bridge engineering lecture 1 a planning of bridges dr. shahzad rahman

Bridge Engineering Lecture 1 A

Planning of Bridges

Dr. Shahzad Rahman

Bridge Planning

• Traffic Studies• Hydrotechnical Studies• Geotechnical Studies• Environmental Considerations• Alternatives for Bridge Type• Economic Feasibility • Bridge Selection and Detailed Design

Traffic Studies

River

City Center

New Bridge

New Road Link

Existing Network

Traffic Studies

• Traffic studies need to be carried out to ascertain the amount of traffic that will utilize the New or Widened Bridge

• This is needed to determine Economic Feasibility of the Bridge

• For this Services of a Transportation Planner and or Traffic Engineer are Required

• Such Studies are done with help of Traffic Software such as TransCAD, EMME2 etc.

Traffic Studies

• Traffic Studies should provide following information– Traffic on Bridge immediately after opening– Amount of traffic at various times during life of the

Bridge– Traffic Mix i.e. number of motorcars, buses, heavy

trucks and other vehicles – Effect of the new link on existing road network– Predominant Origin and Destination of traffic that will

use the Bridge– Strategic importance of the new/improved Bridge

Hydrotechnical Studies

• A thorough understanding of the river and river regime is crucial to planning of Bridge over a river

• Hydrotechnical Studies should include:• Topographic Survey 2km upstream and

2km downstream for small rivers including Longitudinal section and X-sections

• For big rivers 5kms U/S and 2kms D/S should be surveyed

• Navigational Requirements


• Scale of the topographic map – 1:2000 for small rivers– 1:5000 for large rivers

• The High Flood Levels and the Observed Flood Level should be indicated map

• Sufficient Number of x-sections should be taken and HFL and OFL marked on them

• River Bed surveying would require soundings


• Catchment Area Map• Scale recommended

– 1:50,000 or– 1:25,000

• Map can be made using GT Sheets available from Survey of Pakistan

• All Reservoirs, Rain Gauges Stns., River Gauge Stns., should be marked on map Catchment of River Indus


River Catchment Area


River Catchment Boundaries with Tributaries


River Catchment Boundaries with Sub-Basin Boundaries

Hydrological Data

• Following Hydrological Data should be collected:

• Rainfall Data from Rain Gauge Stations in the Catchment Area

• Isohyetal Map of the Catchment Area showing contours of Annual Rainfall

• Hydrographs of Floods at River Gauge Stations

• Flow Velocities • Sediment Load in River Flow during floods

Hydrologic Data

Example of an ISOHYETAL MAP

Hydrologic Data

Example of River Hydrograph

Hydrologic Data

Example of a River Hydrograph

Design Flood Levels

• AASHTO Gives Following Guidelines for Estimating Design Flood Levels

Design Flood Levels

• CANADIAN MINISTRY OF TRANSPORTATION

Gives Following Guidelines for Estimating Design Flood Levels

Design Flood Levels

• CANADIAN MINISTRY OF TRANSPORTATION

Gives Following Guidelines for Estimating Freeboard Requirements

FREEBOARD REQUIREMENTS

Estimating Design Flood

• Flood Peak Discharge at Stream or River Location Depends upon:

• Catchment Area Characteristics– Size and shape of catchment area

– Nature of catchment soil and vegetation

– Elevation differences in catchment and between catchment and bridge site location

• Rainfall Climatic Characteristics– Rainfall intensity duration and its spatial distribution

• Stream/River Characteristics– Slope of the river

– Baseline flow in the river

– River Regulation Facilities/ Dams, Barrages on the river

Methods of Estimating Design Flood

1. Empirical Methods

2. Flood Frequency Analysis

3. Rational Method

Empirical Methods of Peak Flood Estimation

• Empirical Formulae have been determined that relate Catchment Area and other weather or river parameters to Peak Flood Discharge

• Popular Formulae for Indo-Pak are:– Dickens Formula

4/3825 AQ Q = Discharge in CusecsA = Catchment Area in Sq. Miles

– Inglis Formula4

7000

A

AQ

– Ryve’s Formula 3/2ACQ C = 450 for areas within 15 miles off coast 560 between 15 – 100 miles off coast

