UNIVERSITY OF NAIROBI
STRUCTURAL DESIGN OF A REINFORCED CONCRETE
SINGLE LANE MOTORIZED BRIDGE AT RIVER NJORO
By: Wachira Anthony Gichuru
F16/36095/2010
PROJECT SUPERVISOR: ENG. S.S. Miringu
A project submitted as a partial fulfillment for the requirement
for the award of the degree of
BACHELOR OF SCIENCE IN CIVIL ENGINEERING
2015
Abstract
As Kenya’s population continues to increase at an annual rate of 2.7%, there is need to
construct more roads to keep up with future demand. Njoro region, being no exception, has
experienced this population growth over the years and hence there was need to construct an
access road to provide access to the various upcoming market centers as well as homesteads.
The proposed access road would cross River Njoro and hence the significance of construction
of a single lane reinforced concrete motorized bridge. It was proposed that the bridge be a
single lane as the number of homesteads owning cars in the area was minimal and
subsequently the traffic volume through the road, ergo bridge, was minimal.
The objectives of this project were to carry out the structural design of a reinforced concrete
bridge in accordance with BS5400 (bridge design) and make detailed drawings and
specifications for it.
The project was significant in that it would provide access across the river for both motorized
and human traffic. Geological, traffic, hydrological and geotechnical surveys were carried out
for the best possible location, type and height of the bridge.
The bridge was designed according to recommended (BS5400) standards and sufficient
structural capacity to carry the loads at both ultimate and serviceability states and
recommendations for maintenance given.
ii
Dedication
To the Almighty God who has brought me this far and to my parents, sister and friends for the
love and moral support throughout the year and for keeping it real. God bless you.
iii
Acknowledgements
To the Almighty God for life, good health and His protection during this project period. I also
wish to acknowledge the contribution of my supervisor Eng. S.S. Miringu whose comments
and suggestions during the preparation of this project are sincerely appreciated.
iv
Table of Contents
Abstract ...................................................................................................................................... ii
Dedication ................................................................................................................................. iii
Acknowledgements ................................................................................................................... iv
Table of Contents ....................................................................................................................... v
List of Plates .............................................................................................................................. vi
List of Tables ............................................................................................................................. vi
Chapter One ................................................................................................................................ 1
1.0 Introduction .......................................................................................................................... 1
1.1 Background Information .................................................................................................. 1
1.3 Objectives ......................................................................................................................... 3
1.3.1 Main objective. .......................................................................................................... 3
1.3.2 Specific objectives ..................................................................................................... 3
Chapter Two ............................................................................................................................... 4
2.0 Literature Review ................................................................................................................. 4
2.1 Introduction ...................................................................................................................... 4
2.2 History of bridges ............................................................................................................. 4
2.3 Types of bridges ............................................................................................................... 5
2.3.1 Beam bridges ............................................................................................................. 5
2.3.2 Truss bridge ............................................................................................................... 5
2.3.4 Arch bridge ................................................................................................................ 6
2.3.5 Tied arch .................................................................................................................... 6
2.3.6 Suspension bridges .................................................................................................... 7
2.3.7 Fixed or movable bridges .......................................................................................... 7
2.3.8 Viaducts ..................................................................................................................... 7
2.4 Bridge design considerations............................................................................................ 8
2.4.1 Functional .................................................................................................................. 8
2.4.2 Economic ................................................................................................................... 8
2.4.4 Aesthetics .................................................................................................................. 8
2.5 Construction Materials: .................................................................................................... 9
2.5.1 Stone .......................................................................................................................... 9
2.5.2 Reinforced and Pre-stressed Concrete:...................................................................... 9
2.6 Blinding layer ................................................................................................................... 9
2.7 Bridge maintenance ........................................................................................................ 10
2.8 Bridge failures ................................................................................................................ 10
2.9 Bridge monitoring .......................................................................................................... 10
Chapter Three ........................................................................................................................... 11
3.0 Methodology ...................................................................................................................... 11
3.1 Introduction .................................................................................................................... 11
Chapter Four ............................................................................................................................. 12
4.0 Hydrological analysis ......................................................................................................... 12
4.1 Determination of catchment area ................................................................................... 12
4.2 Calculation of land slope ................................................................................................ 12
4.3 Calculation of channel slope .......................................................................................... 13
4.4 Calculation of design rainfall ......................................................................................... 13
4.5 Calculation of peak flow ................................................................................................ 13
4.6
Calculation of maximum flood level (y) .................................................................. 16
Chapter Six ............................................................................................................................... 17
6.1 Bar bending schedule ..................................................................................................... 17
v
Chapter seven ........................................................................................................................... 24
7.0 Recommendations and conclusion ..................................................................................... 24
7.1 Recommendations .......................................................................................................... 24
7.2 Conclusion ...................................................................................................................... 24
Chapter eight ............................................................................................................................ 25
8.0 References ......................................................................................................................... 25
8.1 List of references ................................................................................................................ 25
List of Plates
Plate 1. 1 Existing steel footbridge ............................................................................................. 2
Plate 1. 2 completed reinforced concrete bridge ........................................................................ 2
Plate 2. 1 beam bridge ................................................................................................................ 5
Plate 2. 2 truss bridge ................................................................................................................. 5
Plate 2. 3 cantilever bridge ......................................................................................................... 6
Plate 2.4 arch bridge .................................................................................................................. 6
Plate 2.5 tied arch bridge ........................................................................................................... 7
Plate 2. 6 suspension bridge ....................................................................................................... 7
Plate 2. 7 viaduct ........................................................................................................................ 8
List of Tables
Table 4. 1 Calculation of land slope ......................................................................................... 12
Table 4. 2 Calculation of channel slope ................................................................................... 13
Table 4. 1 Calculation of land slope
……………………………………………………
Table 4. 2 Calculation of channel slope
………………………………………………….
