Bridge Engineering
Lecture 1 A
Planning of Bridges
Dr. Shahzad Rahman
Bridge Planning
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•
•
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Traffic Studies
Hydrotechnical Studies
Geotechnical Studies
Environmental Considerations
Alternatives for Bridge Type
Economic Feasibility
Bridge Selection and Detailed Design
Traffic Studies
New Road Link
Existing Network
New Bridge
City Center
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
Hydrotechnical Studies
• 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
Hydrotechnical Studies
• 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
Hydrotechnical Studies
River Catchment Area
Hydrotechnical Studies
River Catchment Boundaries with Tributaries
Hydrotechnical Studies
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
• 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 Design Flood Levels
Design Flood Levels
FREEBOARD REQUIREMENTS
• CANADIAN MINISTRY OF TRANSPORTATION
Gives Following Guidelines for Estimating 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
Q = Discharge in Cusecs
A = Catchment Area in Sq. Miles
Q  825 A
3/ 4
– Inglis Formula
7000 A
Q
A4
– Ryve’s Formula
Q  C A2 / 3
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
probability
Normal Distribution Method
QP  QM  KTr  Q
Q
QP = Discharge Associated with Probability of Occurrence P
QM = Mean Discharge over the data set
σQ = Standard Deviation of the Discharge data set
KTr = Frequency factor corresponding to Probability of Occurrence P
Example of Peak Flood Estimation Flood
Example
Flood Frequency Analysis
Actual
Year
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
Year
(No.)
1
2
3
4
5
6
7
8
9
10
11
12
Normal Distribution Method
2
Max Flood Xi - Xavg (Xi - Xavg)
Q
2
(cumecs) (cumecs) (cumecs )
26
2.9
8.3
42
18.9
356.3
17
-6.1
37.5
35
11.9
141.0
16
-7.1
50.8
32
8.9
78.8
48
24.9
618.8
14
-9.1
83.3
13
-10.1
102.5
21
-2.1
4.5
18
-5.1
26.3
16
-7.1
50.8
Ranked Flow
(Decending
Order)
48
45
42
35
35
32
26
25
23
21
21
20
Rank
R
Probability Return Period
P = R/n
Tr = 1/P
(yrs)
1
0.04
24.00
2
0.08
12.00
3
0.13
8.00
4
0.17
6.00
5
0.21
4.80
6
0.25
4.00
7
0.29
3.43
8
0.33
3.00
9
0.38
2.67
10
0.42
2.40
11
0.46
2.18
12
0.50
2.00
Example of Peak Flood Estimation Flood
Actual
Year
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
Year
(No.)
13
14
15
16
17
18
19
20
21
22
23
24
Sample Pts = n =
Mean Qm = M
Sum of Squares =
Variance =
Standard Deviation =
(Xi - Xavg) 2
Max Flood Xi - Xavg
Q
(cumecs) (cumecs)
20
15
35
45
23
14
12
17
25
15
21
15
S
2

-3.1
-8.1
11.9
21.9
-0.1
-9.1
-11.1
-6.1
1.9
-8.1
-2.1
-8.1


S
( n
V
2

1 )

Coefficient of Variation = Cv = σ/M =
3
Skewness Coefficient = SC = 3 Cv + Cv =
Input Return Period (Years) = Tr =
Probability = p = 1/ Tr
Flood Estimate = Qt =
Rank
R
(cumecs2)
24
23.125

1

(x j  x )2 

n 1
V
Ranked Flow
(Decending
Order)

9.8
66.0
141.0
478.5
0.0
83.3
123.8
37.5
3.5
66.0
4.5
66.0
18
17
17
16
16
15
15
15
14
14
13
12
2638.6
114.72
10.71
0
. 4
6
3
1.49
100
0.01
Input Value
13
14
15
16
17
18
19
20
21
22
23
24
Probability Return Period
P = R/n
Tr = 1/P
(yrs)
0.54
0.58
0.63
0.67
0.71
0.75
0.79
0.83
0.88
0.92
0.96
1.00
1.85
1.71
1.60
1.50
1.41
1.33
1.26
1.20
1.14
1.09
1.04
1.00
Example of Peak Flood Estimation Flood
Input Return Period (Years) = Tr =
Probability = p = 1/ Tr
Flood Estimate = Qt =
w 