Flood Frequency Analysis Method

• Usable at gauged sites where river discharge data is available for sufficient time in past

• Following Methods are commonly used– Normal Distribution Method– Log-Normal Distribution– Log-Plot Graphical Method

Flood Frequency Analysis Method

• Normal Distribution Method– Based on Assumption that events follow the

shape of Standard Normal Distribution Curve

Normal Distribution Method

Q

pro

bab

ilit

y

QTrMP KQQ

QP = Discharge Associated with Probability of Occurrence PQM = Mean Discharge over the data setσQ = Standard Deviation of the Discharge data setKTr = Frequency factor corresponding to Probability of Occurrence P

Example of Peak Flood Estimation Flood Example Flood Frequency Analysis Normal Distribution Method

Actual Year Year Max Flood Xi - Xavg (Xi - Xavg) 2

Ranked Flow (Decending

Order) Rank Probability Return Period(No.) Q R P = R/n Tr = 1/P

(cumecs) (cumecs) (cumecs2) (yrs)1970 1 26 2.9 8.3 48 1 0.04 24.001971 2 42 18.9 356.3 45 2 0.08 12.001972 3 17 -6.1 37.5 42 3 0.13 8.001973 4 35 11.9 141.0 35 4 0.17 6.001974 5 16 -7.1 50.8 35 5 0.21 4.801975 6 32 8.9 78.8 32 6 0.25 4.001976 7 48 24.9 618.8 26 7 0.29 3.431977 8 14 -9.1 83.3 25 8 0.33 3.001978 9 13 -10.1 102.5 23 9 0.38 2.671979 10 21 -2.1 4.5 21 10 0.42 2.401980 11 18 -5.1 26.3 21 11 0.46 2.181981 12 16 -7.1 50.8 20 12 0.50 2.00

Example of Peak Flood Estimation Flood

1982 13 20 -3.1 9.8 18 13 0.54 1.851983 14 15 -8.1 66.0 17 14 0.58 1.711984 15 35 11.9 141.0 17 15 0.63 1.601985 16 45 21.9 478.5 16 16 0.67 1.501986 17 23 -0.1 0.0 16 17 0.71 1.411987 18 14 -9.1 83.3 15 18 0.75 1.331988 19 12 -11.1 123.8 15 19 0.79 1.261989 20 17 -6.1 37.5 15 20 0.83 1.201990 21 25 1.9 3.5 14 21 0.88 1.141991 22 15 -8.1 66.0 14 22 0.92 1.091992 23 21 -2.1 4.5 13 23 0.96 1.041993 24 15 -8.1 66.0 12 24 1.00 1.00

Sample Pts = n = 24Mean Qm = M 23.125Sum of Squares = 2638.6

Variance = 114.72

Standard Deviation = 10.71

Coefficient of Variation = Cv = σ/M = 0.463Skewness Coefficient = SC = 3 Cv + Cv3 = 1.49Input Return Period (Years) = Tr = 100 Input ValueProbability = p = 1/ Tr 0.01Flood Estimate = Qt =

22 )(1

1xx

nS j

)1(

2

nV S

V

Actual Year Year Max Flood Xi - Xavg (Xi - Xavg) 2

Ranked Flow (Decending

Order) Rank Probability Return Period(No.) Q R P = R/n Tr = 1/P

(cumecs) (cumecs) (cumecs2) (yrs)

Example of Peak Flood Estimation Flood

Input Return Period (Years) = Tr = 100 Input ValueProbability = p = 1/ Tr 0.01Flood Estimate = Qt =

w = 3.03485528

KTr = 2.32678649Flood Estimate = Qt =

Qt = 48.05 Cumecs

KtrQQmt

1

10

1 10 100

Series1

Log. (Series1)

wwwK

w

ww

Tr 32

2

001308.0189269.0532788.11

010328.0802853.051557.2

pw

2

1ln

Log-Normal Distribution Method

Log Q or Ln Q

pro

bab

ilit

y

QTrMP KQQ lnlnln

lnQP = Log of Discharge Associated with Probability of Occurrence PlnQM = Mean of Log Discharge over the data setσlnQ = Standard Deviation of the Log of Discharge data setKTr = Frequency factor corresponding to Probability of Occurrence P QP = Antilog (ln QP) = Discharge Associated with Probability of Occurrence P

