5 *iver Ecology ,hich includes
0 6arine ife
0 Dildlife along river 'ans0 *iver'ed0 &lora and fauna along river 'ans
2. >$act u$on d,ellings along the river if any
3. >$act u$on ur'an environent if the 'ridge in an
ur'an area
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Bridge Econoic &easi'ility
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Bridge Econoic &easi'ility
1. Econoic #nalysis is reuired at&easi'ility Stage to ustify e/$enditures of
$u'lic or $rivate funds
2. # Bridge is the ost e/$ensive $art of aroad trans$ortation net,or
3. Ty$es of Econoic #nalyses
a8 !ost Benefit *atio #nalysis
'8 >nternal *ate of *eturn 7>**8 #nalysis
Bridge conomic %nalysis3
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Bridge conomic %nalysis3&ife Cycle Cost %nalysis 4&CC%5
n-years*esign &ife
C o s t s S t r e a m
B e n e f i t s S t r e a m
C
o n s t r u c t i o n
S
t a g e
Pro6ect &ife P r o 6 e c t S t a r t
* a
t e
n d P r o 6 e c t
& i f e
S a l v a g e
7 a l u e
P t ! t B fit # l i
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Proect !ost Benefit #nalysis
0 The ob6ective of &CC% is to
5 Estiate the costs associated ,ith the Proect during!onstruction an its service life. These include routineaintenance costs I 6aor *eha' !osts
5 Estiate the Benefits that ,ill accrue fro the Proect includingtie savings to road users 'enefits to 'usiness activities etc.
5 Bring do,n the costs and 'enefits to a coon reference $t. intie i.e. ust $rior to start of $roect 7decision aing tie8
5 &acilitate decision aing a'out econoic feasi'ility 'ycalculating uantifia'le yardstics such as Benefit to !ost *atio7B!*8 and >nternal *ate of *eturn 7>**8
0 +ote Salvage ?alue ay 'e taen as a Benefit
This includes cost of the *ight-of-Day and su'structure
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8hat is &ife Cycle Cost9
0 #n econoic analysis $rocedure that uses
engineering in$uts
0 !o$ares co$eting alternativesconsidering all significant costs
0 E/$resses results in euivalent dollars7$resent ,orth8
Ti P i d f % l i
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Time Period of %nalysis
0 +orally eual for all alternatives
0 Should include at least one aor
reha'ilitation
0 +eeded to ca$ture the true econoic
'enefit of each alternative
0 Bridge design today is 'ased on a
$ro'a'ilistic odel of 1== years
Bridge Econoic #nalysis:
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Bridge Econoic #nalysis:ife !ycle !ost #nalysis 7!!#8
C o s
t s S t r e a m
B e
n e f i t s S t r e a m
C
o n s t r u c t i o n
S
t a g e Pro6ect &ife P
r o 6 e c t
S t a r t * a t e
n d
P r o 6 e c t
& i f e
S a l v a g e
7 a l u e
0 Costs and Benefits Change over the life of the Pro6ect
0 %mount of 'oney3Benefit accrued some time in future is worth less interms of Todays money
0 Same is the case with the benefits accrued over time
0 The Problem now is as to How to find the 8orth of a )inancial %mount in)uture in terms of Todays 'oney
0 This is accom"lished by using the instrument of ;*ISC#,T R%T<
Problem:
n-years*esign &ife
Bridge Econoic #nalysis:
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Bridge Econoic #nalysis:ife !ycle !ost #nalysis 7!!#8
