Lecture No. 1-AUpdate

7/24/2019 Lecture No. 1-AUpdate

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Bridge Engineering

Lecture 1 A

Planning of Bridges

Dr. Shahzad Rahman


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Bridge Planning

Traffic Studies

Hdrotechnical Studies

!eotechnical Studies

En"ironmental #onsiderations

Alternati"es for Bridge T$e

Economic %easi&ilit

Bridge Selection and Detailed Design


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Traffic Studies

Ri"er

#it #enter

'e( Bridge

'e( Road Lin)

E*isting 'et(or)


4/68

Traffic Studies

Traffic studies need to &e carried out toascertain the amount of traffic that (illutilize the Newor WidenedBridge

This is needed to determine Economic

%easi&ilit of the Bridge %or this Ser"ices of a Trans$ortation

Planner and or Traffic Engineer are

Re+uired Such Studies are done (ith hel$ of TrafficSoft(are such as TransCAD, EMME2 etc.


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Traffic Studies

Traffic Studies should $ro"ide follo(ing

information, Traffic on Bridge immediatel after o$ening

,Amount of traffic at "arious times during life of the

Bridge

, Traffic -i* i.e. num&er of motorcars &uses hea"

truc)s and other "ehicles

, Effect of the ne( lin) on e*isting road net(or)

, Predominant /rigin and Destination of traffic that (illuse the Bridge

, Strategic im$ortance of the ne(0im$ro"ed Bridge


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A thorough understanding of the ri"er andri"er regime is crucial to $lanning of Bridgeo"er a ri"er

Hdrotechnical Studies should include

To$ogra$hic Sur"e 2)m u$stream and2)m do(nstream for small ri"ers includingLongitudinal section and 34sections

%or &ig ri"ers 5)ms 60S and 2)ms D0Sshould &e sur"eed

Navigational Requirements


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Scale of the to$ogra$hic ma$

, 12777 for small ri"ers

, 15777 for large ri"ers

The High %lood Le"els and the

/&ser"ed %lood Le"el should &eindicated ma$

Sufficient 'um&er of *4sections

should &e ta)en and H%L and

/%L mar)ed on them

Ri"er Bed sur"eing (ould re+uire

soundings


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#atchment Area -a$

Scale recommended, 157777 or

, 125777

-a$ can &e madeusing !T Sheetsa"aila&le from Sur"eof Pa)istan

All Reser"oirs Rain!auges Stns. Ri"er!auge Stns. should&e mar)ed on ma$ Catchment of River Indus


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Ri"er #atchment Area


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River Catchment Boundaries with Tributaries


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River Catchment Boundaries with Sub-Basin Boundaries


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Hdrological Data

%ollo(ing Hdrological Data should &ecollected

Rainfall Data from Rain !auge Stations inthe #atchment Area

8sohetal -a$ of the #atchment Areasho(ing contours of Annual Rainfall

Hdrogra$hs of %loods at Ri"er !auge

Stations %lo( 9elocities

Sediment Load in Ri"er %lo( during floods


13/68

Hdrologic Data

Example of an ISOHET!" #!$


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Hdrologic Data

Example of River H%dro&raph


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Hdrologic Data

Example of a River H%dro&raph


16/68

Design %lood Le"els

AASHT/ !i"es %ollo(ing !uidelines for Estimating

Design %lood Le"els


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Design %lood Le"els

AASHT/ !i"es %ollo(ing !uidelines for Estimating

Design %lood Le"els


18/68

Design %lood Le"els

#A'AD8A' -8'8STR: /% TRA'SP/RTAT8/'

!i"es %ollo(ing !uidelines for Estimating Design %lood Le"els


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Design %lood Le"els


!i"es %ollo(ing !uidelines for Estimating Design %lood Le"els


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Design %lood Le"els


!i"es %ollo(ing !uidelines for Estimating %ree&oard Re+uirements

'REEBO!R( RE)*IRE#E+TS


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Estimating Design %lood

%lood Pea) Discharge at Stream or Ri"er Location

De$ends u$on #atchment Area #haracteristics

, Size and sha$e of catchment area

, 'ature of catchment soil and "egetation

, Ele"ation differences in catchment and &et(een catchmentand &ridge site location