• Yields better Results Compared to Normal Distribution Method

Example of Peak Flood Estimation FloodLog-Plot Method

Log Plot Discharge Vs Return Period

y = 12.724Ln(x) + 11.733

0

10

20

30

40

50

60

70

80

1 10 100Retun Period (Yrs)

Dis

ch

arg

e (

cu

me

cs

)

Observed Discharge

Log. (Observed Discharge)

Trendline Equation is

Qt = 12.724 Ln(Tr) + 11.213

For Return Period Tr = 50 yrsQt = 12.724 Ln (50) + 11.213 = 61.0 cumecsFor Return Period Tr = 100 yrsQt = 12.724 Ln (100) + 11.213 = 69.8 cumecs

Rational Method of Peak Flood Estimation

• Attempts to give estimate of Design Discharge taking into account:– The Catchment Characteristics– Rainfall Intensity– Discharge Characteristics of the Catchment

AICQ TQ = Design DischargeIT = Average rainfall intensity (in/hr) for some recurrence interval, T during that period of time equal to Tc.Tc = Time of Concentration A = Area of the catchment in Sq. milesC = Runoff coefficient; fraction of runoff, expressed as a dimensionless decimal fraction, that appears as surface runoff from the contributing drainage area.

Rational Method of Peak Flood Estimation

• Time of Concentration can be estimated using Barnsby Williams Formula which is widely used by US Highway Engineers

2.01.0

9.0

SA

LTc

L = Length of Stream in MilesA = Area of the catchment in Sq. milesS = Average grade from source to site in percent

Rational Formula – Runoff Coefficient Area Characteristic Run-off Coefficient C

Steep Bare Rock 0.90

Steep Rock with Woods 0.80

Plateau with light cover 0.70

Densely built-up areas 0.90 – 0.70

Residential areas 0.70 – 0.50

Stiff Clayey soils 0.50

Loam 0.40 – 0.30

Suburbs with gardens 0.30

Sandy soils 0.1 – 0.20

Jungle area 0.10 – 0.25

Parks, Lawns, Fields 0.25 - 0.50

Geotechnical Studies

• Geotechnical Studies should provide the following Information:

• The types of Rocks, Dips, Faults and Fissures

• Subsoil Ground Water Level, Quality, Artesian Conditions if any

• Location and extent of soft layers

• Identification of hard bearing strata

• Physical properties of soil layers


Example Geological Profile:Cross section of the soil on the route of the Paris The diagram above shows the crossing over the Seine via the Bir Hakeim bridge and the limestone quarries under Trocadéro


Example: Cross section of the Kansas River, west of Silver Lake, Kansas

Typical Borehole

Seismic Considerations

Source: Building Code of Pakistan

Tectonic Setting of the Bridge Site

Source: Geological Survey of Pakistan

Environmental Considerations

• Impact on Following Features of Environment need to considered:– River Ecology which includes:

• Marine Life• Wildlife along river banks• Riverbed• Flora and fauna along river banks

– Impact upon dwellings along the river if any– Impact upon urban environment if the bridge in an

urban area– Possible impact upon archeological sites in vicinity

Bridge Economic Feasibility

• Economic Analysis is Required at Feasibility Stage to justify expenditure of public or private funds

• A Bridge is the most expensive part of a road transportation network

• Types of Economic Analyses– Cost Benefit Ratio Analysis– Internal Rate of Return (IRR) Analysis

Bridge Economic Analysis/Life Cycle Cost Analysis (LCCA)

Time

Co

sts

Str

eam

Ben

efit

s S

trea

m

Co

nst

ruct

ion

S

tag

e

Project LifePro

ject

Sta

rt

Dat

e

Pro

ject

Lif

e

En

d

Dat

e

Sal

vag

e V

alu

e

Project Cost Benefit Analysis

• The objective of LCCA is to– Estimate the costs associated with the Project during Construction

an its service life. These include routine maintenance costs + Major Rehab Costs

– Estimate the Benefits that will accrue from the Project including time savings to road users, benefits to business activities etc.