Table 6. 1 Bar bending schedule
…………………………………………………
Table 6. 2 Bar bending schedule summary……………………………………………………...
Table 6. 3 Cost estimates for reinforced concrete bridge at River Njoro………………………..
vi
List of Symbols
Symbol
fcu
fy
c
Asv
Asc
Ast
b
d
h
x
e
α1,α2
Ԑst
Ԑc
Ec
Est
D.L
L.L
MR
MO
ᵞf3
ᵞf1
U.L.S
S.L.S
U.D.L
HA
HB
N.A
Mpx
Mpy
M
T
Sf
df
F.E.M
Vp
L
Wcr
Acr
V
Meaning
characteristic strength of
concrete
characteristic strength of steel
reinforcement cover
cross sectional area of shear
reinforcement
cross sectional area of
compression reinforcement
cross sectional area of tension
reinforcement
width of the section
effective depth of the section
overall depth of the section
depth to the neutral axis
eccentricity
lane factors
strain in steel
strain in concrete
static modulus of elasticity of
concrete
static modulus of elasticity of
steel
dead load
live load
restoring moments
overturning moments
partial safety factor
partial load factor
ultimate limit state
serviceability limit state
uniformly distributed load
normal loading
abnormal loading
neutral axis
longitudinal moments
transverse moments
moment
tension
Stiffness factor
distribution factor
fixed end moments
punching shear
effective span
crack width
distance from the crack position
to the point of zero strain
shear force
vii
Chapter One
1.0 Introduction
1.1 Background Information
The County Government of Nakuru in conjunction with the Ministry of Roads and Public
Works has seen it viable to construct new roads in various parts of the county as population
continues to increase at an enormous annual rate. Njoro region, being part of this county, has
experienced this population growth over the years and hence there was need to construct an
access road to provide access to the various upcoming market centers as well as homesteads.
The proposed access road would cross River Njoro and hence the significance of construction
of a single lane reinforced concrete motorized bridge providing motor access to both sides of
the divide thus promoting regional development in line with Kenya’s vision 2030. It was
proposed that the bridge be a single lane as the number of homesteads owning cars in the area
was minimal and subsequently the traffic volume through the road, ergo bridge, was minimal.
The proposed construction of the bridge was to replace the existing steel foot bridge which is
now outdated as it does not cater for the growing increase in use of vehicular traffic in the
region.
Currently vehicular traffic has to navigate a distance of almost thrice as long in order to access
this homesteads and therefore construction of a reinforced concrete bridge would reduce this
distance and thus boost the farming practice by providing an easily accessible market to the
residents for their produce as most of this homesteads practice farming
1.2 Problem statement
Continued population increase in the area and increased trading activities especially by
farmers across both sides of the river has warranted the need for construction of a reinforced
concrete motorized bridge in replacement of the existing steel foot bridge to provide access to
vehicles not only transporting goods but also to those owning vehicles and who wish to access
their homesteads with them. A single lane bridge was preferred as the traffic levels are at a
minimum.
1
Plate 1. 1 Existing steel footbridge
Plate 1. 2 Completed reinforced concrete bridge
2
1.3 Objectives
1.3.1 Main objective.
To design and ergo construct according to specifications, a single lane motorized reinforced
concrete bridge across River Njoro.
1.3.2 Specific objectives
 To enable transportation of both persons and goods across the river by either
motorized or non- motorized traffic thus enhancing economic development through
trade in the region.
 To provide access to those owning cars to their homesteads.