*ISC#,T R%T:
The annual effective discount rate is the annual interest divided by the ca"italincluding that interest2 which is the interest rate divided by =>>? "lus theinterest rate0 It is the annual discount factor to be a""lied to the future cashflow2 to find the discount2 subtracted from a future value to find the valueone year earlier0
)or e!am"le2 su""ose there is an investment made of @A and "ays @=>> in a
years time0 The discount rate according the given definition is:
%0.5100
95100=
−== d Rate Discount
%26.595
95100 =−== i Rate Interest
Interest Rate is calculated as @ A as Base
Interest Rate and *iscount Rate are Related as )ollows
2
1
ii
i
id Rate Discount −≈
+
==
)i t * t
http://en.wikipedia.org/wiki/Discount_factorhttp://en.wikipedia.org/wiki/Discount_factor
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)iscount *ate0 Thus )iscount *ate is that rate ,hich can 'e
used to o'tain the Present ?alue of 6oney that
is s$ent or collected in future
et Present value of Cost incurred D Co D 4= - d5n Cn
In $ear n
et Present value of Cost incurred D Bo D 4= - d5n Bn
In $ear n
Time
C o s t s
S t r e a m
B e n e f i t s
S t r e a m
Pro6ect
&ife
P r o 6 e c t
S t a r t * a t e
$ear nCn
Bn
Cost3 Benefit Pro6ectedBac.ward
Bo
Co
Dh t )i t * t t < J
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Dhat )iscount *ate to
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!ost !onsiderations
Maintenance andInspectionCost
Initial Cost
C o s t s
Present Worth
Years
Rehabilitation Cost
Salvage Value
Salvage Costs
! t B fit * ti
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!ost Benefit *atio
&orula for !ost
Benefit *atio
Benefit To Cost Ratio D
∑
∑
−
−
= L
n
L
n
Cnd
Bnd
0
0
)1(
)1(
Costsof ValuePresent
Benefitsof ValuePresent
Dhere ife S$an of the Proect in @ears
d )iscount *ate
Bn Benefit in year n !n !ost incurred in year n
+et Present Dorth: ?al e
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+et Present Dorth: ?alue
0 +et Present Dorth: ?alue +PD or +P?
is defined as follo,s
P8 D P7 D Present 7alue of Benefits E Present 7alue of Costs
ote: If a umber of alternatives are being com"ared2 the alternativethat has the highest et Present 8orth is the "referable one andwill also have the higher Benefit to Cost Ratio
Dhat is >nternal *ate of *eturn 7>**8
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Dhat is >nternal *ate of *eturn 7>**8
0 >** ay 'e defined as that )iscount *ate
at ,hich the Benefit to !ost *atio 7B!*8of a Proect 'ecoes e/actly 1.=
0 >t is a 'etter easure of econoic via'ility
of a $roect co$ared to Benefit to !ost*atio
0 >t is a good indicator of ho, uch inflation
increase and interest rate hie a $roectcan tolerate and still 'e via'le
Present Dorth &actor
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Present Dorth &actor
pwf = Present Worth Factor for discount rate dand year n
d = Discount raten = Number of year when the cost/ benet will
occur
n
d pwf )1( −=
%lternate )ormula 4,sually %do"ted5
( ) nd pwf
+=
1
1
Present Dorth #nalysis
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Present Dorth #nalysis
• Discounts all future costs and benets to the
present:
t=LPW = F ! Σ pwf "#!$!F%!&' ! pwf "(' t=)
PW = Present Worth/ *alue of the Pro+ect F = First ,$nitial- ost
t = .ime Period of nalysis ,ran0es from ) L-# = #aintenance osts$ = $nspection ostsF% = Future %ehabilitation osts
& = &sers osts( = (al1a0e *alues or ostspwf = Present Worth Factor
Tie Period of #nalysis
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Tie Period of #nalysis
0 +orally eual for all alternatives
0 Should include at least one aor reha'ilitation
5 +eeded to ca$ture the true econoic 'enefit of each
alternative
0 Bridge design today is 'ased on a $ro'a'ilistic odel of
1== years
6aintenance !osts
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6aintenance !osts
0 #nnual cost associated ,ith the u$ee$ of the
structure0 >nforation is difficult to o'tain for a given
$roect
0 !ost varies on the 'asis of sie of the structure
7sft80 Best Guess ?alues
5 &reuency: #nnu
5 !oncrete =.=" K of >nitial !ost 5 Structural Steel=.=" K of >nitial !ost
>ns$ection !osts
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>ns$ection !osts
0 Should 'e taen for all alternatives $refera'ly
every t,o years0 !ost varies on the 'asis of sie of the structure
7sft8 and 'y construction aterial
0 Best Guess ?alues 5 &reuency - Biannual
5 !oncrete =.1" K of >nitial !ost
5Structural Steel =.2= K of >nitial !ost
&uture Painting !osts
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&uture Painting !osts
0 9nly a$$lies to structural steel structures
0 Should occur every 2= years
0 !ost varies on the 'asis of sie of the structure
7sft8
0 Best Guess ?alues 5 &reuency 5 every 2= years
5 !oncrete =.= K of >nitial !ost
5 Structural Steel (.= K of >nitial !ost
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&uture *eha'ilitation !osts
0 The freuency is not only a function of tie 'ut also thegro,ing traffic volue and the structural 'ea syste
0 !ost varies on the 'asis of sie of the structure 7sft8 andstructural 'ea syste
0 Best Guess ?alues
5 &reuency
0 &irst occurrence 5 !oncrete 4= years
0 &irst occurrence 5 Structural Steel 3" years
0 #nnual traffic gro,th rate .(" K 7shortens reha'cycles8
5 !oncrete 2=.= K of >nitial !ost
5 Structural Steel 22.= K of >nitial !ost
Salvage ?alue:!osts
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Salvage ?alue:!osts
0 9ccurs once at end of life of structure
0 )ifference 'et,een
5 *eoval cost
5 Salvage value
0 Best (uess 7alues
5 *eoval cost 1= K of >nitial !ost
5 Salvage ?alue 5 !oncrete - = K of >nitial !ost 5 Salvage ?alue 5 Structural Steel - 2 K of >nitial !ost
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Benefits fro a Bridge
6onetary Benefits
0 Tie savings to road users
0 Gro,th in econoic activity0 Saving of ?ehicular ,ear and tear
0 *eduction of accidents if a$$lica'le
E/a$le of Econoic #nalysis
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E/a$le of Econoic #nalysis
Carry out an conomic %nalysis of a Pro"osed Bridge given the following *ata:
Estiated #verage #nnualied )aily Traffic is 12=== ?ehicles $er )ay
Dith the &ollo,ing 6i/ of Traffic
!ars 1====
Trucs 1===
Buses 1===
#ssue that the Traffic Gro,th *ate 1.2 K
is Geoetric over the-ife S$an of the Bridge