– Bring down the costs and benefits to a common reference pt. in time i.e. just prior to start of project (decision making time)

– Facilitate decision making about economic feasibility by calculating quantifiable yardsticks such as Benefit to Cost Ratio (BCR) and Internal Rate of Return (IRR)

• Note: Salvage Value may be taken as a Benefit This includes cost of the Right-of-Way and substructure

What is Life Cycle Cost?

• An economic analysis procedure that uses engineering inputs

• Compares competing alternatives considering all significant costs

• Expresses results in equivalent dollars (present worth)

Time Period of Analysis

• Normally equal for all alternatives

• Should include at least one major rehabilitation

• Needed to capture the true economic benefit of each alternative

• Bridge design today is based on a probabilistic model of 100 years


Time

Co

sts

Str

ea

mB

en

efi

ts S

tre

am

Co

ns

tru

cti

on

S

tag

e Project LifePro

jec

t S

tart

Da

te

Pro

jec

t L

ife

E

nd

D

ate

Sa

lva

ge

V

alu

e

• Costs and Benefits Change over the life of the Project

• Amount of Money/Benefit accrued some time in future is worth less in terms of Today’s money

• Same is the case with the benefits accrued over time

• The Problem now is as to How to find the Worth of a Financial Amount in Future in terms of Today’s Money

• This is accomplished by using the instrument of “DISCOUNT RATE”

Problem:


DISCOUNT RATE:

The annual effective discount rate is the annual interest divided by the capital including that interest, which is the interest rate divided by 100% plus the interest rate. It is the annual discount factor to be applied to the future cash flow, to find the discount, subtracted from a future value to find the value one year earlier.

For example, suppose there is an investment made of $95 and pays $100 in a year's time. The discount rate according the given definition is:

%0.5100

95100

dRateDiscount

%26.595

95100

iRateInterest

Interest Rate is calculated as $ 95 as Base

Interest Rate and Discount Rate are Related as Follows

2

1ii

i

idRateDiscount

http://en.wikipedia.org/wiki/Discount_factor

Discount Rate• Thus Discount Rate is that rate which can be

used to obtain the Present Value of Money that is spent or collected in future

Net Present value of Cost incurred = Co = (1 - d)n Cn In Year n

Net Present value of Cost incurred = Bo = (1 - d)n Bn In Year n

Time

Co

sts

Str

eam

Ben

efit

s S

trea

m

Project Life

Pro

jec

t S

tart

Dat

e

Year nCn

Bn

Cost/ Benefit Projected Backward

Bo

Co

What Discount Rate to Use?• A first estimate of appropriate Discount

rate can be made as follows:Estimate of Discount Rate = Federal Bank Lending Rate – Average Long-term Inflation Rate

Note: By subtracting the Inflation Rate in arriving at a Discount Rate the effect of Inflation can be removed from consideration during Economic Analysis

The Discount Rate after subtracting the Inflation Rate is also Referred to as the “Real Discount Rate”

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

Asian Development Bank uses a Discount rate of 12% for evaluation of projects Discount Rate is less than the Real interest Rate as Governments do not take a purely commercial view of an infrastructure project

Cost Considerations

Maintenance and Inspection

Cost

Initial Cost

Costs

Present Worth

Years

Rehabilitation Cost

Salvage Value

Salvage Costs

Cost Benefit Ratio

Formula for CostBenefit Ratio

Benefit To Cost Ratio =

L

n

Ln

Cnd

Bnd

0

0

)1(

)1(

Costs of ValuePresent

Benefits of ValuePresent

Where L = Life Span of the Project in Years d = Discount Rate Bn = Benefit in year n Cn = Cost incurred in year n

Net Present Worth/ Value

• Net Present Worth/ Value = NPW or NPV is defined as follows:

NPW = NPV = Present Value of Benefits – Present Value of Costs

Note: If a Number of alternatives are being compared, the alternative that has the highest Net Present Worth is the preferable one and will also have the higher Benefit to Cost Ratio

What is Internal Rate of Return (IRR)

• IRR may be defined as that Discount Rate at which the Benefit to Cost Ratio (BCR) of a Project becomes exactly 1.0

• It is a better measure of economic viability of a project compared to Benefit to Cost Ratio

