Tribhuwan University

Institute of Engineering
Himalaya College of Engineering,
Chyasal, Lalitpur
DEPARTMENT OF CIVIL ENGINEERING
Final Project report on

DESIGN OF RCC BRIDGE

BAGMATI RIVER
SANKHAMUL, KATHMANDU-LALITPUR

Supervisor
DR. BHARAT MANDAL
Prepared by
AJAY KUMAR MEHTA (071/BCE/02)
ASHMIN PARAJULI (071/BCE/12)
BHAGWAN SHRESTHA (071/BCE/18)
KUSHAL ACHARYA (071/BCE/40)
August, 2018
 Tribhuwan University
Institute of Engineering
Himalaya College of Engineering,
Chyasal, Lalitpur

DEPARTMENT OF CIVIL ENGINEERING

This is to certify that the final year project entitled “DESIGN OF RCC BRIDGE
OVER BAGMATI RIVER, SANKHAMUL, KATHMANDU- LALITPUR” was
submitted to the DEPARTMENT OF CIVIL ENGINEERING in the partial
fulfillment of requirement for the degree of Bachelor in Civil Engineering. The
project was carried under special supervision and within the time frame prescribed by
the syllabus.

…………………..
Dr. Bharat Mandal
Project supervisor

………….…. …………………
Er. Md. Abrar Alam Dr. Rajan Suwal
Project Co-Ordinator External Examiner

…………
Er. Hari Lal Kharel
Head of Department
Department of Civil Engineering
 ACKNOWLEDGEMENT
We would like to express deep gratitude to everybody who helped us to complete our
final year project on topic Design of RC Bridge. Without the immense support of you
all, the completion of project in this short frame of time would not have been possible.
To begin with, we would like to thank our college Himalaya College of Engineering
and our project coordinator Er. Md. Abrar Alam sir for giving us this opportunity to
carry out the final year project on this topic. We would like to specially thank our
project supervisor Dr. Bharat Mandal sir for guiding us throughout our work and
helping us to complete our project in time. We would also like to thank our Principal ,
Er. Madan Sharma sir and our Head of Department Er. Hari Lal Kharel sir for their
continuous support throughout the project. Lastly, we would like to thank all our
friends and family for their immense support and help for completion of this project.
 CONTENTS
SALIENT FEATURES ................................................................................................... i
1. INTRODUCTION ..................................................................................................... 1
1.1 Background .......................................................................................................... 1
1.2 Objectives ............................................................................................................. 2
1.3 Scope of Work & Limitations .............................................................................. 2
2. METHODOLOGY .................................................................................................... 3
2.1 Acquisition of data ............................................................................................... 3
2.2 Loading IRC loads for the bridge design: ............................................................ 5
2.3 Superstructure....................................................................................................... 6
2.4 Idealization and Analysis of bridge structure ....................................................... 8
2.4.1 Influence Line Diagram ................................................................................. 8
2.4.2 Design of Deck Slab ...................................................................................... 9
2.4.3 Design of T- Girder ..................................................................................... 13
2.5 Selection of bridge and its components.............................................................. 15
2.6 Method of Design of Bridge............................................................................... 15
3. TOPOGRAPHICAL SURVEY ............................................................................... 16
4. HYDROLOGICAL STUDY ................................................................................... 18
4.1 Catchment Area .................................................................................................. 18
4.2 Hydrological Data .............................................................................................. 19
4.3 Selection of Discharge of River ......................................................................... 23
4.4. Linear Waterway: .............................................................................................. 27
4.5 Contracted water way ......................................................................................... 27
4.6 Scour Depth ........................................................................................................ 27
5. GEOTECHNICAL INVESTIGATION ................................................................... 29
BIBLIOGRAPHY ........................................................................................................ 31
CODES/STANDARDS ............................................................................................... 32
Apendix 1: DESIGN OF SUPERSTRUCTURE ......................................................... 33
Analysis and Design of Deck Slab ........................................................................... 34
Analysis and Design of Cantilever Slab ................................................................... 62
Analysis and Design of Longitudinal Girder ........................................................... 65
Analysis and Design of Cross Girder ....................................................................... 77
Apendix 2: DESIGN OF SUBSTRUCTURE .............................................................. 81
Analysis and Design of Bearing ............................................................................... 82
Analysis and Design of Abutment ........................................................................... 90
Analysis and Design of Pier and Pier Foundation ................................................... 99
Apendix 3: ESTIMATION OF QUANTITY ............................................................ 117
SITE PHOTOGRAPH ............................................................................................... 120
Apendix 4: DRAWINGS AND DETAILING ........................................................... 123
Sheet 01: TOPOGRAPHIC MAP OF THE BRIDGE SITE
Sheet 02: LONGITUDINAL SECTION OF THE BRIDGE SITE
Sheet 03: PLAN AND ELEVATION OF BRIDGE
Sheet 04: PLAN AND SECTION OF BRIDGE DECK
Sheet 05:TOP REINFORCEMENT DETAILING OF DECK SLAB
Sheet 06: BOTTOM REINFORCEMENT DETAILING OF DECK SLAB
Sheet 07: DESIGN DETAILING OF DECK SLAB AND CANTILEVER
SLAB
Sheet 08: DESIGN DETAILING OF MAIN AND CROSS GIRDER
Sheet 09: DESIGN DETAIL OF ABUTMENT
Sheet 10: REINFORCEMENT DETAILING OF ABUTMENT STEM
Sheet 11: DESIGN DETAIL OF PIER AND PIER CAP
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

SALIENT FEATURES
Particulars Required information/Values

Name of the project Design of RCC bridge

Location

State State no :- 3

District Kathmandu- Lalitpur

Municipality Kathmandu & Lalitpur

Name of the road Baneshwor - Shankhamul – Baglamukhi

Road

Chainage of Bridge site 2+100 m

Geographic Location

Bridge Axis 1) 335308.5149N,

3063007.4737E

2) 335218.0334N,
3062927.8161E

Reduced level 1) 1242.2m 2) 1242.3m

Classification of road Urban Road

Type of road surface Bituminous

Terrain type Valley

Information on the Structure

Total length of bridge 100 m

Span arrangement 4 * 25 m

Total width of the bridge 11 m

Number of lanes Two

Width of:

Carriage way 7.5 m

Footpath/Kerb 1.75 + 1.75 m

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Type of superstructure RCC T-girder bridge

Type of bearing Elastomeric pad bearing

Type of abutment RCC Cantilever Type

Type of pier Hammer Head

Type of foundations used Mat Foundation

Design Data

Live Load IRC class AA (wheel and Track)

IRC class A
IRC class 70 R (Wheel and Track)

Net Bearing Capacity of Soil 350 KN/m2

Catchment Area 379 Km2

Design Discharge 500 cumecs

Lacey's Waterway 100 m

Contracted Waterway 93.4 m

HFL 1239.02 m

LBL 1234.7 m

Scour Depth

Abutment 4.57 m

Pier 7.2 m

Quantity Estimate

Concrete M20 =586.854m3

M25=80.265m3
M30= 560.062m3

Steel TMT Fe500 = 90.6 Tons

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

NOTATIONS

∅ Diameter of Bar

𝜏uv Shear Stress

γm Partial Safety Factor

Ag Gross Area
Ah Horizontal Seismic Coefficient
Ast Area of Steel in Tension
Asv Area of Stirrups
bf Flange width
bw Web width
d Effective depth
d’ Effective Cover
D Overall Depth
E Young’s modulus of Elasticity
fck Characteristic Strength of Concrete
fy Characteristic Strength of Steel
I Importance Factor
Ip Polar Moment of Inertia
Ld Development Length
pc Percentage of Steel in Compression
pt Percentage of Steel in Tension
R Response Reduction Factor
Sa/g Average Response Acceleration Coefficient
Sv Spacing of Stirrups
Xu Actual depth of Neutral Axis
Xul Ultimate depth of Neutral Axis
Z Zone Factor

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

1. INTRODUCTION
1.1 Background
Bridge, a civil engineering structure, a structure used since ancient times for crossing any
obstruction beneath it. Who would have imagined that a simple structure used for
crossing obstruction will be used in so many ways with so many materials involved that it
will become such a large field of study at this period of time. Today, bridge is one of the
most prominent civil engineering structures. Different types of bridge are being built
these days due to sophisticated equipment and developed material science.

In context of Nepal, being a mountainous country with a lot of river and rivulets, we need
many bridges just to join one part of the country to another. Therefore, we need to
construct many bridges to ease the extension of road network as well as to carry out other
development works in an efficient way. Therefore, there is a huge potential of bridge
engineering in Nepal.