Rainfall #limatic #haracteristics

, Rainfall intensit duration and its s$atial distri&ution

Stream0Ri"er #haracteristics, Slo$e of the ri"er

, Baseline flo( in the ri"er

, Ri"er Regulation %acilities0 Dams Barrages on the ri"er


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-ethods of Estimating Design %lood

1. Em$irical -ethods

2. %lood %re+uenc Analsis

;. Rational -ethod


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Em$irical -ethods of Pea) %lood Estimation

Em$irical %ormulae ha"e &een determined that

relate #atchment Area and other (eather orri"er $arameters to Pea) %lood Discharge

Po$ular %ormulae for 8ndo4Pa) are

, Dic)ens %ormula4/3

825AQ=< = Discharge in #usecs

A = #atchment Area in S+. -iles

, 8nglis %ormula

4

7000

+

=

A

AQ

, R"e>s %ormula 3/2ACQ=# = ?57 for areas (ithin 15 miles off coast

5@7 &et(een 15 , 177 miles off coast


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%lood %re+uenc Analsis -ethod

6sa&le at gauged sites (here ri"er

discharge data is a"aila&le for sufficient

time in $ast

%ollo(ing -ethods are commonl used

, 'ormal Distri&ution -ethod

, Log4'ormal Distri&ution

, Log4Plot !ra$hical -ethod


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%lood %re+uenc Analsis -ethod

'ormal Distri&ution -ethod

, Based on Assum$tion that e"ents follo( thesha$e of Standard 'ormal Distri&ution #ur"e


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'ormal Distri&ution -ethod

)

pro

babilit%

QTrMP KQQ +=


27/68

E*am$le of Pea) %lood Estimation %lood


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1C2 1; 27 4;.1 C. 1 1; 7.5? 1.5

1C; 1? 15 4.1 @@.7 1 1? 7.5 1.1

1C? 15 ;5 11.C 1?1.7 1 15 7.@; 1.@7

1C5 1@ ?5 21.C ?.5 1@ 1@ 7.@ 1.57

1C@ 1 2; 47.1 7.7 1@ 1 7.1 1.?1

1C 1 1? 4C.1 ;.; 15 1 7.5 1.;;

1C 1C 12 411.1 12;. 15 1C 7.C 1.2@

1CC 27 1 [email protected] ;.5 15 27 7.; 1.271CC7 21 25 1.C ;.5 1? 21 7. 1.1?

1CC1 22 15 4.1 @@.7 1? 22 7.C2 1.7C

1CC2 2; 21 42.1 ?.5 1; 2; 7.C@ 1.7?

1CC; 2? 15 4.1 @@.7 12 2? 1.77 1.77

Sam$le Pts = n = 2?

-ean


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8n$ut Return Period G:ears = Tr = 177 8n$ut 9alue

Pro&a&ilit = $ = 10 Tr 7.71%lood Estimate =


30/68

Log4'ormal Distri&ution -ethod

"o& ) or "n )

pro

babilit%

QTrMP KQQ lnlnln +=

ln


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Log4Plot -ethod

"o& $lot (ischar&e 8s Return $eriod

= 12.E2?LnG*H F 11.E;;

6

26

36

96

46

76

:6

;6

56

2 26 266Retun $eriod -rs/

(ischar&

e-cumec

/&ser"ed Discharge

Log. G/&ser"ed DischargeH

Trendline E


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Rational -ethod of Pea) %lood Estimation

Attem$ts to gi"e estimate of Design Discharge

ta)ing into account, The #atchment #haracteristics

, Rainfall 8ntensit

, Discharge #haracteristics of the #atchment

AICQ T=

< = Design Discharge

8T= A"erage rainfall intensit Gin0hr for some recurrence inter"al T

during that $eriod of time e+ual to Tc.Tc = Time of #oncentration

A = Area of the catchment in S+. miles

# = Runoff coefficientI fraction of runoff e*$ressed as a

dimensionless decimal fraction that a$$ears as surface runoff

from the contri&uting drainage area.