• It is a good indicator of how much inflation increase and interest rate hike a project can tolerate and still be viable

Present Worth Factor

pwf = Present Worth Factor for discount rate d and year nd = Discount raten = Number of year when the cost/ benefit will occur

pwf = Present Worth Factor for discount rate d and year nd = Discount raten = Number of year when the cost/ benefit will occur

ndpwf )1(

Alternate Formula (Usually Adopted)

ndpwf

1

1

Present Worth Analysis

• Discounts all future costs and benefits to the present:

t=L

PW = FC + pwf [MC+IC+FRC+UC] + pwf [S] t=0

PW = Present Worth/ Value of the Project FC = First (Initial) Cost

t = Time Period of Analysis (ranges from 0 L)MC = Maintenance CostsIC = Inspection CostsFRC = Future Rehabilitation CostsUC = Users CostsS = Salvage Values or Costspwf = Present Worth Factor

PW = Present Worth/ Value of the Project FC = First (Initial) Cost

t = Time Period of Analysis (ranges from 0 L)MC = Maintenance CostsIC = Inspection CostsFRC = Future Rehabilitation CostsUC = Users CostsS = Salvage Values or Costspwf = Present Worth Factor

Time Period of Analysis

• Normally equal for all alternatives

• Should include at least one major rehabilitation– Needed to capture the true economic benefit of each

alternative

• Bridge design today is based on a probabilistic model of 100 years

Maintenance Costs

• Annual cost associated with the upkeep of the structure

• Information is difficult to obtain for a given project

• Cost varies on the basis of size of the structure (sqft)

• Best Guess Values– Frequency - Annual– Concrete 0.05 % of Initial Cost– Structural Steel 0.05 % of Initial Cost

Inspection Costs

• Should be taken for all alternatives preferably every two years

• Cost varies on the basis of size of the structure (sqft) and by construction material

• Best Guess Values– Frequency - Biannual– Concrete 0.15 % of Initial Cost– Structural Steel 0.20 % of Initial Cost

Future Painting Costs

• Only applies to structural steel structures but excludes weathering steel

• Should occur every 20 years• Cost varies on the basis of size of the structure

(sqft)• Best Guess Values

– Frequency – every 20 years– Concrete 0.0 % of Initial Cost– Structural Steel 7.0 % of Initial Cost

Future Rehabilitation Costs

• The frequency is not only a function of time but also the growing traffic volume and the structural beam system

• Cost varies on the basis of size of the structure (sqft) and structural beam system

• Best Guess Values– Frequency

• First occurrence – Concrete 40 years• First occurrence – Structural Steel 35 years• Annual traffic growth rate .75 % (shortens rehab

cycles)– Concrete 20.0 % of Initial Cost– Structural Steel 22.0 % of Initial Cost

Salvage Value/Costs

• Occurs once at end of life of structure

• Difference between– Removal cost– Salvage value

• Best Guess Values– Removal cost 10 % of Initial Cost– Salvage Value – Concrete - 0 % of Initial Cost– Salvage Value – Structural Steel - 2 % of Initial Cost

Benefits from a Bridge

Monetizable Benefits

• Time savings to road users

• Growth in economic activity

• Saving of Vehicular wear and tear

• Reduction of accidents if applicable

Other Non-Monetizable Benefits

• Strategic Benefits

Example of Economic Analysis

Carry out an Economic Analysis of a Proposed Bridge given the following Data:

Estimated Average Annualized Daily Traffic is = 12,000 Vehicles per DayWith the Following Mix of TrafficCars = 10,000Trucks = 1,000Buses = 1,000Assume that the Traffic Growth Rate = 1.2 %is Geometric over the Life Span of the BridgeBridge Life Span = 80 yearsThe Construction Cost is = 200.0 Million Rs. spread over 2 yearsThe Trade and economic benefits are = 10.0 Million Rs. per yearestimated to be Annual Growth Rate of Trade Benefits = 2.0 %is Geometric at the rate of over the Life Span of the BridgeThe Bridge would Result in Time Saving of = 1 hour to Road UsersAverage Time Value of Single Road User = 50.0 Rs. Per Hour