In this project, we were assigned to design a bridge over Bagmati River connecting the
roads "Baneshwor - Sankhamul - Bangalamukhi - Road" at Sankhamul joining
Kathmandu District with Lalitpur District. As it is a quite busy urban road, two lanes for
design are minimal. We are supposed to design the most economic bridge for this section
based on the various data collected by us. This report is prepared as a part of project work
for the fulfillment of the Project-II as per the syllabus of Bachelor of Civil Engineering
fourth year second part.

In Nepal, mostly RCC T-beam superstructure is preferred as the resources to design and
construct are readily available in Nepal. For our project purpose, we have also designed
RCC T-beam Bridge for learning the bridge engineering skills and practice. The variation
in design procedures for the superstructures, bearings and substructures has helped us to
enhance our understanding of the essentials of Bridge Engineering.

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

1.2 Objectives
The main objectives are to analyze and design the bridge based on Working State method
of design. In addition to that, before start of the work we came with following objectives:
• To obtain the basic ideas of bridge building.
• To be familiar with the different types of bridge and its design principles.
• To know about various type of loading and their forms of application.
• To understand various methods used in the design of the structural components of
bridge and their limitations.
• To be familiar with the design standards and code specifications of bridge
• To be familiar with the standard specification regarding the design of bridge.
The main objective of this project is to design a bridge over Bagmati River by using the
Working State approach of design. Hence, we entitled name of this project as “Design of
RCC T-Bridge over Bagmati River, Sankhamul, Kathmandu- Lalitpur”.

1.3 Scope of Work & Limitations

The assignments done while designing the proposed RC T-beam bridge design are:
• Study of topographic, geological, hydrological, geotechnical and traffic study of
bridge site.
• Visit of bridge site and preparation of site observation report including
verification of data required.
• Carryout design and detailing of selected bridge type.
• Design of appropriate bearing.
• Design of abutment and pier.
• Design of foundation.
• Preparation of detail drawing of bridge superstructures with its all components,
abutments, pier, bearing and footing required for the construction of selected
bridge type.
Limitations
In Nepal, T-beam Bridge is highly preferred but it has some limitations as:
• It is only economic for spans less than 30 m
• Due to presence of large girders and its arrangement, it has less clean appearance.

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

2. METHODOLOGY
2.1 Acquisition of data
For the design of our bridge, the preliminary data needed was acquired after carrying out
different surveys.
I. Site selection survey
For the site selection, we kept in mind the following criteria: -
• A straight reach of river.
• Steady river flow without whirls and across currents.
• A narrow channel with firm banks.
• Sustainable high banks above high flood level on each side.
• Rock or other hard in-erodible strata close to the river bed level.
• Proximity to a direct alignment of the road to be connected.
• Absence of sharp curves in the approaches.
• Absence of expensive river training works.
• Avoidance of excessive underwater construction
In selection of site, care should be taken to investigate a number of probable alternative
sites and then decide on the site which is likely to serve the needs of the bridges at the
least cost.

II. Topographical survey

Topographical survey was carried out for detailed engineering survey of the
proposed bridge site. Total station, reflector and measuring tape were usually
used for detailed survey.
After consultation with the technical personnel and the local villagers and as
directed by the river morphology; an axis joining line joining left bank and right
bank was fixed.
The bridge site detailing area covers a suitable region along the length of river
both upstream and downstream. It also covers left and right banks along the
existing approach roads.

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

III. Geotechnical Investigation

Geotechnical investigation is one of the major parts of the project work for the
design of the proposed bridge at Bagmati River in Kathmandu & Lalitpur
district. Geotechnical investigation works includes core drilling, test pitting,
visual investigation at site. For our project this was not quite possible. Thus, the
geotechnical data were adopted suitable with our locality and as per the similar
works done in the region. However, we carried out the sieve analysis of the bed
soil, finding out its mean size, specific gravity and water content.

Vertical Clearance above H.F.L

For the high-level bridges, a vertical clearance should be allowed between the H.F.L, and
the lowest point of the superstructure. This is required to allow for any possible error in
the estimation of the H.F.L., and the design discharge. It also allows floating debris to
pass under the bridge without damaging the structure
The difference between the vertical clearance and the free-board is sometimes not clearly
understood. While vertical clearance is the difference in level between H.F.L. and the
lowest point of the superstructure, freeboard is associated with the approaches and guides
bunds. The freeboard at any point is the difference between the highest flood level after
allowing afflux, if any, and the formation level of the embankment on the approaches or
the top level of guide bunds at that point, for high level bridges, the freeboard should not
be less than 600 mm.

Scour Depth
Scour of stream bed occurs during the passage of a flood discharge, when the velocity of
stream exceeds the limiting velocity that can be withstand by the particles of the bed
material. The scour depth should be measured with reference to existing structures near
the proposed bridge site, if this is possible. Due allowance should be made in the
observed value for additional scour that may occur due to the designed discharge being
greater than the flood discharge for which the scour was observed, and also due to
increased velocity due to obstruction to flow caused by the construction of bridge.

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

When the above practical method is not possible, the normal depth of scour may be
computed by equation for natural streams in alluvial beds
d =0.473(Q/f).33

Where,
d = normal depth of scour below H.F.L. for regime
conditions in a stable channel in meters.
Q=designed discharge in m3 per second
The minimum depth of foundation is kept at:
• 1.27×d for abutments
• 2×d for piers (IRC 78:2014)

2.2 Loading IRC loads for the bridge design:

According to IRC: 6-2014, road bridges and culverts are classified on the basis of
loadings that they are designed to carry.

IRC class AA loading

This loading is to be adopted within certain

limits, in certain existing or contemplated
industrial areas, and along certain specified
highways and areas. Bridges designed for class
AA loading should be checked for class A
loading is considered in each lane.

IRC class A loading

This loading is normally considered on all in
which dominant bridges and culverts are
constructed. One train of class A loading is
considered in each lane

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

IRC class B loading

This loading is normally considered when the structure is temporary and for bridges in
specified area. Structures with timber spans are to be regarded as temporary structures.

2.3 Superstructure
The basic function of bridge superstructure is to permit the uninterrupted smooth passage
of traffic over it and to transmit the loads and forces to the substructure safely through the
bearings. Although it is difficult to stipulate the aesthetic requirements, it should,
however, be ensured that the type of superstructure adopted is simple, pleasing to the eye,
and blends with the environment.
The superstructure of any bridge must be designed such that it satisfies geometric and
load carrying requirements set forth by its owner. This geometric requirement depends
upon the number and width of traffic lanes and footpaths that have to be carried across.
They also depend on overall alignment and various horizontal and vertical clearances
required above and below the roadway. The superstructure designed has to meet various
structural design requirements such as strength, stiffness and stability.
The horizontal and vertical alignment of a bridge is governed by the geometrics of the
highway, roadway or channel, it is crossing. For girder type bridges, the girders may
either be curved or straight, and may be aligned on chords between supports with the deck
slab built on the curve. The following points require close examination when girders are
aligned on a chord:
• Non-symmetric deck cross section
• Deck finish of the warped surface
• Vertical alignment of the curbs and railings, to preclude visible
discontinuities
• Proper development of super elevation
The various components of superstructure and their limiting dimensions with function as
per IRC 5 is given as follows:
I. Lighting
The lighting of the bridge is generally in accordance with the provisions of the
authority having jurisdiction on that area.

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

II. Drainage
The transverse drainage of the roadway is usually accomplished by providing
suitable crown in the roadway surface, and the longitudinal drainage is
accomplished by camber or gradient.
III. Traffic lane
Roads designed for traffic flow can be single lane, double lane or more. Road
width in meters should be divided by 3.65 and the quotient approximated to the
nearest whole number of design traffic lanes. We have designed our bridge with
two traffic lane.
IV. Road width
Road width is the distance between the roadside faces of the kerbs which depends
on the number and width of traffic lanes and the width of the bounding hard
shoulders. For our project, we have designed road width of 11 m.
V. Footpaths
Footpaths or walkways are generally provided where pedestrian traffic is
anticipated, but not on major arteries or in country sides. Its width is 1.5 m
generally, but may be as narrow as 0.6 m and as wide as 2.5 m depending on the
requirements. For our project, we have designed footpath of 1.75 m wide and 225
mm deep. (DOR)
VI. Road kerb
The road kerb is either surmountable type or insurmountable type. In the absence
of walkways, a road kerb is combined with parapet.
VII. Parapets
Parapets can be of many shapes and of variable sturdiness. They are designed to
prevent a fast moving vehicle of a given mass from shooting off the roadway in
the event of an accidental hit. Their height varies, but it should be at least 700
mm.
VIII. Railing Post
The parapets are usually mounted by metal Railing Post, about 350 mm high.
Their roadside face is double sloped. For our project, we have designed handrail
of size 200×200×1200 mm at end of span and 200×150×1200 mm at middle.
IX. Crash barriers

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Sometimes walkways are protected from the vehicular traffic by crash barriers
which act as insurmountable kerbs and deflect the hitting vehicles back into the
traffic lane.