3
Chapter Two
2.0 Literature Review
2.1 Introduction
A bridge is a structure built to span physical obstacles such as a body of water, valley, or road,
for the purpose of providing passage over the obstacle. There are many different designs that
all serve unique purposes and apply to different situations. Designs of bridges vary depending
on the function of the bridge, the nature of the terrain where the bridge is constructed and
anchored, the material used to make it, and the funds available to build it.
2.2 History of bridges
The first bridges were made by nature itself, as simple as a log fallen across a stream or stones
in a river. The first bridges made by humans were probably spans of cut wooden logs or
planks and eventually stones, using a simple support and crossbeam arrangement. Some early
Americans used trees or bamboo poles to cross small caverns or wells to get from one place to
another. A common form of lashing sticks, logs, and deciduous branches together involved
the use of long reeds or other harvested fibers woven together to form a connective rope
capable of binding and holding together the materials used in early bridges.
The greatest bridge builders of antiquity were the ancient Romans. The Romans built arch
bridges and aqueducts that could stand in conditions that would damage or destroy earlier
designs. Some stand today. An example is the Alcántara Bridge, built over the river Tagus, in
Spain. The Romans also used cement, which reduced the variation of strength found in natural
stone. One type of cement, called pozzolana, consisted of water, lime, sand, and volcanic
rock. Brick and mortar bridges were built after the Roman era, as the technology for cement
was lost then later rediscovered.
During the 18th century there were many innovations in the design of timber bridges by Hans
Ulrich, Johannes Grubenmann, and others. The first book on bridge engineering was written
by Hubert Gautier in 1716. A major breakthrough in bridge technology came with the erection
of the Iron Bridge in Coalbrookdale, England in 1779. It used cast iron for the first time as
arches to cross the river Severn.
With the Industrial Revolution in the 19th century, truss systems of wrought iron were
developed for larger bridges, but iron did not have the tensile strength to support large loads.
With the advent of steel, which has a high tensile strength, much larger bridges were built,
many using the ideas of Gustave Eiffel.
In 1927 welding pioneer Stefan Bryła designed the first welded road bridge in the world, the
Maurzyce Bridge which was later built across the river Słudwia at Maurzyce near Łowicz,
Poland in 1929. In 1995, the American Welding Society presented the Historic Welded
Structure Award for the bridge to Poland.
4
2.3 Types of bridges
Bridges can be categorized in several different ways. Common categories include the type of
structural elements used, by what they carry, whether they are fixed or movable, and by the
materials used.
2.3.1 Beam bridges
Beam bridges are horizontal beams supported at each end by substructure units and can be
either simply supported when the beams only connect across a single span, or continuous
when the beams are connected across two or more spans. When there are multiple spans, the
intermediate supports are known as piers. The earliest beam bridges were simple logs that sat
across streams and similar simple structures. In modern times, beam bridges can range from
small, wooden beams to large, steel boxes. The vertical force on the bridge becomes a shear
and flexural load on the beam which is transferred down its length to the substructures on
either side. They are typically made of steel, concrete or wood.
Plate 2. 1 beam bridge
2.3.2 Truss bridge
A truss bridge is a bridge whose load-bearing superstructure is composed of a truss. This truss
is a structure of connected elements forming triangular units. The connected elements
(typically straight) may be stressed from tension, compression, or sometimes both in response
to dynamic loads. Truss bridges are one of the oldest types of modern bridges. A truss bridge
is economical to construct owing to its efficient use of materials.
Plate 2. 2 truss bridge
5
2.3.3 Cantilever bridge
A cantilever bridge is a bridge built using cantilevers, structures that project horizontally into
space, supported on only one end. For small footbridges, the cantilevers may be simple
beams; however, large cantilever bridges designed to handle road or rail traffic use trusses
built from structural steel, or box girders built from pre-stressed concrete.
Plate 2. 3 cantilever bridge
2.3.4 Arch bridge
Arch bridges have abutments at each end. The weight of the bridge is thrust into the
abutments at either side
Plate 2.4 arch bridge
2.3.5 Tied arch
Tied arch bridges have an arch-shaped superstructure, but differ from conventional arch
bridges. Instead of transferring the weight of the bridge and traffic loads into thrust forces into
the abutments, the ends of the arches are restrained by tension in the bottom chord of the
structure. They are also called bowstring arches.
6
Plate 2.5 tied arch bridge
2.3.6 Suspension bridges
Suspension bridges are suspended from cables. The earliest suspension bridges were made of
ropes or vines covered with pieces of bamboo. In modern bridges, the cables hang from
towers that are attached to caissons or cofferdams. The caissons or cofferdams are implanted
deep into the floor of a lake or river. Sub-types include the simple suspension bridge, the
stressed ribbon bridge, the under-spanned suspension bridge, the suspended-deck suspension
bridge, and the self-anchored suspension bridge.