R ti l - th d f P ) %l d E ti ti


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Rational -ethod of Pea) %lood Estimation

Time of #oncentration can &e estimated using

Barns& Jilliams %ormula (hich is (idel used& 6S High(a Engineers

2.01.0

9.0

SA

LTc=

L = Length of Stream in -iles

A = Area of the catchment in S+. miles

S = A"erage grade from source to site in $ercent

R ti l % l R ff # ffi i t


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Rational %ormula , Runoff #oefficient

Area #haracteristic Run4off #oefficient #

Stee$ Bare Roc) 7.C7Stee$ Roc) (ith Joods 7.7

Plateau (ith light co"er 7.7

Densel &uilt4u$ areas 7.C7 , 7.7

Residential areas 7.7 , 7.57

Stiff #lae soils 7.57

Loam 7.?7 , 7.;7

Su&ur&s (ith gardens 7.;7Sand soils 7.1 , 7.27

Kungle area 7.17 , 7.25

Par)s La(ns %ields 7.25 4 7.57

! t h i l St di


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!eotechnical Studies should $ro"ide the

follo(ing 8nformation

The t$es of Roc)s Di$s %aults and

%issures

Su&soil !round Jater Le"el


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E*am$le !eological Profile

#ross section of the soil on the route of the Paris

The diagram a&o"e sho(s the crossing o"er the Seine "ia the Bir Ha)eim &ridge

and the limestone +uarries under Trocadro

! t h i l St di


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Example? Cross section of the @ansas RiverA west of Silver "a,eA @ansas

T$ical Borehole

S i i # id ti


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Seismic #onsiderations

Source? Buildin& Code of $a,istan

T t i S tti f th B id Sit


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Tectonic Setting of the Bridge Site

Source? eolo&ical Surve% of $a,istan

En ironmental #onsiderations


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En"ironmental #onsiderations

8m$act on %ollo(ing %eatures of En"ironment need toconsidered, Ri"er Ecolog (hich includes

-arine Life Jildlife along ri"er &an)s Ri"er&ed %lora and fauna along ri"er &an)s

, 8m$act u$on d(ellings along the ri"er if an, 8m$act u$on ur&an en"ironment if the &ridge in an

ur&an area, Possi&le im$act u$on archeological sites in "icinit

Bridge Economic %easi&ilit


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Bridge Economic %easi&ilit

Economic Analsis is Re+uired at

%easi&ilit Stage to Mustif e*$enditure of$u&lic or $ri"ate funds

A Bridge is the most e*$ensi"e $art of a

road trans$ortation net(or)

T$es of Economic Analses

, #ost Benefit Ratio Analsis

, 8nternal Rate of Return G8RR Analsis

Bridge Economic Analsis0


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dge co o c a s s0Life #cle #ost Analsis GL##A

Time

CostsStream

BenefitsStream

C

onstruction

S

ta&e

$roect "ife$roectStart

(a

te

$

roect"ife

E

nd

(ate

Salv

a&e

8alu

e

ProMect #ost Benefit Analsis


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ProMect #ost Benefit Analsis

The o&Mecti"e of L##A is to

, Estimate the costs associated (ith the ProMect during #onstructionan its ser"ice life. These include routine maintenance costs F-aMor Reha& #osts

, Estimate the Benefits that (ill accrue from the ProMect includingtime sa"ings to road users &enefits to &usiness acti"ities etc.

, Bring do(n the costs and &enefits to a common reference $t. intime i.e. Must $rior to start of $roMect Gdecision ma)ing time

, %acilitate decision ma)ing a&out economic feasi&ilit &calculating +uantifia&le ardstic)s such as Benefit to #ost RatioGB#R and 8nternal Rate of Return G8RR

'ote Sal"age 9alue ma &e ta)en as a Benefit

This includes cost of the Right4of4Ja and su&structure

Jhat is Life #cle #ostN


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Jhat is Life #cle #ostN

An economic analsis $rocedure that uses

engineering in$uts

#om$ares com$eting alternati"es

considering all significant costs

E*$resses results in e+ui"alent dollars

G$resent (orth

Time Period of Analsis


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'ormall e+ual for all alternati"es

Should include at least one maMor

reha&ilitation

'eeded to ca$ture the true economic

&enefit of each alternati"e

Bridge design toda is &ased on a

$ro&a&ilistic model of 177 ears



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g Life #cle #ost Analsis GL##A

Time

Cos

tsStream

Be

nefitsStream

Construction

Sta&e $roect "ife$

roect

Start(ate

$roect

"ife

End

(ate

S

alva&e

8

alue

Costs and Benefits Chan&e over the life of the $roect

!mount of #one%1Benefit accrued some time in future is worth less interms of Toda%Ds mone%

Same is the case with the benefits accrued over time

The $roblem now is as to How to find the orth of a 'inancial !mount in'uture in terms of Toda%Ds #one%

This is accomplished b% usin& the instrument of F(ISCO*+T R!TEG

$roblem?