X. Expansion and roadway joints

To provide for expansion and contraction, joints should be provided at the
expansion end of spans, at other points, where they may be desirable. Joints are
preferably sealed to prevent erosion and filling of debris.
XI. Medians
On expressways and freeways, the opposing traffic flows are separated by median
strips. These reduce the possibility of accidents due to head on collisions.
XII. Super-elevation
The super-elevation of the surface of a bridge on a horizontal curve is provided in
accordance with the applicable standard. This should preferably not exceed 0.06
m per meter, and never exceed 0.08 m per meter.

2.4 Idealization and Analysis of bridge structure

2.4.1 Influence Line Diagram
Usually the structures are analyzed for loads which do not change their points of
application on the structure. Very often structures have to be analyzed for a number of
parallel moving loads which keep on changing their positions on the structure. In such
cases the internal stresses in the structure at any given point, which depend on the
positions of the loads, keep on varying as the loads take up different positions on the
structure.
A typical instance is a bridge loaded with a number of moving vehicles, which are then
said to constitute a train of wheel loads. In order to design such structures, it is not
enough to analyze the structure for a given position of loads and calculate the stress
resultants namely: bending moments, radial and normal shear forces at any section in a
member of the structure. The engineer must know the maximum values of stress
resultants, both positive and negatives, at any section of the structure. Sometimes the
designer would even like to know the maximum deflection at a given point when a
structure is subjected to moving loads.

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

The maximum value of the stress resultants or the deflection at a given section could be
found by taking a number of trial positions of the loads. Such a procedure apart from
being time consuming is also uncertain. The task is very much simplified by using the
concept of influence line.
An influence line is a graph or curve showing the variation of any function such as
reaction, bending moment, shearing force, deflection etc. at a given point of a structure,
as a unit load parallel to a given direction, crosses the structure.
The direction of the moving unit load depends on the nature of loading to be expected in
the structure.

Use of Influence Line Diagram

Using the principle of superposition, the following two types of problems can be solved
with the help of influence lines:
• First, if the influence line for a function is known, its value for a given position
of a number of parallel moving loads can be found.
• The second application is of far more practical importance, influence lines can
be used to locate very easily that particular position of a number of parallel
moving loads on a structure, which will give the maximum positive or
maximum negative value of a function at a given point on the structure.

2.4.2 Design of Deck Slab

Pigeaud’s method is used for the analysis of slabs spanning in two directions for the
bridge design as the bridge design receives heavy patch load.
Hence, Pigeaud's method is most appropriate for the design of deck slab.
Analysis of slab decks
I. Slab spanning in one direction
For slabs spanning in one direction, the dead load moments can directly be computed
assuming the slab to be simply supported between the supports. Bridges deck slabs
have to be designed for I.R.C. loads, specified as class AA or A depending on the

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

importance of the bridge. For slabs supported on two sides, the maximum bending
moment caused by a wheel load may be assumed to be resisted by an effective width
of slab measured parallel to the supporting edges. For a single concentrated load the
effective width of dispersion may be calculated by the equation,
beff = K×x(x-x/L) + bw
Where, beff = Effective width of slab on which load acts
L= effective span
x = Distance of center of gravity from nearer
support
bw = Breadth of concentration of load
K = a constant depending on the ratio (B/L) and is
compiled in IRC 21
II. Slab spanning in two directions
In the case of bridge decks with tee beams and cross girders, the deck slab is
supported on all four sides and is spanning in two directions. The moments in two
directions can be computed by using the design curves developed by M. Pigeaud.
The method developed by Pigeaud is applicable to rectangular slabs
supported freely on all four sides and subjected to a symmetrically
placed concentrated load as shown in the figure below.
The notations used are as follows:
L = long span length
B = short span length
u, v = dimensions of the load spread after allowing for dispersion
through the deck
K = ratio of short to long span = B/L
M1= moment in short span direction
M2= moment in long span direction
m1 and m2 = coefficient of moment along long and short direction
µ = poison’s ratio for concrete generally assumed as 0.15
W = wheel load under consideration.

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

The dispersion of the load may be assumed to be at 45⁰ through the wearing coat
and deck slab according to IRC: 21code specifications. Consequently, the effect
of contact of wheel or track load in the direction of span shall be taken as equal to
the dimension of the tyre contact area over the wearing surface of the slab in the
direction of slab plus twice the overall depth of the slab inclusive of the thickness
of the wearing surface. It is sometimes assumed to be at 45⁰ through the wearing
coat but at steeper angle through the deck slab. The bending moments are
computed as:
M1= (m1+ µm2)×W
M2= (m2+ µm1)×W

Figure Dispersion of Wheel load through deck slab

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Figure Dispersion of wheel load through wearing coat

The values of the moment coefficients m1 and m2, depend upon parameters (u/B), (v/L)
and K.

Curve to compute moment coefficients of slabs completely loaded uniformly distributed

load or dead load of slab for different values of K and 1/K is also given below. The
Pigeaud’s curves used for the estimation of the moment coefficients m1 and m2 for value
of k= 0.5 used in our design are as follows:

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

2.4.3 Design of T- Girder

A very simple, popular and powerful method to analyze girder for live load in simply
supported T-beam bridges is Courbon’s method.

Courbon’s method is popular due the simplicity of the computations and is applicable
when the following conditions are satisfied:

• The ratio of span to the width of bridge greater than 2 but less than 4
• The longitudinal girders are interconnected by at least 5 symmetrically spaced
cross girders.
• Depth of transverse beam should be at least 0.75 times the depth of main beam.

Hence, we adopted Courbon’s method for the analysis and design of girders.

In Courbon’s method, it is assumed that the transverse profile of the bridge deck under
loading remains straight & load shared by each girder in central region of bridge deck is
found by the distribution factors.

When the live loads are positioned nearer to the kerb as shown in figure the CG of live
load acts eccentrically with the CG of the girder system. Due to this eccentricity, the
loads shared by each girder is increased or decreased depending upon the position of
girder. This is calculated by Courbon’s theory by reaction factors given by,

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

axis of bridge
CL

w
e

kerb 1.2m

0.85

dx

Fig. Position of live loads for maximum BM in Girder A

∑𝑊 ∑𝐼
𝑅𝑥 = [1 + (∑ 𝑑2 × 𝐼) 𝑑𝑥 . 𝑒]
𝑛 𝑥

Rx=reaction factor to the girder under consideration

I= moment of inertia of each longitudinal girder

dx= Distance of the girder under consideration form the central axis of the bridge

W= Total concentrated live load

n= Number of longitudinal girders

e= Eccentricity of live load with respect to the axis of the bridge

The live load bending moments and shear forces are computed for each of the girders.
The maximum design moments and shear forces are obtained by adding the live load and
dead load bending moments. The reinforcement in the main longitudinal girders are
designed for the maximum moments and shears developed in the girders.

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

2.5 Selection of bridge and its components

I. T-beam bridge
In context of Nepal, T-beam bridges are highly preferred and are much more in
practice than other bridges. Due to economic cost, usability up to 30 m span,
locally available resources and ease in construction with fewer requirements of
highly skilled manpower and sophisticated equipment T-beam was preferred for
design purpose.
II. Elastomeric bearing
Since our bridge span length is 25 m, the superimposed load was comparatively
less due to its short span length, elastomeric bearings are used. They have less
initial and maintenance cost. Besides occupying a smaller space, elastomeric
bearings are easy to maintain and also to replace when damaged, chloroprene
rubber termed as neoprene is the most commonly used type of elastomer in bridge
bearings. Neoprene pad bearings are compact, weather resistant and flame
resistant.
III. Reinforced concrete abutment
Our height of abutment is above 6 m and hence, reinforced concrete abutment is
preferred.
IV. Hammerhead type pier
Due to high surcharge load and height of pier more than 6 m hammer head type
pier was selected.

2.6 Method of Design of Bridge

Due to abundant use in the construction of RCC bridges all over Nepal, w availability of
and recommendation from our supervisor, we used Working State Method for the design
of bridge components. However, for the design of piers, pier caps and pier foundation, we
used the Limit State Method as it was more accessible than the Working State Method.