Assume that the Bridge would require: Annual Maintenance = 0.03 % of Construction CostMajor Rehabilitation after every 30 years = 20.0 % of Construction CostSalvage Value of Piers and Abutments = 25 % of Construction CostSalvage Cost is assumed to be = 0.0 %Average Occupancy Of a Single Car = 3.0 PassengersAverage Occupancy Of a Single Truck = 2.0 PassengersAverage Occupancy Of a Single Bus = 50 Passengers

Calculate the Present Worth, Net Present Worth, Benefit to Cost Ratio of the Bridge at Discount Rate = 6.0 %

Calculate the Internal Rate of Return of the Bridge


Benefits in Time Saving Upon Bridge Opening

Vehicle Type Number Occupancy Time Saving Time Value Benefit

(Persons) (hrs) (Rs.per Hour) (Rs.)Cars 10,000 3.0 1.0 50.0 1,500,000 Buses 1,000 50.0 1.0 50.0 2,500,000 Trucks 1,000 2.0 1.0 50.0 100,000

Total Benefit Per Year = 4,100,000 Assumed to then Grow at Geometrically at the Rate of 1.2% per year


Actual Year Year No.Present Worth Factor (PWF)

Construction/Maintenance Cost Rehab Cost Total Costs

Benefit: Time Saving

Benefit: Trade/ Economic

Salvage Benefit

Total Benefits

Total Discounted Costs

Total Discounted Benefits Net Benefit

(1-d)^n (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) 2010 0 1.0000 100,000,000 100,000,000 - - 100,000,000 - (100,000,000) 2011 1 0.9400 100,000,000 100,000,000 - 94,000,000 - (100,000,000) 2012 2 0.8836 60,000 60,000 4,100,000 10,000,000 14,100,000 53,016 12,458,760 14,040,000 2013 3 0.8306 60,000 60,000 4,149,200 10,200,000 14,349,200 49,835 11,918,216 14,289,200 2014 4 0.7807 60,000 60,000 4,198,400 10,400,000 14,598,400 46,845 11,397,686 14,538,400 2015 5 0.7339 60,000 60,000 4,247,600 10,600,000 14,847,600 44,034 10,896,713 14,787,600 2016 6 0.6899 60,000 60,000 4,296,800 10,800,000 15,096,800 41,392 10,414,826 15,036,800 2017 7 0.6485 60,000 60,000 4,346,000 11,000,000 15,346,000 38,909 9,951,537 15,286,000 2018 8 0.6096 60,000 60,000 4,395,200 11,200,000 15,595,200 36,574 9,506,350 15,535,200 2019 9 0.5730 60,000 60,000 4,444,400 11,400,000 15,844,400 34,380 9,078,759 15,784,400 2020 10 0.5386 60,000 60,000 4,493,600 11,600,000 16,093,600 32,317 8,668,256 16,033,600 2021 11 0.5063 60,000 60,000 4,542,800 11,800,000 16,342,800 30,378 8,274,330 16,282,800 2022 12 0.4759 60,000 60,000 4,592,000 12,000,000 16,592,000 28,555 7,896,470 16,532,000 2023 13 0.4474 60,000 60,000 4,641,200 12,200,000 16,841,200 26,842 7,534,165 16,781,200 2024 14 0.4205 60,000 60,000 4,690,400 12,400,000 17,090,400 25,231 7,186,910 17,030,400 2025 15 0.3953 60,000 60,000 4,739,600 12,600,000 17,339,600 23,718 6,854,202 17,279,600 2026 16 0.3716 60,000 60,000 4,788,800 12,800,000 17,588,800 22,294 6,535,546 17,528,800