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g Life #cle #ost Analsis GL##A

(ISCO*+T R!TE?

The annual effective discount rate is the annual interest divided b% the capitalincludin& that interestA which is the interest rate divided b% 266 plus theinterest rate. It is the annual discount factorto be applied to the future cashflowA to find the discountA subtracted from a future value to find the valueone %ear earlier.

'or exampleA suppose there is an investment made of >7 and pa%s 266 in a

%earJs time. The discount rate accordin& the &iven definition is?

%0.5100

95100=

==dRateDiscount

%26.595

95100 === iRateInterest

Interest Rate is calculated as >7 as Base

Interest Rate and (iscount Rate are Related as 'ollows

2

1

ii

i

idRateDiscount

+

==

Discount Rate
http://en.wikipedia.org/wiki/Discount_factorhttp://en.wikipedia.org/wiki/Discount_factor


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Discount Rate Thus Discount Rate is that rate (hich can &e

used to o&tain the Present 9alue of -one that

is s$ent or collected in future

+et $resent value of Cost incurred 0 Co 0 2 - d/nCn

In ear n

+et $resent value of Cost incurred 0 Bo 0 2 - d/nBn

In ear n

Time

Costs

Stream

Benefits

Stream

$roect

"ife

$roect

Start(ate

ear nCn

Bn

Cost1 Benefit $roectedBac,ward

Bo

Co

Jhat Discount Rate to 6seN


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Jhat Discount Rate to 6seN

A first estimate of a$$ro$riate Discount ratecan &e made as follo(s

Estimate of

Discount Rate = %ederal Ban) Lending Rate , A"erage Long4term 8nflation Rate

+ote? B% subtractin& the Inflation Rate in arrivin& at a (iscount Rate theeffect of Inflation can be removed from consideration durin&

Economic !nal%sis

The (iscount Rate after subtractin& the Inflation Rate is alsoReferred to as the Real Discount Rate

Govt. of Pakistan uses a Discount Rate of 6-7% for

econoic anal!sis

"sian Develo#ent $ank uses a Discount rate of 2% for

evaluation of #ro&ects

Discount Rate is less t'an t'e Real interest Rate as Governents

(o not take a #urel! coercial vie) of an infrastructure #ro&ect

#ost #onsiderations


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#ost #onsiderations

Maintenance andInspectionCost

Initial Cost

Costs

Present Worth

Years

Rehabilitation Cost

Salvage Value

Salvage Costs

#ost Benefit Ratio


51/68

#ost Benefit Ratio

%ormula for #ost

Benefit Ratio

Benefit To Cost Ratio 0

=L

n

Ln

Cnd

Bnd

0

0

)1(

)1(

CostsofValuePresent

BenefitsofValuePresent

Jhere L = Life S$an of the ProMect in :ears

d = Discount Rate

Bn = Benefit in ear n #n = #ost incurred in ear n

'et Present Jorth0 9alue


52/68

'et Present Jorth0 9alue

'et Present Jorth0 9alue = 'PJ or 'P9

is defined as follo(s

+$ 0 +$8 0 $resent 8alue of Benefits K $resent 8alue of Costs

+ote? If a +umber of alternatives are bein& comparedA the alternativethat has the hi&hest +et $resent orth is the preferable one andwill also have the hi&her Benefit to Cost Ratio

Jhat is 8nternal Rate of Return G8RR


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Jhat is 8nternal Rate of Return G8RR

8RR ma &e defined as that Discount Rate

at (hich the Benefit to #ost Ratio GB#Rof a ProMect &ecomes e*actl 1.7

8t is a &etter measure of economic "ia&ilit

of a $roMect com$ared to Benefit to #ostRatio

8t is a good indicator of ho( much inflation

increase and interest rate hi)e a $roMectcan tolerate and still &e "ia&le

Present Jorth %actor


54/68

Present Jorth %actor

pwf = Present Worth Factor for discount rate d and year nd = Discount rate

n = Number of year when the cost/ benet will occur

n

dpwf )1( =

!lternate 'ormula *suall% !dopted/

( ) ndpwf

+=

1

1

Present Jorth Analsis


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Present Jorth Analsis

Discounts all future costs and benets to the

present:

t=LPW = F ! 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



56/68


'ormall e+ual for all alternati"es

Should include at least one maMor reha&ilitation

, 'eeded to ca$ture the true economic &enefit of each

alternati"e

Bridge design toda is &ased on a $ro&a&ilistic model of

177 ears

-aintenance #osts


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-aintenance #osts

Annual cost associated (ith the u$)ee$ of the

structure 8nformation is difficult to o&tain for a gi"en

$roMect

#ost "aries on the &asis of size of the structure

Gs+ft Best !uess 9alues

, %re+uenc 4 Annual

, #oncrete 7.75 O of 8nitial #ost, Structural Steel 7.75 O of 8nitial #ost

8ns$ection #osts


58/68

8ns$ection #osts

Should &e ta)en for all alternati"es $refera&l

e"er t(o ears #ost "aries on the &asis of size of the structure

Gs+ft and & construction material

Best !uess 9alues, %re+uenc 4 Biannual

, #oncrete 7.15 O of 8nitial #ost

, Structural Steel 7.27 O of 8nitial #ost

%uture Painting #osts


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%uture Painting #osts

/nl a$$lies to structural steel structures &ut

e*cludes (eathering steel Should occur e"er 27 ears

#ost "aries on the &asis of size of the structure

Gs+ft Best !uess 9alues

, %re+uenc , e"er 27 ears


, Structural Steel .7 O of 8nitial #ost


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%uture Reha&ilitation #osts

The fre+uenc is not onl a function of time &ut also thegro(ing traffic "olume and the structural &eam sstem

#ost "aries on the &asis of size of the structure Gs+ft andstructural &eam sstem

Best !uess 9alues

, %re+uenc

%irst occurrence , #oncrete ?7 ears

%irst occurrence , Structural Steel ;5 ears

Annual traffic gro(th rate .5 O Gshortens reha&ccles


, Structural Steel 22.7 O of 8nitial #ost

Sal"age 9alue0#osts


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Sal"age 9alue0#osts

/ccurs once at end of life of structure

Difference &et(een

, Remo"al cost

,Sal"age "alue

Best !uess 9alues

, Remo"al cost 17 O of 8nitial #ost

, Sal"age 9alue , #oncrete 4 7 O of 8nitial #ost, Sal"age 9alue , Structural Steel 4 2 O of 8nitial #ost

Benefits from a Bridge


62/68

Benefits from a Bridge

-onetiza&le Benefits

Time sa"ings to road users

!ro(th in economic acti"it

Sa"ing of 9ehicular (ear and tear

Reduction of accidents if a$$lica&le

/ther 'on4-onetiza&le Benefits Strategic Benefits

E*am$le of Economic Analsis


63/68


Carr% out an Economic !nal%sis of a $roposed Brid&e &iven the followin& (ata?

Estimated A"erage Annualized Dail Traffic is = 12777 9ehicles $er Da

Jith the %ollo(ing -i* of Traffic

#ars = 17777

Truc)s = 1777

Buses = 1777

Assume that the Traffic !ro(th Rate = 1.2 O

is !eometric o"er theLife S$an of the Bridge

Bridge Life S$an = 7 ears

The #onstruction #ost is = 277.7 -illion Rs.