Bridge -ife S$an F= years
The !onstruction !ost is 2==.= 6illion *s.
s$read over 2 years
The Trade and econoic 'enefits are 1=.= 6illion *s. $er year
estiated to 'e
#nnual Gro,th *ate of Trade Benefits 2.= Kis Geoetric at the rate of over the
-ife S$an of the Bridge
The Bridge ,ould *esult in Tie Saving of 1 hour
to *oad
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E/a$le of Econoic #nalysis
#ssue that the Bridge ,ould reuire4
#nnual 6aintenance =.=3 K of !onstruction !ost
6aHor *eha'ilitation after every 3= years 2=.= K of !onstruction !ost
Salvage ?alue of Piers and #'utents 2" K of !onstruction !ost
Salvage !ost is assued to 'e =.= K
#verage 9ccu$ancy 9f a Single !ar 3.= Passengers #verage 9ccu$ancy 9f a Single Truc 2.= Passengers
#verage 9ccu$ancy 9f a Single Bus "= Passengers
Calculate the Present 8orth2 -et Present 8orth2
Benefit to Cost Ratio of the Bridge at *iscount Rate %.= K
Calculate the Internal Rate of Return of the Bridge
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E/a$le of Econoic #nalysis
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!am"le of conomic %nalysis
E/a$le of Econoic #nalysis
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E/a$le of Econoic #nalysis
2=2( 1( =.343 %==== %==== 4F3F=== 13====== 1(F3F=== 2="( %23=4"4 1(((F=== 2=2F 1F =.32F3 %==== %==== 4FF(2== 132===== 1F=F(2== 1% "3F44" 1F=2(2==
2=2 1 =.3=F% %==== %==== 43%4== 134===== 1F33%4== 1F"1( "%"=4( 1F2(%4==
2=3= 2= =.2=1 %==== %==== 4F"%== 13%===== 1F"F"%== 1(4=% "31( 1F"2"%==
2=31 21 =.2(2( %==== %==== "=34F== 13F===== 1FF34F== 1%3%2 "13%24( 1F((4F==
2=32 22 =.2"%3 %==== %==== "=F4=== 14====== 1=F4=== 1"3F= 4F1"2 1=24===
2=33 23 =.241= %==== %==== "1332== 142===== 13332== 144"( 4%"F4F2 12(32==
2=34 24 =.22%" %==== %==== "1F24== 144===== 1"F24== 13"= 443"41% 1"224==
2=3" 2" =.212 %==== %==== "231%== 14%===== 1F31%== 12((" 422234 1((1%==
2=3% 2% =.2==1 %==== %==== "2F=F== 14F===== 2==F=F== 12==F 4=1FFF2 2==2=F==
2=3( 2( =.1FF1 %==== %==== "33==== 1"====== 2=33==== 112FF 3F24%3= 2=2(====
2=3F 2F =.1(%F %==== %==== "3(2== 1"2===== 2="(2== 1=%1= 3%3221 2="12==
2=3 2 =.1%%2 %==== %==== "42F4== 1"4===== 2=F2F4== (4 34%222 2=(%F4==
2=4= 3= =.1"%3 %==== 4======= 4==%==== "4((%== 1"%===== 21=((%== %2"%== 32343 71FF24==8
2=41 31 =.14% %==== %==== ""2%F== 1"F===== 2132%F== FF13 31324F% 212%%F==
2=42 32 =.13F1 %==== %==== ""(%=== 1%====== 21"(%=== F2F4 2(F43 21"1%===
2=43 33 =.12F %==== %==== "%2"2== 1%2===== 21F2"2== ((F( 2F32"4 21(%"2==
2=44 34 =.122= %==== %==== "%(44== 1%4===== 22=(44== (32= 2%2( 22=144==
2=4" 3" =.114( %==== %==== "(23%== 1%%===== 22323%== %FF1 2""" 222%3%==
2=4% 3% =.1=(F %==== %==== "((2F== 1%F===== 22"(2F== %4%F 24332"F 22"12F==
2=4( 3( =.1=13 %==== %==== "F22=== 1(====== 22F22=== %=F= 2312"14 22(%2===
2=4F 3F =.="2 %==== %==== "F(12== 1(2===== 23=(12== "(1" 21(4 23=112==
2=4 3 =.=F" %==== %==== "2=4== 1(4===== 2332=4== "3(2 2=F(%1 232%=4==
2="= 4= =.=F42 %==== %==== "%%== 1(%===== 23"%%== "="= 1F3%"% 23"=%==
2="1 41 =.=(1 %==== %==== %=1FF== 1(F===== 23F1FF== 4(4( 1FF43"1 23("FF==
2="2 42 =.=(44 %==== %==== %=%F=== 1F====== 24=%F=== 44%2 1(FF22 24==F=== 2="3 43 =.=% %==== %==== %11(2== 1F2===== 2431(2== 414 1%F"3 242"(2==