Salvage Benefit

Total Benefits



(1-d)^n (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) 2027 17 0.3493 60,000 60,000 4,838,000 13,000,000 17,838,000 20,957 6,230,454 17,778,000 2028 18 0.3283 60,000 60,000 4,887,200 13,200,000 18,087,200 19,699 5,938,445 18,027,200 2029 19 0.3086 60,000 60,000 4,936,400 13,400,000 18,336,400 18,517 5,659,047 18,276,400 2030 20 0.2901 60,000 60,000 4,985,600 13,600,000 18,585,600 17,406 5,391,799 18,525,600 2031 21 0.2727 60,000 60,000 5,034,800 13,800,000 18,834,800 16,362 5,136,247 18,774,800 2032 22 0.2563 60,000 60,000 5,084,000 14,000,000 19,084,000 15,380 4,891,952 19,024,000 2033 23 0.2410 60,000 60,000 5,133,200 14,200,000 19,333,200 14,457 4,658,482 19,273,200 2034 24 0.2265 60,000 60,000 5,182,400 14,400,000 19,582,400 13,590 4,435,416 19,522,400 2035 25 0.2129 60,000 60,000 5,231,600 14,600,000 19,831,600 12,775 4,222,349 19,771,600 2036 26 0.2001 60,000 60,000 5,280,800 14,800,000 20,080,800 12,008 4,018,882 20,020,800 2037 27 0.1881 60,000 60,000 5,330,000 15,000,000 20,330,000 11,288 3,824,630 20,270,000 2038 28 0.1768 60,000 60,000 5,379,200 15,200,000 20,579,200 10,610 3,639,221 20,519,200 2039 29 0.1662 60,000 60,000 5,428,400 15,400,000 20,828,400 9,974 3,462,292 20,768,400 2040 30 0.1563 60,000 40,000,000 40,060,000 5,477,600 15,600,000 21,077,600 6,259,600 3,293,493 (18,982,400) 2041 31 0.1469 60,000 60,000 5,526,800 15,800,000 21,326,800 8,813 3,132,486 21,266,800 2042 32 0.1381 60,000 60,000 5,576,000 16,000,000 21,576,000 8,284 2,978,943 21,516,000 2043 33 0.1298 60,000 60,000 5,625,200 16,200,000 21,825,200 7,787 2,832,549 21,765,200 2044 34 0.1220 60,000 60,000 5,674,400 16,400,000 22,074,400 7,320 2,692,997 22,014,400 2045 35 0.1147 60,000 60,000 5,723,600 16,600,000 22,323,600 6,881 2,559,995 22,263,600 2046 36 0.1078 60,000 60,000 5,772,800 16,800,000 22,572,800 6,468 2,433,258 22,512,800 2047 37 0.1013 60,000 60,000 5,822,000 17,000,000 22,822,000 6,080 2,312,514 22,762,000 2048 38 0.0952 60,000 60,000 5,871,200 17,200,000 23,071,200 5,715 2,197,499 23,011,200 2049 39 0.0895 60,000 60,000 5,920,400 17,400,000 23,320,400 5,372 2,087,961 23,260,400 2050 40 0.0842 60,000 60,000 5,969,600 17,600,000 23,569,600 5,050 1,983,656 23,509,600 2051 41 0.0791 60,000 60,000 6,018,800 17,800,000 23,818,800 4,747 1,884,351 23,758,800 2052 42 0.0744 60,000 60,000 6,068,000 18,000,000 24,068,000 4,462 1,789,822 24,008,000 2053 43 0.0699 60,000 60,000 6,117,200 18,200,000 24,317,200 4,194 1,699,853 24,257,200 2054 44 0.0657 60,000 60,000 6,166,400 18,400,000 24,566,400 3,943 1,614,236 24,506,400 2055 45 0.0618 60,000 60,000 6,215,600 18,600,000 24,815,600 3,706 1,532,774 24,755,600 2056 46 0.0581 60,000 60,000 6,264,800 18,800,000 25,064,800 3,484 1,455,276 25,004,800 2057 47 0.0546 60,000 60,000 6,314,000 19,000,000 25,314,000 3,275 1,381,560 25,254,000 2058 48 0.0513 60,000 60,000 6,363,200 19,200,000 25,563,200 3,078 1,311,451 25,503,200 2059 49 0.0482 60,000 60,000 6,412,400 19,400,000 25,812,400 2,893 1,244,782 25,752,400 2060 50 0.0453 60,000 60,000 6,461,600 19,600,000 26,061,600 2,720 1,181,391 26,001,600