s$read o"er 2 ears

The Trade and economic &enefits are = 17.7 -illion Rs. $er ear

estimated to &e

Annual !ro(th Rate of Trade Benefits = 2.7 Ois !eometric at the rate of o"er the

Life S$an of the Bridge

The Bridge (ould Result in Time Sa"ing of = 1 hour

to Road 6sers

A"erage Time 9alue of Single Road 6ser = 57.7 Rs. Per Hour



64/68


Assume that the Bridge (ould re+uire1

Annual -aintenance = 7.7; O of #onstruction #ost

-aMor Reha&ilitation after e"er ;7 ears = 27.7 O of #onstruction #ost

Sal"age 9alue of Piers and A&utments = 25 O of #onstruction #ost

Sal"age #ost is assumed to &e = 7.7 O

A"erage /ccu$anc /f a Single #ar = ;.7 Passengers

A"erage /ccu$anc /f a Single Truc) = 2.7 Passengers

A"erage /ccu$anc /f a Single Bus = 57 Passengers

Calculate the $resent EorthA +et $resent EorthA

Benefit to Cost Ratio of the Brid&e at (iscount Rate = @.7 O

Calculate the Internal Rate of Return of the Brid&e



65/68


Benefits in Time Savin& *pon Brid&e Openin&

8ehicle

T%pe *u+er ,ccu#anc! ie aving ie /alue $enefit

(ersons! ("rs! (Rs.#er $our! (Rs.!#ars 17777 ;.7 1.7 57.7 1577777

Buses 1777 57.7 1.7 57.7 2577777

Truc)s 1777 2.7 1.7 57.7 177777

Total Benefit $er ear 0 4A266A666

Assumed to then !ro( at !eometricall at

the Rate of 1.2O $er ear



66/68


!ctual ear ear +o.

$resent orth

'actor -$'/

ons ruc on

#aintenance

Cost Rehab Cost Total Costs

ene ?

Time

Savin&

ene ?

Trade1

Economic

Salva&e

Benefit

Total

Benefits

o a

(iscounted

Costs

o a

(iscounted

Benefits +et Benefit

G14dn GRs. GRs. GRs. GRs. GRs. GRs. GRs. GRs. GRs. GRs.

2717 7 1.7777 177777777 177777777 4 4 177777777 4 G177777777

2711 1 7.C?77 177777777 177777777 4 C?777777 4 G177777777

2712 2 7.;@ @7777 @7777 ?177777 17777777 1?177777 5;71@ 12?5@7 1?7?7777

271; ; 7.;7@ @7777 @7777 ?1?C277 17277777 1?;?C277 ?C;5 11C121@ 1?2C277271? ? 7.7 @7777 @7777 ?1C?77 17?77777 1?5C?77 ?@?5 11;C@@ 1?5;?77

2715 5 7.;;C @7777 @7777 ?2?@77 17@77777 1??@77 ??7;? 17C@1; 1?@77

271@ @ 7.@CC @7777 @7777 ?2C@77 1777777 157C@77 ?1;C2 17?1?2@ 157;@77

271 7.@?5 @7777 @7777 ?;?@777 11777777 15;?@777 ;C7C CC515; 152@777

271 7.@7C@ @7777 @7777 ?;C5277 11277777 155C5277 ;@5? C57@;57 155;5277

271C C 7.5;7 @7777 @7777 ?????77 11?77777 15???77 ;?;7 C75C 15??77

2727 17 7.5;@ @7777 @7777 ??C;@77 11@77777 1@7C;@77 ;2;1 @@25@ 1@7;;@77

2721 11 7.57@; @7777 @7777 ?5?277 1177777 1@;?277 ;7; 2?;;7 1@2277

2722 12 7.?5C @7777 @7777 ?5C2777 12777777 1@5C2777 2555 C@?7 1@5;2777

272; 1; 7.??? @7777 @7777 ?@?1277 12277777 1@?1277 2@?2 5;?1@5 1@1277

272? 1? 7.?275 @7777 @7777 ?@C7?77 12?77777 17C7?77 252;1 1@C17 17;7?772725 15 7.;C5; @7777 @7777 ?;C@77 12@77777 1;;C@77 2;1 @5?272 12C@77

272@ 1@ 7.;1@ @7777 @7777 ?77 1277777 1577 222C? @5;55?@ 15277



67/68


!ctual ear ear +o.

$resent orth

'actor -$'/

Construction1

#aintenance


Benefit?

Time

Savin&

Benefit?