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

3. TOPOGRAPHICAL SURVEY
Topographical survey was carried out to prepare topographical map for
pertinent information that may be required for design, construction and
maintenance.
Centre line of proposed bridge site:
After consultation with the technical personnel and the local villagers and as
directed by the river morphology; an axis joining line joining left bank and right
bank is fixed.
Benchmarks
The reference benchmark was established to start with the survey works. The
suitable and convenient place for starting bench mark was marked as BM1 on
the permanent concrete pillar which is situated near by the bridge site on left
bank of the river.

Figure Google earth image showing bridge site

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Site Topography
The area is mostly densely populated, with very less natural terrain but roads
and structures. The Manohara River meets the Bagmati River at around 250 m
upstream of the bridge site.
The site has mild slope of 1 in 1000. The bridge facilitates the 7.5m wide road
connecting Baneshwor – Sankhamul – Bangalamukhi. There is also a road
running under the bridge, along the river on the Kathmandu side. The road
might suffer rare floods with higher return period.

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

4. HYDROLOGICAL STUDY
4.1 Catchment Area
• The catchment area of the river was determined by area declination method.
• The obtained area of catchment is 379 km2.
• The maximum R.L. of the catchment area is 2739.5m whereas the lowest R.L is
1234m
• Coefficient of run offs = 0.8

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

4.2 Hydrological Data

The following hydrological data were studied for our reference.

Average Monthly Discharge

The data studied is of Bagmati river at Khokana which is downstream of our Bridge site
as it was the only data available anywhere near the site. The maximum average monthly
discharge is only 108 m3 /s in 19 years which is less than the adopted discharge. Also,
our site being upstream this gauging station , the discharge is relatively lower than the
studied data, which ensures the adequacy of the discharge adopted.

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Station number: 550.05

Location: Khokana Latitude: 27 37 44
River: Bagmati Longitude: 85 17 41
AVERAGE MONTHLY AND YEARLY DISCHARGE (in m3/s)
==============================================

Year Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. Year
1992 2.41 1.77 0.501 0.267 1.74 2.95 22.5 41.2 31.5 10.0 4.98 3.09 10.2
1993 1.66 1.11 0.943 2.21 4.33 13.9 41.6 66.9 29.4 10.9 4.59 2.16 15.0
1994 2.81 2.41 1.28 1.08 3.43 16.1 31.0 69.6 63.2 14.0 6.46 4.44 18.0
1995 2.38 4.23 3.79 2.70 5.00 40.2 57.0 64.1 33.6 16.2 11.7 10.9 21.0
1996 10.9 5.78 2.95 2.03 1.94 26.6 38.9 61.8 34.0 21.5 11.1 7.33 18.7
1997 4.22 2.74 1.65 5.48 3.84 8.17 61.9 68.3 21.4 13.2 10.6 12.9 17.9
1998 5.82 2.77 3.76 3.57 13.2 14.0 71.7 85.6 37.3 22.0 14.4 8.03 23.5
1999 4.87 4.36 2.19 1.02 3.01 31.8 74.5 73.6 41.4 13.8 11.3 7.28 22.4
2000 5.69 4.55 3.58 4.81 9.60 19.4 39.6 87.2 45.5 13.4 9.27 5.59 20.7
2001 5.35 5.18 4.21 3.39 7.54 11.4 37.6 67.4 42.9 17.4 7.00 5.85 17.9
2002 5.65 5.87 5.97 6.66 14.5 13.4 108 80.4 27.2 8.52 5.00 3.18 23.7
2003 3.83 5.22 3.16 2.39 2.71 6.06 57.4 64.1 48.8 17.1 9.73 7.60 19.0
2004 7.94 5.28 3.97 5.02 9.56 11.4 48.1 36.2 28.1 16.7 8.55 6.63 15.6
2005 8.01 5.19 5.05 3.74 4.65 6.75 20.6 42.7 20.1 14.2 7.83 5.17 12.0
2006 3.88 3.22 3.34 5.23 8.86 11.5 27.4 24.0 25.5 9.40 4.08 3.82 10.8
2007 3.21 6.56 4.87 4.34 6.69 15.5 27.2 32.0 55.2 13.1 6.55 4.57 15.0
2008 3.48 2.85 3.31 2.59 3.63 11.2 19.8 35.2 25.2 10.8 5.81 4.37 10.7
2009 2.78 1.50 1.79 2.94 3.64 3.95 66.0 31.4 21.4 12.9 6.02 3.14 13.1
2010 2.90 2.74 2.44 2.48 4.03 16.3 31.8 44.2 41.3 8.63 4.07 4.22 13.8
---------------------------------------------------------------------------------------------------
Average: 4.62 3.86 3.09 3.26 5.89 14.8 46.4 56.6 35.4 13.9 7.84 5.80 16.8

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Latitude(deg/min): 2742
Longitude(deg/min): 8522
Elevation(m): 1337
Rainfall (mm) for KATHMANDU AIRPORT
Year Jan Feb Mar Apr May Jun JUL AUG SEP OCT NOV DEC
1968 30.1 8.5 45.3 25.5 109.6 305.7 379.5 228.2 86.9 160.4 0.0 0.0
1969 8.6 1.4 47.6 27.4 86.9 166.1 299.7 323.9 175.3 40.3 2.0 0.0
1970 29.1 27.6 26.6 34.4 93.6 193.7 494.3 229.7 163.9 58.2 11.2 0.0
1971 3.0 6.3 28.4 180.8 109.7 608.1 204.6 252.6 36.4 81.2 0.2 0.0
1972 1.4 25.5 80.4 23.8 56.6 157.3 480.9 155.3 174.5 86.1 19.6 0.0
1973 23.7 32.4 48.5 25.3 81.1 340.4 456.0 336.5 321.1 119.3 15.5 0.0
1974 16.9 5.8 23.3 30.9 108.0 74.8 339.6 364.2 204.6 45.6 0.0 11.4
1975 30.6 25.4 8.0 36.1 69.1 138.5 436.1 379.0 267.5 34.2 0.0 0.0
1976 30.2 14.5 0.0 68.6 153.4 387.4 335.0 307.3 169.9 24.3 0.0 0.0
1977 11.5 12.1 17.1 103.9 90.1 265.6 322.7 338.3 78.9 29.1 14.4 13.6
1978 4.7 11.1 69.4 41.7 143.3 298.9 323.6 392.5 159.8 108.6 0.2 2.2
1979 5.6 39.3 0.7 42.1 37.3 258.1 447.3 320.3 99.1 35.7 5.6 65.3
1980 1.0 17.7 45.7 10.1 124.4 349.3 296.1 238.5 183.5 69.0 0.0 5.6
1981 14.5 0.0 60.4 100.9 216.2 140.7 304.0 266.9 225.1 0.0 42.0 0.0
1982 14.2 21.9 35.5 48.8 39.7 200.5 238.2 384.3 155.4 9.0 18.3 3.4
1983 18.2 4.0 30.2 78.7 110.1 81.4 499.9 194.2 287.7 129.9 0.0 15.3
1984 13.9 17.4 13.5 60.1 96.0 275.0 250.1 301.9 260.2 18.4 0.1 7.4
1985 9.7 3.2 4.0 24.8 132.5 160.8 418.3 434.4 375.6 167.2 0.0 54.6
1986 0.0 22.5 15.8 93.4 96.9 315.6 380.8 218.6 221.3 79.5 0.0 49.4
1987 3.2 43.3 35.9 34.4 57.6 116.4 498.8 256.3 171.2 159.3 0.0 18.8
1988 0.6 19.1 68.0 42.3 152.9 239.5 397.3 278.7 134.4 17.6 11.7 78.9
1989 47.4 10.7 12.1 4.0 148.7 135.5 328.0 206.0 196.5 42.4 0.0 0.7
1990 0.0 42.2 59.5 116.2 108.3 364.7 345.6 308.5 188.2 78.7 0.0 2.8
1991 20.7 11.4 45.2 106.3 145.3 114.4 190.3 280.9 127.9 0.4 0.2 24.9