2="4 44 =.=%"( %==== %==== %1%%4== 1F4===== 24"%%4== 343 1%1423% 24"=%4==
2="" 4" =.=%1F %==== %==== %21"%== 1F%===== 24F1"%== 3(=% 1"32((4 24(""%==
2="% 4% =.="F1 %==== %==== %2%4F== 1FF===== 2"=%4F== 34F4 14""2(% 2"==4F==
2="( 4( =.="4% %==== %==== %314=== 1====== 2"314=== 32(" 13F1"%= 2"2"4===
2="F 4F =.="13 %==== %==== %3%32== 12===== 2""%32== 3=(F 13114"1 2""=32==
2=" 4 =.=4F2 %==== %==== %4124== 14===== 2"F124== 2F3 1244(F2 2"("24==
2=%= "= =.=4"3 %==== %==== %4%1%== 1%===== 2%=%1%== 2(2= 11F131 2%==1%==
E/a$le of Econoic #nalysis
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E/a$le of Econoic #nalysis
2=%1 "1 =.=42% %==== %==== %"1=F== 1EF===== 2%31=F== 2""( 112112% 2%2"=F==
2=%2 "2 =.=4=1 %==== %==== %"%==== 2======= 2%"%==== 24=3 1=%3F4= 2%"=====
2=%3 "3 =.=3(( %==== %==== %%=E2== 2=2===== 2%F=E2== 22"E 1==E3E3 2%(4E2== 2=%4 "4 =.=3"4 %==== %==== %%"F4== 2=4===== 2(="F4== 2124 E"(%4E 2%EEF4==
2=%" "" =.=333 %==== %==== %(=(%== 2=%===== 2(3=(%== 1EE% E=F4F= 2(24(%==
2=%% "% =.=313 %==== %==== %("%F== 2=F===== 2(""%F== 1F(% F%1(%4 2(4E%F==
2=%( "( =.=2E4 %==== %==== %F=%=== 21====== 2(F=%=== 1(%4 F1(3F4 2((4%===
2=%F "F =.=2(% %==== %==== %F""2== 212===== 2F=""2== 1%"F (("22( 2(EE"2==
2=%E "E =.=2%= %==== %==== %E=44== 214===== 2F3=44== 1""F (3"1F% 2F2444==
2=(= %= =.=244 %==== 4======= 4==%==== %E"3%== 21%===== 2F""3%== E(F=EF %E(1"E 711"=%4==8
2=(1 %1 =.=23= %==== %==== (==2F== 21F===== 2FF=2F== 13(( %%1=4E 2F(42F==
2=(2 %2 =.=21% %==== %==== (="2=== 22====== 2E="2=== 12E4 %2%(%2 2FEE2===
2=(3 %3 =.=2=3 %==== %==== (1=12== 222===== 2E3=12== 121( "E421= 2E2412==
2=(4 %4 =.=1E1 %==== %==== (1"=4== 224===== 2E""=4== 1144 "%33=F 2E4E=4==
2=(" %" =.=1(E %==== %==== (1EE%== 22%===== 2E(EE%== 1=(" "33E(" 2E(3E%==
2=(% %% =.=1%F %==== %==== (24FF== 22F===== 3==4FF== 1=11 "=%134 2EEFFF== 2=(( %( =.=1"F %==== %==== (2EF=== 23====== 3=2EF=== E"= 4(E(12 3=23F===
2=(F %F =.=14E %==== %==== (34(2== 232===== 3="4(2== FE3 4"4%3F 3=4F(2==
2=(E %E =.=14= %==== %==== (3E%4== 234===== 3=(E%4== F3E 43=F4% 3=(3%4==
2=F= (= =.=132 %==== %==== (44"%== 23%===== 31=4"%== (FE 4=F2(2 3=EF"%==
2=F1 (1 =.=124 %==== %==== (4E4F== 23F===== 312E4F== (42 3F%F"% 31234F==
2=F2 (2 =.=11% %==== %==== ("44=== 24====== 31"44=== %E( 3%%"41 314F4===
2=F3 (3 =.=1=E %==== %==== ("E32== 242===== 31(E32== %"" 34(2(= 31(332==
2=F4 (4 =.=1=3 %==== %==== (%424== 244===== 32=424== %1% 32FEE3 31EF24==
2=F" (" =.==E( %==== %==== (%E1%== 24%===== 322E1%== "(E 311%"F 32231%==
2=F% (% =.==E1 %==== %==== ((4=F== 24F===== 32"4=F== "44 2E"22= 324F=F==
2=F( (( =.==F" %==== %==== ((E==== 2"====== 32(E==== "12 2(E%32 32(3====
2=FF (F =.==F= %==== %==== (F3E2== 2"2===== 33=3E2== 4F1 2%4F"1 32E(E2==
2=FE (E =.==(" %==== %==== (FFF4== 2"4===== 332FF4== 4"2 2"=F3F 3322F4== 2=E= F= =.==(1 %==== %==== (E3(%== 2"%===== 33"3(%== 42" 23(""3 334((%==
2=E1 F1 =.==%( %==== %==== (EF%F== 2"F===== "======= F3(F%F== 3EE ""(F%F F3(2%F==
Total F>F2=>/2=AG FH=2=H2=GF
Total *iscounted Costs D F>F2=>/2=AG Rs0
Total *iscounted Benefits D FH=2=H2=GF Rs0
Present 8orth D F>F2=>/2=AG Rs0
-et Present 8orth D A2/==2AG/ Rs0
Benefit to Cost Ratio D = FA/