Trade1

Economic

Salva&e

Benefit

Total

Benefits

Total

(iscounted

Costs

Total

(iscounted


G14dHPn GRs.H GRs.H GRs.H GRs.H GRs.H GRs.H GRs.H GRs.H GRs.H GRs.H

272 1 7.;?C; @7777 @7777 ?;777 1;777777 1;777 27C5 @2;7?5? 1777

272 1 7.;2; @7777 @7777 ?277 1;277777 17277 1C@CC 5C;??5 172277

272C 1C 7.;7@ @7777 @7777 ?C;@?77 1;?77777 1;;@?77 151 5@5C7? 12@?77

27;7 27 7.2C71 @7777 @7777 ?C5@77 1;@77777 155@77 1?7@ 5;C1CC 1525@77

27;1 21 7.22 @7777 @7777 57;?77 1;77777 1;?77 1@;@2 51;@2? 1?77

27;2 22 7.25@; @7777 @7777 57?777 1?777777 1C7?777 15;7 ?C1C52 1C72?777

27;; 2; 7.2?17 @7777 @7777 51;;277 1?277777 1C;;;277 1??5 ?@5?2 1C2;277

27;? 2? 7.22@5 @7777 @7777 512?77 1??77777 1C52?77 1;5C7 ??;5?1@ 1C522?77

27;5 25 7.212C @7777 @7777 52;1@77 1?@77777 1C;1@77 125 ?222;?C 1C1@77

27;@ 2@ 7.2771 @7777 @7777 52777 1?77777 277777 1277 ?712 2772777

27; 2 7.11 @7777 @7777 5;;7777 15777777 27;;7777 112 ;2?@;7 2727777

27; 2 7.1@ @7777 @7777 5;C277 15277777 275C277 17@17 ;@;C221 2751C277

27;C 2C 7.1@@2 @7777 @7777 5?2?77 15?77777 272?77 CC? ;?@22C2 27@?77

27?7 ;7 7.15@; @7777 ?7777777 ?77@7777 5?@77 15@77777 217@77 @25C@77 ;2C;?C; G1C2?7727?1 ;1 7.1?@C @7777 @7777 552@77 1577777 21;2@77 1; ;1;2?@ 212@@77

27?2 ;2 7.1;1 @7777 @7777 55@777 1@777777 215@777 2? 2CC?; 2151@777

27?; ;; 7.12C @7777 @7777 5@25277 1@277777 2125277 2;25?C 21@5277

27?? ;? 7.1227 @7777 @7777 5@??77 1@?77777 227??77 ;27 2@C2CC 2271??77

27?5 ;5 7.11? @7777 @7777 52;@77 1@@77777 22;2;@77 @1 255CCC5 222@;@77

27?@ ;@ 7.17 @7777 @7777 5277 1@77777 225277 @?@ 2?;;25 2251277

27? ; 7.171; @7777 @7777 522777 1777777 2222777 @77 2;1251? 22@2777

27? ; 7.7C52 @7777 @7777 51277 1277777 2;71277 515 21C?CC 2;711277

27?C ;C 7.7C5 @7777 @7777 5C27?77 1?77777 2;;27?77 5;2 27C@1 2;2@7?77

2757 ?7 7.7?2 @7777 @7777 5C@C@77 1@77777 2;5@C@77 5757 1C;@5@ 2;57C@77

2751 ?1 7.7C1 @7777 @7777 @7177 177777 2;177 ?? 1?;51 2;577

2752 ?2 7.7?? @7777 @7777 @7@777 1777777 2?7@777 ??@2 1C22 2?77777275; ?; 7.7@CC @7777 @7777 @11277 1277777 2?;1277 ?1C? 1@CC5; 2?25277

275? ?? 7.7@5 @7777 @7777 @1@@?77 1?77777 2?5@@?77 ;C?; 1@1?2;@ 2?57@?77

2755 ?5 7.7@1 @7777 @7777 @215@77 1@77777 2?15@77 ;7@ 15;2? 2?55@77

275@ ?@ 7.751 @7777 @7777 @2@?77 177777 257@?77 ;?? 1?552@ 2577?77

275 ? 7.75?@ @7777 @7777 @;1?777 1C777777 25;1?777 ;25 1;15@7 2525?777

275 ? 7.751; @7777 @7777 @;@;277 1C277777 255@;277 ;7 1;11?51 2557;277

275C ?C 7.7?2 @7777 @7777 @?12?77 1C?77777 2512?77 2C; 12??2 2552?77

27@7 57 7.7?5; @7777 @7777 @?@1@77 1C@77777 2@7@1@77 227 111;C1 2@771@77



68/68

a $ e o co o c a s s

27@1 51 7.7?2@ @7777 @7777 @51777 1C77777 2@;1777 255E 112112@ 2@25777

27@2 52 7.7?71 @7777 @7777 @5@7777 27777777 2@5@7777 2?7; 17@;?7 2@577777

27@; 5; 7.7;EE @7777 @7777 @@7C277 27277777 2@7C277 225C 177C;C; 2@E?C27727@? 5? 7.7;5? @7777 @7777 @@5?77 27?77777 2E75?77 212? C5E@?C 2@CC?77