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Year Jan Feb Mar Apr May Jun JUL AUG SEP OCT NOV DEC
1992 6.4 17.2 0.2 44.5 69.9 232.7 223.6 219.9 209.1 51.0 15.5 3.1
1993 10.2 15.4 42.0 86.8 184.6 204.4 296.3 293.8 156.2 14.5 1.8 0.0
1994 27.3 19.4 13.9 8.3 141.8 413.6 254.1 445.6 243.2 0.0 12.0 0.0
1995 3.3 28.8 39.8 3.2 60.5 590.5 336.1 404.1 100.6 38.3 61.6 7.0
1996 70.8 15.2 7.1 47.4 57.7 337.8 318.5 485.5 207.3 52.4 0.0 0.0
1997 16.4 5.5 13.9 100.1 90.3 245.4 511.0 370.5 70.9 12.0 4.9 87.4
1998 0.1 28.2 70.6 75.9 282.0 247.7 440.2 376.3 193.6 44.2 12.0 0.0
1999 4.2 4.2 0.0 6.0 106.5 315.6 485.2 393.5 266.9 152.2 0.0 1.2
2000 1.3 5.3 20.9 61.9 209.9 266.5 336.3 384.7 119.4 0.6 0.0 0.2
2001 6.8 15.7 8.4 34.6 179.9 250.4 498.8 460.3 145.5 20.5 0.0 0.0
2002 33.8 29.9 93.0 93.9 158.8 227.4 544.8 499.9 148.0 15.0 26.5 0.0
2003 19.5 68.4 85.9 38.0 37.7 222.3 591.5 347.0 293.4 17.7 0.0 18.6
2004 26.9 0.0 32.3 164.1 168.8 183.0 459.5 219.4 199.1 120.5 36.0 0.0
2005 55.1 17.0 50.1 34.8 40.6 222.9 253.5 309.3 126.5 126.1 0.0 0.0
2006 0.0 0.0 30.9 132.8 145.5 216.2 337.0 248.4 217.5 43.9 1.5 17.5
2007 0.0 72.8 36.3 77.9 90.7 263.0 227.3 223.7 332.5 18.5 3.2 0.0
2008 4.9 0.0 35.9 43.7 99.9 237.7 255.4 240.8 291.3 10.3 0.0 0.0
2009 0.0 0.0 28.4 21.3 132.0 125.0 326.3 382.9 113.4 71.5 1.0 3.6
2010 1.9 23.3 35.7 45.3 148.0 141.7 354.9 486.3 217.1 24.5 0.0 0.0
2011 6.2 54.9 16.4 56.8 167.4 306.0 437.8 265.4 318.0 13.0 12.9 0.0
2012 17.8 41.8 15.6 80.1 42.2 149.2 452.3 289.6 362.2 13.2 0.7 0.0
2013 11.5 45.4 27.3 44.5 278.6 299.1 428.5 451.4 217.3 95.7 0.0 0.0
2014 4.2 26.7 58.7 6.0 153.5 165.8 461.9 294.5 279.4 91.2 0.0 36.7
2015 3.4 35.2 98.7 51.0 155.9 125.6 470.6 452.0 189.4 67.6 0.0 0.0
2016 0.4 25.3 6.3 11.0 92.3 370.2 477.8 126.8 281.7 91.0 0.0 0.0

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

4.3 Selection of Discharge of River

The discharge of river was computed using various methods described in the
methodology section.

Rational Method
𝐶∗𝑖∗𝐴
𝑄𝑝 =
360
A= Area in hectares
i = Rainfall intensity
C= Coefficient of Runoff

𝐾𝑇 𝑎 1
𝑖= 𝑛
; 𝑇 = = 100
(𝑡𝑐 + 𝑏) 𝑃
𝑘 = 5.92, 𝑎 = 0.162, 𝑏 = 0.5, 𝑛 = 1.013
0.77 −0.385
𝑡𝑐 = 0.019478𝐿 𝑆
𝐿 = 21,748 𝑚
𝐻 = 2729.5 − 1234 = 1495.5 𝑚
H= Difference in elevation between remotest point of the basin & outlet in m

= 1495.5 m

Area (A) = 37900 hectares

1495.5
S= = 0.0688
21748

𝑡𝑐 = 0.019478 ∗ 217480.77 ∗ 0.0688−0.385

= 119.37 𝑚𝑖𝑛𝑠

5.92 ∗ 1000.162
𝑖= 1.013
120.968
( + 0.5)
60

= 4.955 𝑚𝑚/ℎ𝑟

𝐶 ∗ 𝑖 ∗ 𝐴 0.8 ∗ 4.955 ∗ 37900

𝑄= = = 371.49 𝑚3 /𝑠
360 360

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Gumbel Method
DISCHARGE DISCHARGE
̅
𝑋 −𝑋 2 ̅
𝑋 −𝑋 2
(Q) (m3/SEC) (Q) (m3/SEC)
41.2 431.39 108 2118.76
66.9 24.3 64.1 4.54
69.6 58.22 48.1 192.38
64.1 4.54 42.7 371.33
61.8 0.0289 27.4 1195.38
68.3 40.07 55.2 45.83
85.6 558.38 35.2 716.63
74.5 157 66 16.24
87.2 636.55 44.2 315.77
67.4 29.48

∑ 𝑋 = 1177.5 ∑(𝑋 − 𝑋̅) = 6916.52 N= 19

∑(𝑋−𝑋̅ )2 6916.52
𝜎𝑥 = √ =√ =19.6
𝑁−1 19−1

For N= 19 years,
Form table:
𝑦̅n= 0.52076
𝑆̅n=1.05148
For T=100 years,
𝑇
yt = −ln(ln(𝑇−1))
100
y100 = −ln(ln(100−1)) = 4.6
𝑦100 −𝑦̅𝑛 4.6−0.52076
∴ 𝐾100 = = =3.87966
𝑆𝑛 1.05148

𝑄100 = 61.97 + 3.87966 × 19.60 = 138.01𝑚3 /𝑠𝑒𝑐

Modified Dickens' Method

Using Dickens' method, the T year flood discharge QT, in m3/s, shall be determined as
QT = CT A0.75
Where,
A= total catchment area of river = 380 sq.Km.
1185
CT = 2.642 log( )+4
𝑝

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

𝑎+6
p = 100 𝐴+𝑎

a= perpetual snow area = 0

T = return period in years = 100 years
p = 1.579
CT = 15.97
Then,
QT = CT A0.75
= 15.97 * 3800.75
= 1374.85 m3/s

Fuller's method
𝐴 −0.3
Q max = QT [1 + 2 (2.59) ]

QT = maximum 24 hr flood
= Qav ( 1+0.8log 𝑇) = 120(1+0.8log 100) = 242.76 m3/s
𝐴 −0.3
Q max = QT [1 + 2 (2.59) ]

380 −0.3
=242.76 [1 + 2 (2.59) ]

=351.46 m3/s

WECS method
Q2 = 1.8767 (𝐴3000 + 1)0.8783
Q100 = 14.63 (𝐴3000 + 1)0.7342
= 14.63 ( 380 + 1)0.7342
=1148.57 m3/s

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Slope Area Method

Manning’s Coefficient, n = 0.03
Area, A = 276.79 m2
Perimeter, P = 110 m
Bed Slope, S = 1 in 1000
1 2
𝑄= ∗ 𝐴 ∗ 𝑅 3 ∗ √𝑆
𝑛
= 492.73 𝑚3 /𝑠
𝑄 492.73
𝑣= =
𝐴 276.79
𝑣 = 1.78 𝑚/𝑠
The values were analyzed and maximum of all was selected as:

Flood Discharges of Return Periods by Various Methods:

Flood discharge
S.N. Methods in m3/sec
100 Years
1 Rational Method 371.49
2 WECS Method 1148.57
3 Modified Dickens 1374.85
492.73
4 Slope Area Method

5 Gumbel Method 138.01

Fullers Method 351.46
6

Design Discharge 500

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

4.4. Linear Waterway:

S.N Methods Design discharge (Q) Mean channel length (B)
1 Kellerhals formula 500 m3/s 72.9m

2 Lacey's formula 500 m3/s 106.21m

In case of Hilly region and alluvial bed river, the waterway calculated by this method
seems to be reasonable in other rivers and streams. We adopted the linear waterway of
about 100 m according to the profile of HFL and practical judgement.