Plate 2. 6 suspension bridge
2.3.7 Fixed or movable bridges
Most bridges are fixed bridges, meaning they have no moving parts and stay in one place until
they fail or are demolished. Temporary bridges, such as Bailey bridges, are designed to be
assembled, and taken apart, transported to a different site, and re-used. They are important in
military engineering, and are also used to carry traffic while an old bridge is being rebuilt.
Movable bridges are designed to move out of the way of boats or other kinds of traffic, which
would otherwise be too tall to fit. These are generally electrically powered
2.3.8 Viaducts
A viaduct is a bridge composed of several small spans for crossing a valley or a gorge. The
term viaduct is derived from the Latin via for road and ducere, to lead. However, the ancient
Romans did not use the term; it is a modern derivation from an analogy with aqueduct. Like
the Roman aqueducts, many early viaducts comprised a series of arches of roughly equal
length. Viaducts may span land or water or both.
7
Plate 2. 7 Viaduct
2.4 Bridge design considerations
A bridge should be designed to satisfy the following basic design principles in its design.
2.4.1 Functional
A bridge must be usable and serve its intended purpose in its design life.
2.4.2 Economic
The cost of constructing a bridge and its maintenance costs should be within reasonable
values in relation to the purpose of the bridge. This is done by assessing the relative costs of
alternatives.
2.4.3 Structural
Bridges may be classified by how the forces of tension, compression, bending, torsion and
shear are distributed through their structure. Most bridges will employ all of the principal
forces to some degree, but only a few will predominate. The separation of forces may be quite
clear. In a suspension or cable-stayed span, the elements in tension are distinct in shape and
placement. In other cases the forces may be distributed among a large number of members, as
in a truss, or not clearly discernible to a casual observer as in a box beam.
2.4.4 Aesthetics
High standards of architectural quality which address cultural and physical factors are
expected in the construction process.
Most bridges are utilitarian in appearance, but in some cases, the appearance of the bridge can
have great importance. Often, this is the case with a large bridge that serves as an entrance to
a city, or crosses over a main harbor entrance. These are sometimes known as signature
bridges. Designers of bridges in parks and along parkways often place more importance to
aesthetics, as well. Examples include the stone-faced bridges along the Taconic State Parkway
in New York.
To create a beautiful image, some bridges are built much taller than necessary. This type,
often found in east-Asian style gardens, is called a Moon bridge, evoking a rising full moon.
8
Other garden bridges may cross only a dry bed of stream washed pebbles, intended only to
convey an impression of a stream. Often in palaces a bridge will be built over an artificial
waterway as symbolic of a passage to an important place or state of mind. A set of five
bridges cross a sinuous waterway in an important courtyard of the Forbidden City in Beijing,
China. The central bridge was reserved exclusively for the use of the Emperor, Empress, and
their attendants.
2.5 Construction Materials:
The traditional building materials for bridges are stones, timber and steel, and more recently
reinforced and pre-stressed concrete. For special elements aluminum and its alloys and some
types of plastics are used. These materials have different qualities of strength, workability,
durability and resistance against corrosion. They differ also in their structure, texture and
color or in the possibilities of surface treatment with differing texture and color. For bridges
one should use that material which results in the best bridge regarding shape, technical
quality, economics and compatibility with the environment.
2.5.1 Stone
The great old bridges of the Etruscans, the Romans, the Fratres Pontifices of the middle ages
(since about 1100) and of later master builders were built with stone masonry. The arches and
piers have lasted for thousands of years when hard stone was used and the foundations
constructed on firm ground. With stone one can build bridges which are both beautiful,
durable and of large span (up to 150 m).
Unfortunately, stone bridges have become very expensive. Over a long period, however, stone
bridges, which are well designed and well built, might perhaps turn out be the cheapest,
because they are long-lasting and need almost no maintenance over centuries unless attacked
by extreme air pollution.
2.5.2 Reinforced and Pre-stressed Concrete:
Concrete is a construction material used in almost all construction works. Having a dull grey
color, usually concrete is not preferred in construction like bridges but some of concrete
bridges have turned out to be beauties, if someone knows the art. Good concrete attains high
compressive strength and resistance against most natural attacks, however, its tensile strength
is low, so is not preferred in areas of tensile stresses. For tensile reinforcement of concrete
steel bars are embedded into it. Steel bars start functioning when concrete cracks i.e. when
concrete can no longer resist further tensile stresses. The cracks remain harmless called “hair
cracks", if bars are designed and place correctly. A second method of resisting tensile forces
in concrete structures is by pre-stressing.
2.6 Blinding layer
In case of foundations or where walls e.g. wing walls are founded on the ground, a screeded
layer of plain concrete not less than 50 mm thick should be placed over the ground.