27@5 55 7.7;;; @7777 @7777 @E7E@77 27@77777 2E;7E@77 1CC@ C7?7 2E2?E@77

27@@ 5@ 7.7;1; @7777 @7777 @E5@77 2777777 2E55@77 1E@ @1E@? 2E?C@77

27@E 5E 7.72C? @7777 @7777 @7@777 21777777 2E7@777 1E@? 1E;? 2EE?@777

27@ 5 7.72E@ @7777 @7777 @55277 21277777 2755277 1@5 EE522E 2ECC5277

27@C 5C 7.72@7 @7777 @7777 @C7??77 21?77777 2;7??77 155 E;51@ 22???77

27E7 @7 7.72?? @7777 ?7777777 ?77@7777 @C5;@77 21@77777 255;@77 CE7C @CE15C G1157@?77H

27E1 @1 7.72;7 @7777 @7777 E77277 2177777 27277 1;EE @@17?C 2E?277

27E2 @2 7.721@ @7777 @7777 E752777 22777777 2C752777 12C? @2@E@2 2CC2777

27E; @; 7.727; @7777 @7777 E171277 22277777 2C;71277 121E 5C?217 2C2?1277

27E? @? 7.71C1 @7777 @7777 E157?77 22?77777 2C557?77 11?? 5@;;7 2C?C7?77

27E5 @5 7.71EC @7777 @7777 E1CC@77 22@77777 2CECC@77 17E5 5;;CE5 2CE;C@77

27E@ @@ 7.71@ @7777 @7777 E2?77 2277777 ;77?77 1711 57@1;? 2CC7727EE @E 7.715 @7777 @7777 E2C777 2;777777 ;72C777 C57 ?ECE12 ;72;777

27E @ 7.71?C @7777 @7777 E;?E277 2;277777 ;75?E277 C; ?5?@; ;7?E277

27EC @C 7.71?7 @7777 @7777 E;C@?77 2;?77777 ;7EC@?77 ;C ?;7?@ ;7E;@?77

277 E7 7.71;2 @7777 @7777 E??5@77 2;@77777 ;17?5@77 EC ?72E2 ;7C5@77

271 E1 7.712? @7777 @7777 E?C?77 2;77777 ;12C?77 E?2 ;@5@ ;12;?77

272 E2 7.711@ @7777 @7777 E5??777 2?777777 ;15??777 @CE ;@@5?1 ;1??777

27; E; 7.717C @7777 @7777 E5C;277 2?277777 ;1EC;277 @55 ;?E2E7 ;1E;;277

27? E? 7.717; @7777 @7777 E@?2?77 2??77777 ;27?2?77 @1@ ;2CC; ;1C2?77

275 E5 7.77CE @7777 @7777 E@C1@77 2?@77777 ;22C1@77 5EC ;11@5 ;22;1@77

27@ E@ 7.77C1 @7777 @7777 EE?777 2?77777 ;25?777 5?? 2C5227 ;2?777

27E EE 7.775 @7777 @7777 EEC7777 25777777 ;2EC7777 512 2EC@;2 ;2E;7777

27 E 7.777 @7777 @7777 E;C277 25277777 ;;7;C277 ?1 2@?51 ;2CEC277

27C EC 7.77E5 @7777 @7777 E?77 25?77777 ;;2?77 ?52 257; ;;22?7727C7 7 7.77E1 @7777 @7777 EC;E@77 25@77777 ;;5;E@77 ?25 2;E55; ;;?EE@77

27C1 1 7.77@E @7777 @7777 EC@77 2577777 57777777 ;E@77 ;CC 55E@ ;E2@77

Total 363A264A2>5 3:2A72:A253

!ctual ear ear +o.

$resent orth

'actor -$'/

Construction1

#aintenance


Benefit?

Time

Savin&

Benefit?

Trade1

Economic

Salva&e

Benefit

Total

Benefits

Total

(iscounted

Costs

Total

(iscounted


G14dHPn GRs.H GRs.H GRs.H GRs.H GRs.H GRs.H GRs.H GRs.H GRs.H GRs.H

Total (iscounted Costs 0 363A264A2>5 Rs.

Total (iscounted Benefits 0 3:2A72:A253 Rs.

$resent orth 0 363A264A2>5 Rs.

+et $resent orth 0 7>A422A>54 Rs.

Lecture No. 1-AUpdate

Documents

Transcript of Lecture No. 1-AUpdate