ln 


1
p
2
100
0.01





w=
K
Input Value
3.03485528
Tr
 w
2 . 51557  0 . 802853 w  0 . 010328
1  1 .532788 w  0 .189269
KTr =
Flood Estimate = Qt =
w
2
w
2
 0 . 001308
2.32678649
Q Q
t
m
Qt =
 Ktr 
48.05 Cumecs
10
w
3
Log-Normal Distribution Method
probability
• Yields better Results
Compared to Normal
Distribution Method
ln QP  ln QM  KTr  ln Q
Log Q or Ln Q
lnQP = Log of Discharge Associated with Probability of Occurrence P
lnQM = Mean of Log Discharge over the data set
σlnQ = Standard Deviation of the Log of Discharge data set
KTr = Frequency factor corresponding to Probability of Occurrence P
QP = Antilog (ln QP) = Discharge Associated with Probability of Occurrence P
Example of Peak Flood Estimation Flood
Log-Plot Method
Log Plot Discharge Vs Return Period
80
70
Discharge (cumecs)
60
50
40
Observed Discharge
Log. (Observed Discharge)
30
20
y = 12.724Ln(x) + 11.733
10
0
1
10
100
Retun Period (Yrs)
Trendline Equation is
Qt = 12.724 Ln(Tr) + 11.213
For Return
Qt =
For Return
Qt =
Period Tr =
12.724 Ln (50) + 11.213 =
Period Tr =
12.724 Ln (100) + 11.213 =
50 yrs
61.0
cumecs
69.8
cumecs
100 yrs
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
Q  C IT A
Q = Design Discharge
IT = 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. miles
C = 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
0 .9 L
Tc  0.1 0.2
A S
L = Length of Stream in Miles
A = Area of the catchment in Sq. miles
S = Average grade from source to site in percent
Rational Formula – Runoff Coefficient
Area Characteristic
Steep Bare Rock
Steep Rock with Woods
Run-off Coefficient C
0.90
0.80
Plateau with light cover
Densely built-up areas
Residential areas
0.70
0.90 – 0.70
0.70 – 0.50
Stiff Clayey soils
Loam
Suburbs with gardens
Sandy soils
0.50
0.40 – 0.30
0.30
0.1 – 0.20
Jungle area
Parks, Lawns, Fields
0.10 – 0.25
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
Geotechnical Studies
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
Geotechnical Studies
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
Construction
Stage
Project Start
Date
Benefits Stream
Project Life
Project Life
End Date
Salvage
Value
Costs Stream
Bridge Economic Analysis/
Life Cycle Cost Analysis (LCCA)
Time
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
•
Project Life
Project
Life End
Date
Time
Salvage
Value
Construction
Stage
Project
Start Date
Problem:
Benefits Stream
Costs Stream
Bridge Economic Analysis/
Life Cycle Cost Analysis (LCCA)
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”
Bridge Economic Analysis/
Life Cycle Cost Analysis (LCCA)
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:
Discount Rate  d 
100  95
 5.0%
100
Interest Rate is calculated as $ 95 as Base
100  95
Interest Rate  i 
 5.26%
95
Interest Rate and Discount Rate are Related as Follows
i
Discount Rate  d 
 i  i2
1i
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
Cn
Co
Project
Start Date
Benefits
Stream
Costs
Stream
Cost/ Benefit Projected
Backward
Year n
Time
Bo
Bn
Project
Life
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
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
Present Worth
Salvage
Costs
Costs
Initial Cost
Rehabilitation Cost
Maintenance and
Inspection
Cost
Years
Salvage
Value
Cost Benefit Ratio
Formula for Cost
Benefit Ratio
L
Benefit To Cost Ratio = Present Value of Benefits 
Present Value of Costs
 (1  d )
Bn
n
Cn
0
L
 (1  d )
0
Where L = Life Span of the Project in Years
d = Discount Rate
Bn = Benefit in year n
Cn = Cost incurred in year n
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  (1  d )
pwf
d
n
n
= Present Worth Factor for discount rate d and year n
= Discount rate
= Number of year when the cost/ benefit will occur
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
FC
t
MC
IC
FRC
UC
S
pwf
= Present Worth/ Value of the Project
= First (Initial) Cost
= Time Period of Analysis (ranges from 0  L)
= Maintenance Costs
= Inspection Costs
= Future Rehabilitation Costs
= Users Costs
= Salvage Values or Costs
= 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