In normal circumstances this concrete should have proportions weaker than that used in the
remainder of the structure, but not weaker than grade C15. Where aggressive soil or
9
aggressive groundwater is expected, the concrete should not be weaker than grade C25, and if
necessary, a sulphate-resisting or other special cement should be specified.
2.7 Bridge maintenance
Bridge maintenance consists of a combination of structural health monitoring and testing. This
is regulated in country-specific engineer standards and includes e.g. an ongoing monitoring
every three to six months, a simple test or inspection every two to three years and a major
inspection every six to ten years. In Europe, the cost of maintenance is higher than spending
on new bridges. The lifetime of welded steel bridges can be significantly extended by after
treatment of the weld transitions . This results in a potential high benefit, using existing
bridges far beyond the planned lifetime. Highway bridge with steel hollow box sections,
performed for lifetime extension by welding after treatment
2.8 Bridge failures
The failure of bridges is of special concern for structural engineers in trying to learn lessons
vital to bridge design, construction and maintenance.
2.9 Bridge monitoring
There are several methods used to monitor the stress on large structures like bridges. The most
common method is the use of an accelerometer, which is integrated into the bridge while it is
being built. This technology is used for long-term surveillance of the bridge.
Another option for structural-integrity monitoring is "non-contact monitoring", which uses the
Doppler effect (Doppler shift). A laser beam from a Laser Doppler Vibrometer is directed at
the point of interest, and the vibration amplitude and frequency are extracted from the Doppler
shift of the laser beam frequency due to the motion of the surface. The advantage of this
method is that the setup time for the equipment is faster and, unlike an accelerometer, this
makes measurements possible on multiple structures in as short a time as possible.
Additionally, this method can measure specific points on a bridge that might be difficult to
access.
10
Chapter Three
3.0 Methodology
3.1 Introduction
The following steps were taken to carry out the project:
 The necessary surveys were carried out to determine the best possible location, type of
bridge, its vertical and horizontal alignments and whether or not it would require
super-elevation.
 A geotechnical survey was carried out to determine the maximum bearing capacity of
the ground conditions at the point of proposed abutment footing construction and the
allowable soil bearing pressure(qA) was found to be 490 KN/M2
 A hydrological analysis to determine the maximum flood levels of the river was also
carried out.
 The proposed bridge structure was then modeled, loaded according to
specifications(BS 5400), analyzed and designed manually through calculations.
11
Chapter Four
4.0 Hydrological analysis
4.1 Determination of catchment area
Number of complete squares = 87
Number of incomplete squares(covering more than 50%) = 40
Number of complete squares(covering less than 50%) = 37
40+37
Total number of squares = 87 + 2 = 125.5 𝑠𝑞𝑢𝑎𝑟𝑒𝑠 ;approximate=126 squares
Actual area of one square = 1KM2
Hence total catchment area = 1*126 =126 KM2
4.2 Calculation of land slope
Table 4. 3 Calculation of land slope
Contour
Height
2660
2600
2700
2600
2380
2340
2400
2340
2740
2660
2740
2660
Average land slope =
60
Length between Slope
contours
900
100
700
40
400
60
800
80
400
80
700
7+14+10+8+20+11
2
60
∗ 100 = 𝟕%
900
100
∗ 100 = 𝟏𝟒%
700
40
∗ 100 = 𝟏𝟎%
400
60
∗ 100 = 𝟖%
800
80
∗ 100 = 𝟐𝟎%
400
80
∗ 100 = 𝟏𝟏%
700
= 11.67% ; 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒𝑙𝑦 𝟏𝟐%
12
4.3 Calculation of channel slope
Table 4. 4 Calculation of channel slope
Contour
Height
Length between Slope
contours
200
6100
2800 200
2600
2600 200
2400
2400 200
2200
Average channel slope =
7200
6500
3.28+2.78+3.08
3
∗ 100 = 𝟑. 𝟐𝟖%
6100
200
∗ 100 = 𝟐. 𝟕𝟖%
7200
200
∗ 100 = 𝟑. 𝟎𝟖%
6500
= 3.05% ; 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒𝑙𝑦 𝟑
4.4 Calculation of design rainfall
REFERENCE : The prediction of storm rainfall in East Africa.
1. Using grid reference (35o 52.5’00”E, 0 o27.5’00” S) ,the 2 year 24 hour rainfall was located on
figure 1 of Appendix 1 as 50mm.