4.5 Contracted water way

The contracted water way = Linear way water – obstruction due to piers
= 100 − 3 ∗ 1.8 − 2 ∗ 0.6
= 93.4 m

4.6 Scour Depth

Actual channel width at site according to HFL at 1239.02 m = 100 m

Mean regime channel width = 48.861m

For catchment area of 0-3000m3/s

Adopted design discharge=500 m3/s

Adopted channel width=100 m

Effective water way= 100-1.8*3-0.6*2= 93.4 m

I. IRC 78/2014
d sm=1.34(q2/f)1/3

Q 500
where, q = B =1.3 ∗ 93.4= 6.96 m2/s

dm=weighted mean diameter of the particles in mm (from lab sieve

analysis) =2 mm

silt factor=f=1.76√2 = 2.49

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

mean scour depth = 3.6 m

Maximum scour depth for abutment =1.27× dsm=4.57 m

Maximum scour depth for pier=2×dsm= 7.2 m

II. IRC Special Publication 13

Scour depth (d) = 0.473(Q/f)1/3

Silt factor(f)=1.76√𝑑m =2.49

d=0.473(1.3 * 500/2.49)1/3=3.02 m

W=C×Q0.5=4.75×194.0380.5=58.032 m

D1=D(W/L)0.61 =1.816(58.032/30.4)0.6=2.694m

where L=width of flow

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

5. GEOTECHNICAL INVESTIGATION

Fig :- Geological Map of Nepal

The bridge site lies in the Tibetan Tethys Zone. Furthermore, Kathmandu valley being a
drained lake, possess alluvial soil and sedimentary rocks beneath. However, due to the
river action, we can find eroded evidences of sedimentary rocks as well as silty sand
deposits.

Soil/Bearing Capacity
The average particle size of soil particles was found to be 1 mm through sieve analysis
with the following characteristics.

Summary of soil investigation:

Water content = 11.94 %

Specific gravity = 2.645

Sieve Analysis Curve (depth 0.0-0.5m)

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

The bearing capacity of soil was adopted to be 350 KN/m2 by observing the general soil
properties and similar works done in the region.

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

BIBLIOGRAPHY
I. Victor, D.J. 2012. Essentials of Bridge Engineering, Oxford and IBH Publishing
Company Pvt. Ltd., New Delhi
II. Design Examples Provided by Asso. Prof. N.C. Sharma, IOE, Pulchowk
III. N.Krishna raju, Design of Bridges, Oxford and IBH Publishing Company Pvt.
Ltd., New Delhi
IV. Swamisaran, Design of substructures
V. Jain, A.K. 2002. Reinforced Concrete Limit State Design, Nem Chand and Bros,
Roorkee, India
VI. Design examples and detail drawings provided by Er. Aanand Kr. Mishra.

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

CODES/STANDARDS
Following codes were followed during the course of our bridge design :-

Codes Uses

IRC : 5 – 1998 (Section I) General feature of design

IRC: 6- 2014 (Section II) Load and stresses

IRC: 21-2000 (Section III) Cement concrete

IRC : 78- 2014 (Section VII) Foundation and substructure

IRC : 83- 1987 (Section IX) Bearings

SP 16 RCC

IRC 112 RCC

IS 456-2002 Plain and Reinforced concrete

Nepal bridge standard

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Apendix 1: DESIGN OF SUPERSTRUCTURE

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Analysis and Design of Deck Slab

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Design of deck slab

Clear roadway= 7.5 m
Spacing of main girder= 2.5m
Effective span= 25m
Spacing of cross girder= 5m
Thickness of wearing coat= 80mm
Effective span= 5-0.3= 4.7m
Effective width= 2.5-0.3= 2.2m
Dead load:
Weight of deck slab= 0.2×25= 5KN/m2
Wearing coat= 0.08×22= 1.76KN/m2
Total dead load= 6.76 KN/m2
𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑤𝑖𝑑𝑡ℎ 2.2
k = 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑙𝑒𝑛𝑔𝑡ℎ =4.7 = 0.47

1
=2.14
𝑘

From Pigeaud’s curve,

m1= 0.047
m2= 0.008
Total dead weight, w= 6.76×2.2×4.7
= 62.46KN
Moment in short span= (m1+𝜇m2) ×w
= 3.012KNm
Moment in long span = (m2+𝜇m1) ×w
= 1.12KNm

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Live load BM due to IRC class AA tracked Vehicle:

300
MAIN GIRDER
WIDTH

LENGTH ONE TRACK OF IRC

CLASS AA TRACK
GIRDER
VEHICLE
CROSS

CROSS GIRDER
851

2200
3600

5000

300 MAIN GIRDER

FIG: PLACEMENT OF IRC CLASS AA TRACKED VEHICLE FOR MAXIMUM LOADING

Size of panel of deck slab = 2.2m × 4.7m

One track of tracked vehicle is placed symmetrically on the panel as shown in figure
Impact factor fraction = 25%
Width of load spread along short span (u) = 0.85 + 2 × 0.08
= 1.01 m
Width of load spread along long span (v) = 3.6 + 2 × 0.08
= 3.76 m
𝑢 1.01
k = 0.468, = = 0.46
𝐵 2.2
𝑣 3.76
= = 0.8
𝐿 4.7

Using Pigeaud's curves

m1 = 8.6× 10 -2
m2 = 0.9 ×10 – 2
Total load per track including impact = 1.25 × 350 = 437.5 KN
Effective load on span = 437.5

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Moment along shorter span = (m1 + µ m2) × effective load on span

= (8.6+ 0.15 × 0.9) × 10 – 2 × 437.5
= 38.22KNm
Moment along longer span = (m2 + µ m1) × effective load on span
= (0.9 + 0.15 × 8.4) × 10 – 2 × 437.5
= 9.45KNm
Live load BM due to IRC class 70 R tracked Vehicle
300

MAIN GIRDER

WIDTH
ONE TRACK OF IRC
LENGTH CLASS 70R TRACK
VEHICLE
GIRDER

CROSS GIRDER
CROSS

2200
851

4570
5000

300 MAIN GIRDER

FIG: PLACEMENT OF IRC CLASS 70R TRACED VEHICLE FOR MAXIMUM LOADING

Size of panel of deck slab = 2.2 m × 4.7 m

One track of tracked vehicle is placed symmetrically on the panel as shown in figure
Impact factor fraction = 25%
Width of load spread along short span (u) = 0.84 + 2 × 0.08
=1m
Width of load spread along long span (v) = 4.57 + 2 × 0.08
= 4.73 m>4.7m
= 4.7m

Page | 37
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

k = 0.468 ,
𝑢 1.0
= 2.2 = 0.45
𝐵
𝑣 4.7
= 4.7 = 1
𝐿

Using Pigeaud's curves

m1 = 7 × 10 -2
m2 = 0.7×10 – 2
Total load per track including impact = 1.25 × 350 = 437.5 KN
4.7
Effective load on span = 437.5× 4.73

= 434.725 KN
Moment along shorter span = (m1 + µ m2) × effective load on span
= (7+ 0.15 × 0.7) × 10 – 2 × 434.725
= 30.887KNm
Moment along longer span = (m2 + µ m1) × effective load on span
= (0.7 + 0.15 × 7) × 10 – 2 × 434.725
= 7.607KNm

Page | 38
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Moment due to class AA wheeled vehicle

VEHICLE VEHICLE
DIRECTION DIRECTION

2350

270
460
190
300 W1
62.5 KN 62.5 KN
310

37.5 KN
W3 W2
1000

1200 1000
2350

600

310
37.5 KN 62.5 KN 62.5 KN
W6 W4 W5
460

2200
FIG: POSITION OF CLASS AA WHEELED VEHICLE FOR
MAXIMUM MOMENT

Wheel-1
u= 0.3+2×0.08= 0.46
v= 0.15+2×0.08= 0.31
𝑢
=0.21
𝐵
𝑣
=0.07
𝐿

k= 0.047
m1= 21×10-2
m2=18×10-2
Mshort= (21+0.15×18) ×10-2×1.25×62.5=18.51KNm
Mlong= (18+0.15×21) ×10-2×1.25×62.5=16.52KNm

Page | 39
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Wheel-2

DUMMY LOADING
62.5 KN

(62.5×1.25)
Intensity of loading= = 547.86KN/m2
0.46×0.31

Considering loaded area =2.2×0.31

𝑢
=1
𝐵
𝑣 0.31
= 4.7 = 0.08
𝐿

k= 0.47
m1= 9.3×10-2
m2=6.3×10-2
Mshort= (9.3+0.15×6.3) ×10-2×2.2×0.31 ×547.86=38.77KNm
Mlong= (6.3+0.15×9.3) ×10-2∗ 2.2 × 0.31 × 547.86=28.75KNm
Considering the area between real and dummy wheel =1.54 m ×0 .31 m
u= 1.54
v= 0.31
𝑢
= 1.54/2.2
𝐵

= 0.7
𝑣
= 0.07
𝐿

k= 0.047
m1= 12×10-2
m2=9 ×10-2

Page | 40
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Mshort= 34.92 KNm

Mlong= 28.25KNm
Net Mshort= 0.5×(38.3-34.92) = 1.69 KNm
Net Mlong=0.5×(28.75-28.25) = 0.25 KNm
Wheel-3