2061 51 0.0426 60,000 60,000 6,510,800 19,800,000 26,310,800 2,557 1,121,126 26,250,800 2062 52 0.0401 60,000 60,000 6,560,000 20,000,000 26,560,000 2,403 1,063,840 26,500,000 2063 53 0.0377 60,000 60,000 6,609,200 20,200,000 26,809,200 2,259 1,009,393 26,749,200 2064 54 0.0354 60,000 60,000 6,658,400 20,400,000 27,058,400 2,124 957,649 26,998,400 2065 55 0.0333 60,000 60,000 6,707,600 20,600,000 27,307,600 1,996 908,480 27,247,600 2066 56 0.0313 60,000 60,000 6,756,800 20,800,000 27,556,800 1,876 861,764 27,496,800 2067 57 0.0294 60,000 60,000 6,806,000 21,000,000 27,806,000 1,764 817,384 27,746,000 2068 58 0.0276 60,000 60,000 6,855,200 21,200,000 28,055,200 1,658 775,227 27,995,200 2069 59 0.0260 60,000 60,000 6,904,400 21,400,000 28,304,400 1,558 735,186 28,244,400 2070 60 0.0244 60,000 40,000,000 40,060,000 6,953,600 21,600,000 28,553,600 978,098 697,159 (11,506,400) 2071 61 0.0230 60,000 60,000 7,002,800 21,800,000 28,802,800 1,377 661,049 28,742,800 2072 62 0.0216 60,000 60,000 7,052,000 22,000,000 29,052,000 1,294 626,762 28,992,000 2073 63 0.0203 60,000 60,000 7,101,200 22,200,000 29,301,200 1,217 594,210 29,241,200 2074 64 0.0191 60,000 60,000 7,150,400 22,400,000 29,550,400 1,144 563,308 29,490,400 2075 65 0.0179 60,000 60,000 7,199,600 22,600,000 29,799,600 1,075 533,975 29,739,600 2076 66 0.0168 60,000 60,000 7,248,800 22,800,000 30,048,800 1,011 506,134 29,988,800 2077 67 0.0158 60,000 60,000 7,298,000 23,000,000 30,298,000 950 479,712 30,238,000 2078 68 0.0149 60,000 60,000 7,347,200 23,200,000 30,547,200 893 454,638 30,487,200 2079 69 0.0140 60,000 60,000 7,396,400 23,400,000 30,796,400 839 430,846 30,736,400 2080 70 0.0132 60,000 60,000 7,445,600 23,600,000 31,045,600 789 408,272 30,985,600 2081 71 0.0124 60,000 60,000 7,494,800 23,800,000 31,294,800 742 386,856 31,234,800 2082 72 0.0116 60,000 60,000 7,544,000 24,000,000 31,544,000 697 366,541 31,484,000 2083 73 0.0109 60,000 60,000 7,593,200 24,200,000 31,793,200 655 347,270 31,733,200 2084 74 0.0103 60,000 60,000 7,642,400 24,400,000 32,042,400 616 328,993 31,982,400 2085 75 0.0097 60,000 60,000 7,691,600 24,600,000 32,291,600 579 311,658 32,231,600 2086 76 0.0091 60,000 60,000 7,740,800 24,800,000 32,540,800 544 295,220 32,480,800 2087 77 0.0085 60,000 60,000 7,790,000 25,000,000 32,790,000 512 279,632 32,730,000 2088 78 0.0080 60,000 60,000 7,839,200 25,200,000 33,039,200 481 264,851 32,979,200 2089 79 0.0075 60,000 60,000 7,888,400 25,400,000 33,288,400 452 250,838 33,228,400 2090 80 0.0071 60,000 60,000 7,937,600 25,600,000 33,537,600 425 237,553 33,477,600 2091 81 0.0067 60,000 60,000 7,986,800 25,800,000 50,000,000 83,786,800 399 557,868 83,726,800 Total 202,104,198 261,516,182





Salvage Benefit

Total Benefits



(1-d)^n (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (Rs.)

Total Discounted Costs = 202,104,198 Rs.Total Discounted Benefits = 261,516,182 Rs.Present Worth = 202,104,198 Rs.Net Present Worth = 59,411,984 Rs.

Benefit to Cost Ratio = 1.294

Internal Rate of Return (IRR) = 8.028%

bridge engineering lecture 1 a planning of bridges dr. shahzad rahman

Documents