2. From Appendix 1, figure 2, the 10 year:2 year ratio was found to be 1.49(Inland).
3. From Appendix 1,figure 3,for a 10 year:2 year ratio of 1.49 and a recurrence interval of
25years,the flood factor was found to be 1.75
𝟏𝟎
𝑹𝟐𝟒 =10 year 24 hour point rainfall =1.75*50mm=87.5mm
4. From Appendix 1, figure 4,the areal reduction factor for 126 km2 was 0.82.
4.5 Calculation of peak flow
REFERENCE : The TRRL East African flood model
1. Measured catchment as obtained from the map was 126km2.
Land slope
12%
Channel slope 3%
Channel length 35.3km
2. Type of catchment from table 7.
Poor pasture
Lag time (k)0.5 hours
3. From site inspection and using table 4
Contributing area coefficient, Cs 0.11
4. Using figure 14,antecedent rainfall zone is Nyanza and using table 3,the zone is a Dry zone.
5. Catchment wetness factor, Cw from table 5 was 0.75
6. From site inspection and using table 6,land use factor, CL ,Grass cover,1.0.
7. Contributing area coefficient (CA)
CA= Cs* Cw * CL
=0.11*0.75*1.0
=0.0825
8. Area is a dry zone hence initial retention (Y) is 0
13
9. Using figure 16 and table 8,rainfall time (Tp=0.75) and “n” index was 0.96.
10. Base time,TB= Tp+2.3k+TA
Assuming TA to be zero(0) initially
TB= 0.75+2.3(0.5) = 1.9 hours
11. Volume of runoff ; R.O= CA*(P-Y)*A*103(m3)
P = Storm rainfall during time period equal to time base
Rainfall during base time
𝑻𝑩
𝟐𝟒. 𝟑𝟑 𝒏 𝟏𝟎
𝑹𝑻𝑩 =
(
) . 𝑹𝟐𝟒
𝟐𝟒 𝑻𝑩 + 𝟎. 𝟑𝟑
𝟏𝟎
𝑹𝟐𝟒 =10 year 24 hour point rainfall=87.5mm as earlier obtained.
1.9
24.33 0.96
𝑹𝟏.𝟗 =
(
)
. 87.5 = 𝟔𝟖. 𝟔𝟗𝒎𝒎
24 1.9 + 0.33
P = 68.69 * Areal reduction factor(ARF)0.82=56.32mm
R.O=0.0825(56.32-0)*126*103(m3)= 585480.61
𝟎. 𝟗𝟑 ∗ 𝑹𝑶
𝑸′ =
𝟑𝟔𝟎𝟎 ∗ 𝑻𝑩
0.93 ∗ 585480.61
𝑸′ =
= 𝟕𝟗. 𝟔𝟎𝒎𝟑 /𝒔𝒆𝒄
3600 ∗ 1.9
12. TB (2nd approximation)
𝟎. 𝟎𝟐𝟖𝒍
𝑻𝑨 =
𝟏 𝟏
𝑸′𝟒 𝑺𝟐
𝑻𝑨 =
0.028 ∗ 35.3
1
1
= 𝟏. 𝟗𝟏
79.604 ∗ 0.032
TB=1.9+1.91
=3.81hours
0.96
3.81
24.33
𝑹𝟑.𝟖𝟓 =
(
)
. 87.5 = 𝟕𝟔. 𝟎𝟓𝒎𝒎
24 3.81 + 0.33
P = 76.05 * Areal reduction factor(ARF)0.82=62.36mm
R.O=0.0825(62.36-0)*126*103(m3)= 648240.60
𝑸′ =
𝟎. 𝟗𝟑 ∗ 𝑹𝑶
𝟑𝟔𝟎𝟎 ∗ 𝑻𝑩
𝑸′ =
0.93 ∗ 648240.60
= 𝟒𝟑. 𝟗𝟓𝒎𝟑 /𝒔𝒆𝒄
3600 ∗ 3.81
13. TB (3rd approximation)
14
𝑻𝑨 =
𝟎. 𝟎𝟐𝟖𝒍
𝟏 𝟏
𝑸′𝟒 𝑺𝟐
𝑻𝑨 =
0.028 ∗ 35.3
1
1
= 𝟐. 𝟐𝟏
43.954 ∗ 0.032
TB=1.9+2.21
=4.1hours
4.1
24.33 0.96
𝑹𝟒.𝟏𝟕 =
(
)
. 87.5 = 𝟕𝟔. 𝟔𝟗𝒎𝒎
24 4.1 + 0.33
P = 76.69* Areal reduction factor(ARF)0.82=62.88mm
R.O=0.0825(62.88-0)*126*103(m3)= 653684.01
𝟎. 𝟗𝟑 ∗ 𝑹𝑶
𝑸′ =
𝟑𝟔𝟎𝟎 ∗ 𝑻𝑩
𝑸′ =
0.93 ∗ 653684.01
= 𝟒𝟏. 𝟏𝟗𝒎𝟑 /𝒔𝒆𝒄
3600 ∗ 4.1
14. TB (4th approximation)
𝑻𝑨 =
𝟎. 𝟎𝟐𝟖𝒍
𝟏 𝟏
𝑸′𝟒 𝑺𝟐
𝑻𝑨 =
0.028 ∗ 35.3
1
41.194
∗
1
0.032
= 𝟐. 𝟐𝟓
TB=1.9+2.25
=4.2hours
4.2
24.33 0.96
𝑹𝟒.𝟏𝟕 =
(
)
. 87.5 = 𝟕𝟔. 𝟖𝟗𝒎𝒎
24 4.2 + 0.33
P = 76.89* Areal reduction factor(ARF)0.82=63.05mm
R.O=0.0825(63.05-0)*126*103(m3)= 655430.43
𝟎. 𝟗𝟑 ∗ 𝑹𝑶
𝑸′ =
𝟑𝟔𝟎𝟎 ∗ 𝑻𝑩
𝑸′ =
0.93 ∗ 655430.43
= 𝟒𝟎. 𝟑𝟏𝒎𝟑 /𝒔𝒆𝒄
3600 ∗ 4.2
15.