DUMMY LOADING

37.5 KN

387 387

1.25×37.5
Intensity of loading= 0.46×0.31 = 328.72KN/m2

Area= 1.66×0.31m
𝑢
=0.75
𝐵
𝑣
= 0.07
𝐿

k= 0.47
m1= 11.5×10-2
m2=9×10-2
Mshort= (11.5+0.15×9) ×10-2×328.72×1.66×0.31=21.74 KNm
Mlong= (9+0.15×11.5) ×10-2×328.72×1.66×0.31=18.14 KNm
Between dummy and wheel
Area= 0.74m×0.31m
𝑢
𝐵
=0.34

Page | 41
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

𝑣
= 0.07
𝐿

k= 0.47
m1= 18×10-2
m2=17×10-2
Mshort= (18+0.15×17) ×10-2×328.72×0.74×0.31=15.97 KNm
Mlong= (17+0.15×18) ×10-2×328.72×0.74×0.31=14.86 KNm
Net moment
Mshort= 0.5×(21.74-15.97) =2.89KNm
Mlong=0.5×(18.14-14.86) = 1.64KNm
Wheel-4
2350

DUMMY LOADING
2350

62.5 KN

2200

Area=0.46m×2.71m
𝑢 0.46
= 2.2 = 0.21
𝐵
𝑣 2.71
= = 0.58
𝐿 4.7

k= 0.47
m1= 12×10-2
m2=2. 1 ×10-2
Mshort= 84.1 KNm

Page | 42
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Mlong= 26.63KNm
Between wheel and dummy load .46 m × 2.09 m
𝑢
=0.21
𝐵
𝑣 2.09
= 0.44
𝐿 4.7

k= 0.047
m1= 13×10-2
m2=3×10-2
Mshort= 70.84 KNm
Mlong= 26.07 KNm
Net moment
Mshort= 0.5×(84.1-70.84) =6.63KNm
Mlong=0.5×(26.63-26.06) = 0.285KNm
Wheel-5
2350

DUMMY LOADING
2350

62.5 KN

Area= 2.2m×2.71m
𝑢
𝐵
=1

Page | 43
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

𝑣
= 0.58
𝐿

k= 0.47
m1= 6.8×10-2
m2=1×10-2
Mshort= 227KNm
Mlong= 65.98 KNm
Between dummy load and wheel
Area =2.2m×2.09m
𝑢
=1
𝐵

k= 0.47
𝑣
= 0.44
𝐿

m1= 7.5×10-2
m2=1.6×10-2
Mshort= 194.97KNm
Mlong= 68.64KNm
Area = 1.54m×2.71m
𝑢
= 0.7
𝐵
𝑣
= 0.58
𝐿

k= 0.047
m1= 8.8×10-2
m2=1.5×10-2
Mshort= 206.35 KNm
Mlong= 64.47KNm
Area = 1.54m×2.09m
𝑢
= 0.7
𝐵
𝑣
= 0.44
𝐿

k= 0.47

Page | 44
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

m1= 9.7×10-2
m2=2.4×10-2
Mshort= 177.39KNm
Mlong= 67.97KNm
Net moment,
Mshort= 0.25 ×(227 – 194.47 -206.35+177.39) = 0.89 KNm
Mlong= .25 × ( 65.98 – 68.64 – 64.47 + 67.97) = 0.21 KNm
Wheel-6
2350

DUMMY LOADING
2350

37.5 KN

2200

FIG: DEPOSITION OF CLASS AA WHEELED VEHICLE

FOR MAXIMUM MOMENT

Area= 1.66m×2.71m
𝑢
= 0.75
𝐵
𝑣
= 0.58
𝐿

k= 0.47
m1= 8.5×10-2
m2=1.4×10-2

Page | 45
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Mshort= 128.8KNm
Mlong= 39.55KNm

Area= 0.74m×2.71m
𝑢
= 0.34
𝐵
𝑣
= 0.58
𝐿

k= 0.47
m1= 11.5×10-2
m2=1.8×10-2
Mshort= 77.58KNm
Mlong= 23.23KNm

Area= 1.66m×2.09m
𝑢
= 0.75
𝐵
𝑣
= 0.44
𝐿

k= 0.47
m1= 9.4×10-2
m2=2.2×10-2
Mshort= 110.96KNm
Mlong= 41.17KNm

Area= 0.74m×2.09m
𝑢
= 0.34
𝐵
𝑣
= 0. 44
𝐿

k= 0.47
m1= 13.2×10-2
m2=3×10-2

Page | 46
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Mshort= 69.39KNm
Mlong= 25.32KNm
Net moment,
Mshort= 0.25 × (128.8 -77.58-110.96+69.39) = 2.41 KNm
Mlong=0.25×(39.55-23.23-41.17+25.32) =0.12KNm
Moment due to wheel loading,
Mshort= (18.51+1.69+2.89+6.63+0.89+2.14) =32.75 KNm
Mlong= (16.52+0.25+1.64+0.285+0.21+0.12) = 19.025KNm

Live load due to IRC class 70R wheeled vehicle;

W3 W1 W2

2200
860

610 1370
60 KN 85 KN 85 KN

FIG. PLACEMENT OF IRC 70R WHEELED

VEHICLE FOR MAXIMUM LOADING

BM due to wheel 1
Tyre contact dimension = 0.86 × 0.61
u = 0.86 + 2 × 0.08 = 1.02 m
v = 0.61 + 2× 0.08 = 0.77 m
𝑢 1.02
= = 0.4636
𝐵 2.2
𝑣 0.77
= = 0.164
𝐿 4.7
2.2
K = 4.7 = 0.468

Page | 47
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

for k = 0.5
m1 = 13.5 × 10- 2 , m2 = 9 × 10-2
for k = 0.4
m1 = 16 × 10- 2 , m2 = 9.1 × 10-2
for k = 0.468
m1 = 14.3 × 10- 2 , m2 = 9.068 × 10-2
Impact factor = 25 %
Impact load = 85 × 1.25 = 106.25 KN
Moment along short span = (m1 + µ m2) × w
= (14.3 + 0.15 × 9.068) × 106.25 × 10 - 2
= 16.638 KNm
Moment along short span = (m2 + µ m1) × w
= (9.068+ 0.15 × 14.3) × 106.25 × 10 - 2
= 11.914 KNm

BM due to wheel 2:
4700

DUMMY LOAD
W2
2200

675 675
2130

FIG.BM DUE TO W2

Intensity of
85 2
Loading = 0.86 ∗ 0.61 = 162.028 KN/m

Loaded area = 0.86 × (4.7 – 0.675 × 2)

= 0.86 × 3.35

Page | 48
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

For whole loaded area,

u = 0.86 + 2 × 0.08 = 1.02, v= 3.35 + 0.08 × 2 = 3.51
𝑢 1.02 𝑣 3.51
= = 0.463 = = 0.747
𝐵 2.2 𝐿 4.7

For K = 0.4
m1 = 8.9 × 10 – 2 m2 = 1.9 × 10 – 2
for K = 0.5
m1 = 8.8 × 10 – 2 m2 = 0.9 × 10 – 2
for K = 0.468
m1 = 8.832 × 10 – 2 m2 = 1.22 × 10 – 2
Moment along short span = (m1 + µ m2) × w
= ( 8.832 + 0.15 × 1.22 )× 162.028 × 0.86 × 3.35 × 10 – 2
= 42.082 KNm
Moment along short span = (m2 + µ m1) × w = 11.875 KNm
Next, consider the area between the real and dummy load to be ; 2.13 m × 0.86 m
u = 1.02 v = 2.13 + 0.08 ×2 = 2.19
𝑢 1.02 𝑣 2.19
= = 0.464 = = 0.466
𝐵 2.2 𝐿 4.7

K = 0.468
for K = 0.4
m1 = 12 × 10 – 2 m2 = 4 × 10 – 2
for K = 0.5
m1 = 11 × 10 – 2 m2 = 2.6× 10 – 2
for K = 0.468
m1 = 11.32 × 10 – 2 m2 = 3.048 × 10 – 2
Moment along short span = 34.955 KNm
Moment along long span = 14.086 KNm
1
Net BM along short span = 2 ∗ (42.082 − 34.955) = 3.563 KNm
1
Net BM along long span = 2 ∗ (14.086 − 11.879) = 1.1035 KNm