41.19 − 40.31
∗ 100 = 𝟐. 𝟐%
40.31
Q’ is within 5% of previous estimate hence we use Q’ value of 40.31m3/sec
Q=F*Q’
15
F is the peak flood factor and was taken as 2.8 since K was 0.5 which is less than an hour.
Q=F*Q’= 2.8*40.31=112.87m3/sec
4.6 Calculation of maximum flood level (y)
NB: Please used attached diagrams for reference.
𝟏
𝑸=
𝒏
𝟓
[(𝒃 + 𝒙𝒚)𝒚]]𝟑
[𝒃 + 𝟐𝒚√𝟏 +
𝟐
𝟐
𝒙 ]𝟑
𝟏
∗ 𝑺𝟎 𝟐
Where Q=112.87m3/sec
n=0.045 (unlined, rock cut)
x=4.1m
b=2.1m
5
𝟏𝟏𝟐. 𝟖𝟕 =
1
[(2.1+4.1𝒚)𝒚]]3
0.045
2
[2.1+2𝒚√1+4.12 ]3
∗ 0.03
1
2
Substituting into the equation, the maximum flood height (y)= 2.26m
16
Chapter Six
6.0 Bar bending schedule and cost estimates
6.1 Bar bending schedule
Table 6. 4 Bar bending schedule
BAR BENDING SCHEDULE
REINFORCED CONCRETE BRIDGE AT RIVER NJORO
Made by: W.A. Gichuru
Checked by : Eng S.S. Miringu
Element
Mark Bar
No.
No.
Total
Length
Total
No.
type
of
each
No.
each(mm)
length(m)
S1
Y12
1
37
37
4700
174
S2
Y12
1
37
37
6320
234
S3
Y12
1
31
31
11920
370
S4
Y12
1
144
144
1732
249
B1
Y10
1
18
18
2180
39
B2
Y12
1
4
4
5760
23
B3
Y12
1
4
4
5760
23
B4
Y10
1
4
4
4320
17
Crossbeam at B5
Y12
2
4
8
4320
35
Y10
2
18
36
2880
104
Deck Slab
Mid-span
Date: May 2015
crossbeam
abutments
B6
Bar shape
Main
B7
Y16
2
3
6
6060
36
B8
Y16
2
3
6
6060
36
B9
Y32
2
8
16
13520
216
B10
Y16
2
4
8
13520
108
B11
Y10
2
6
12
11920
143
B12
Y10
2
49
98
3080
302
A1
Y32
2
43
86
4700
404
A2
Y12
2
33
66
4200
277
A3
Y12
2
33
66
2600
172
A4
Y12
2
33
66
3200
211
A5
Y12
2
22
44
5270
232
A6
Y12
2
22
44
5270
232
A7
Y12
2
26
52
1620
84
A8
Y8
2
33
66
870
57
A9
Y12
2
6
12
6320
76
A10
Y10
2
6
12
6320
76
A11
Y20
4
29
116
3095
359
A12
Y12
4
29
116
2795
324
beam
Abutment
wall
Wing wall
Wing-wall
A13
Y10
4
23
92
4920
453
A14
Y10
4
23
92
4920
453
A15
Y12
4
21
84
2795
235
A16
Y12
4
21
84
2295
193
A17
Y12
4
23
92
1620
149
F1
Y12
4
34
136
3181
433
F2
Y20
4
34
136
3160
430
F3
Y10
4
11
44
4920
216
F4
Y12
2
17
34
6320
215
F5
Y32
2
52
104
3660
381
F6
Y16
2
52
104
3679
383
footing
Abutment
Footing
Table 6. 5 Bar bending schedule summary
BAR BENDING SCHEDULE SUMMARY
REINFORCED CONCRETE BRIDGE AT RIVER NJORO
Made by:W.A.Gichuru
Checked by: S.S. Miringu
Date : May 2015
F16/36095/2010
Bar type
Y8
Y10
Y12
Y16
Y20
Y25
Y32
Total
57
1587
3941
563
789
0
1001
132.25
328.42
46.92
65.75
0
83.42
0.395
0.616
0.888
1.579
2.466
3.854
6.313
22.515
977.592
3499.608
888.977
1945.674
0
6319.313
length(m)
Full
(12m) 4.75
lengths
Unit weight
(kg/m)
Total
weight
(kg)
Table 6. 6 Cost estimates for reinforced concrete bridge at River Njoro
COST ESTIMATES
REINFORCED CONCRETE BRIDGE AT RIVER NJORO
ITEM
Structural
concrete
DESCRIPTION
UNIT
QUANTITY
RATE
Amount
Kshs
Cts
Provide place and
compact for structural
concrete
M3
4.43
13,500
59805
00
133
17,000
2261000
00
Reinforcing
Class 30 for all other
structural members
M3
Reinforcement bars of
steel
high yield strength to
Class 15 for blinding
BS
4461.Rates
exclusive of labor
Y32
Kg
6319.313
150
947896
95
Y20
Kg
1945.674
150
291851
10
Y16
Kg
888.977
150
133346
55
Y12
Kg
3499.608
150
524941
20
Y10
Kg
977.592
150
146638
80
Y8
Kg
22.515
150
3377
25
5.2
25000
130000
00
40
350
14000
00
4,512,856
85
Bitumen
Provide
surfacing
surfacing
50mm
on
carriageway as well as M3
the midsection of the
footpath.
Drainage
Provide
75mm
pipes
diameter plastic pipes
to drain the bridge M
deck as well as for use
as weep holes
Totals carried forward to the next page
COST ESTIMATES
REINFORCED CONCRETE BRIDGE AT RIVER NJORO
ITEM
DESCRIPTION
Bearing pad Provide
on
UNIT
elastomeric No
QUANTITY
RATE
Amount
Kshs
Cts
6
90000
540000
00
42
2000
84000
00
24
500
12000
00
64
700
44800
00
5,193,656
85
bridge bearing EKR 35
seat
Guard rails
Provide
and
install
parapet
posts
(1m)
height
including M
300*250*20 mm base
plates at 2m meters
apart .(rate inclusive
of base plate)
Provide
and
install M
50mm galvanized iron
pipe hand rail.
Provide
and
install M
flex beam guard rail
Totals carried forward to the next page
COST ESTIMATES
REINFORCED CONCRETE BRIDGE AT RIVER NJORO
ITEM
DESCRIPTION
UNIT
QUANTITY
RATE
Amount
Kshs
Cts
Total carried forward
from
the
previous
page(grand subtotal)
Preliminaries 15%
of
grand
758752
78
of
grand
1011670
37
of
grand
758752
78
252917
59
8656550
37
1385048
06
subtotals
Labour
20%
subtotals
Overhead
15%
costs
subtotals
Profit
5% of grand subtotals
TOTAL
VAT
GRAND
TOTAL
16%
10,041,598 43
Chapter seven
7.0 Recommendations and conclusion
7.1 Recommendations
The right quantities and quality of materials should be ensured during construction in order to
achieve the desired strengths and ensure that the bridge serves its intended purpose during its
design life. The reinforcing steel should be well stored to avoid excessive corrosion which
would interfere with its strength. Guard rails on the deck should be painted to avoid corrosion
and weep holes regularly cleaned to avoid blockage.
7.2 Conclusion
The bridge is to be constructed at a total cost of approximately kshs.10.1million.The
construction of the bridge will open up the region to trade as well as reduce travelling distance
to those wishing to access their homesteads via vehicles thus promoting regional
development.
Chapter eight
8.0 References
8.1 List of references
1. BS 5400 part 2 ,specifications for loads, (1978, 1st edition and 2006, 2nd edition)
2. BS 5400 part 4, code of practice for design of concrete bridges (1990, 3rd edition).
3. Road Design Manual part 4,bridge design by Ministry of Transport and
Communication (1982)
4. Adolf Putcher,1980, Influence Surfaces of Elastic Plates(2nd Edition)
5. Gerald Parke and Nigel Hewson,2008, ICE Manual of Bridge Engineering(2nd Edition)
6. Mosley J.H Bungey, 1987,Reinforced Concrete Design(3rd Edition)
7. Lian Duan and Wai-Fah Chen ,2013, Bridge Engineering Handbook(2nd Edition)
8. D. Fiddes ,1976, The TRRL East African flood model.
9. D. Fiddes,1974, The prediction of storm rainfall in East Africa.
10. http://en.wikipedia.org/wiki/Bridge