Page | 49
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

BM due to wheel 3

4700

DUMMY LOADING

W3

2200
375 3950 375
60 KN

BM DUE TO WHEEL 3

Consider total loaded area of 4700 × 860

u = 1.02, v = 1
𝑢 1.02
= = 0.464
𝐵 2.2

K = 0.468
For K = 0.4
m1 = 7 × 10 – 2 m2 = 1.3 × 10 – 2
For K = 0.5
m1 = 7.8 × 10 – 2 m2 = 3.2 × 10 – 2
For K = 0.468
m1 = 7.544 × 10 – 2 m2 = 2.592 × 10 – 2
Moment along short span = (m1 + µ m2) × w
= (7.544 + 0.15 × 2.592) × 162.028 × 0.86 × 4.7 × 10 – 2
= 51.953 KNm
Moment along short span = (m2 + µ m1) × w = 24.386 KNm
Next,
Consider the area between the real and dummy load to be; 4.7 m × 0.375 m
u = 1.02 v = 4.7 – 2 × 0.375 = 3.95
𝑢 1.02 𝑣 3.95
= = 0.463 = = 0.84
𝐵 2.2 𝐿 4.7

Page | 50
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

K = 0.463
for K = 0.4
m1 = 8.1× 10 – 2 m2 = 1.7 × 10 – 2
for K = 0.5
m1 = 8.2 × 10 – 2 m2 = 0.8 × 10 – 2
For K = 0.463
m1 = 8.163 × 10 – 2 m2 = 1.133 × 10 – 2
Moment along short span = (m1 + µ m2) × w
= (8.163 + 0.15 × 1.133) ×10 – 2 × 3.95 × 0.86 ×162.028
= 45.86 KNm
Moment along long span = (m2 + µ m1) ×w = 12.975 KNm
1
Net BM along short span = 2 ∗ (51.953 − 45.86) = 3.046 KNm
1
Net BM along long span = 2 ∗ (24.386 − 12.975) = 5.705 KNm

Total BM due to all wheels,

BM along short span = (16.638 + 3.563 + 3.046)
=23.247 KNm
BM along long span = (11.914 + 1.103 + 5.705)
= 18.722 KNm
Design of the reinforcement:
Mshort=38.22 KNm
Mlong=19.03 KNm
Due to dead load:
Mshort=3.013KNm
Mlong=1.12 KNm
Total moment:
Mshort=38.22+3.013= 41.235KNm
Mlong=19.03+1.12=20.15KNm
Now, using continuity factor of slab 0.8 then design moment,

Page | 51
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Mshort=0.8×41.235=32.988KNm
Mlong=0.8×20.15= 16.12KNm
Using M30 concrete and TMT steel,
fck= 30MPa fy=500MPa
𝜎cbc=10MPa 𝜎cbc=240MPa
280/3 280/3
k= 280 =280 =0.28
+𝜎st +240
3 3

𝑘 0.28
j= 1-3 =1- 3
1 1
R= 2 × 𝜎cbc× 𝑘 × 𝑗 = × 10 × 0.9067
2

R= 1.2693
Check for depth:
Bending moment= R×b×d2

32.988×106
D=√1.2693×100 =161.21 <165mm (OK)

Hence, overall depth of slab , D= 200mm

Effective depth of slab = 168mm
Design of reinforcement:
Along short direction:
Mshort=𝜎st×Ast×j× 𝑑
32.988×106
Ast= 240×0.9067×170 =902.34mm2
0.12
Ast, min= × 200 × 1000
100

Ast, min=240mm2
Provide 12mm∅bars@110mm c/c
𝜋×62
Ast, provided= 110 × 100= 1028.157mm2>Ast, required

In longer direction:
Mlong= 𝜎st×Ast×j× 𝑑 ′
12 10
d’= 168- 2 - 2 =157mm

Page | 52
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

16.12×106
Ast=240×0.9067×158 =471.82mm2

Provide 10mm∅bars @150mm c/c

𝜋×52
Ast, provided= 150 × 1000= 523.6mm2>Ast, required (OK)

Check of deck slab in shear:

1. For IRC class AA loading:
a) Track vehicle:

350 KN
80mm Bituminous layer

200 mm deck slab

FIG -load distribution for shear force calculation of CLASS AA Track

vehicle

clear span length = 4.7 m

B/L = 4.7/2.2=2.14 m
K =2.6
Effective width calculation :
be = kx(1-x/l)+bw
= 2.6*0.705*(1-0.705/2.2)+3.6+0.08*2
= 5.0056 m
Load per m width =350/5.0056 =69.92 KN /m

Page | 53
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Shear Force
= 69.92*(2.2-0.705)/2.2
= 46.51 KN
Shear force with impact
=1.25*46.51
=59.39 KN
Shear force due to dead load
dead load = 25*0.20+22*0.08
=6.76 KN/m2
shear force due to dead load
=6.76 *2.2/2
=7.436 KN
Total S.F = 7.436 +59.39 = 66.826 KN

Check for shear:

𝑉
Nominal Shear stress (τv)= 𝑏𝑑

= 66.826*103/103 *168
=0.398 N/mm2
k =1.2
pt = 100* A/bd
= 100*1028.16/1000*168
= 0.612
For M30 grade concrete τco =0.337N/mm2
τc=k * τc0
=1.2*0.337
=0.404N/mm2

Page | 54
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

A. Wheeled vehicle
Shear due to live load :
I. For 37.5KN

37.5KN

Fig:wheel position for shear force due to IRC Class AA

wheel load
1ST wheel only

For continuous slab K=2.6

Effective width of slab=kx(1-x/l)+bw
=2.6*0.43(1-0.43/2.2)+0.15+2*0.08
=1.2 m
Load per m width:
=37.5/1.2
=31KN/m
Shear force = 31(2.2-0.43)/2.2
=24.94 KN
Considering impact factor
=1.25*24.94
=31.18 KN

Page | 55
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

II.For 62.5KN

CL

62.5KN

Fig:wheel position for shear force due to IRC Class AA wheel load
2nd wheel only

For continuous slab K=2.6

Effective width of slab=kx(1-x/l)+bw
=2.6*1.03(1-1.03/2.2)+0.15+2*0.08
=2.28 m
Load per m width:
=62.5/2.28
=27.39 KN/m
Shear force = 27.39 (2.2-1.03)/2.2
=14.56 KN
Considering impact factor
=1.25*14.56
=18.2 KN
II. For 62.5KN(edge)
CL

54.35

Fig:wheel position for shear force due to IRC Class AA wheel

load 3rd wheel only

Page | 56
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

For continuous slab K=2.6

Effective width of slab=kx(1-x/l)+bw
=2.6*2(1-2/2.2)+0.15+2*0.08
=0.782m
Load per m width:
=54.35/0.782
=69.5KN/m
Shear force = 69.5 (2.2-2)/2.2
=6.31 KN
Considering impact factor
=1.25*6.31
=7.89 KN

Total shear force due to class AA wheel load

=31.18+18.2+7.89
=57.27 KN

Shear force due to dead load:

Dead load=6.76 KN/mm2
Shear force =7.436 KN

Total design shear force =shear force due to (dead load +live load)
=57.27+7.436
=64.706 KN

Check for shear :

Nominal shear stressI(τv)=v/bd
=(64.706 *103/103*168)
=0.385 N/mm2
From above τc = 0.404 N/mm2

Page | 57
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

a. For 70R loading:

a) Track vehicle:

350KN

700

80
200
280 840

2200

FIG. LOAD DISTRIBUTION FOR SHEAR FORCE

CALCULATION OF 70R TRACK VEHICLE

Shear force due to live load:

Clear span length = 4.7m
B/L= 4.7/2.2=2.14 m
Then ,
K = 2.6
Effective width calculation
b= kx(1-x/l)+bw
=2.6*0.700*(1-0.700/2.2)+4.57+2*0.08
=5.97 m
Load per unit width
=350/5.97
= 58.62 KN/m
Shear force =58.62(2.2-0.70)/2.2
=39.968 KN
Considering impact factor ,
Shear force=1.25*39.968 KN
=49.96 KN
Shear force due to dead load:
Dead load=6.76 KN/m2
Shear force due to dead load=7.436 KN
Design shear force =(7.436+49.96)KN
=57.396 KN

Page | 58
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Check for shear :

Nominal shear stressI(τv)=v/bd
=(57.396*103/103*168)
=0.341KN/m2
from above,
τc = 0.404 N/mm2

a. Wheel vehicle
Shear due to live load:

85KN

710
80
200

280 860

2200

FIG. LOAD DISTRIBUTION FOR SHEAR FORCE

CALCULATION OF 70R WHEELED VEHICLE

For continuous slab K=2.6

Effective width of slab=kx(1-x/l)+bw
=2.6*0.710(1-0.710/2.2)+0.61+2*0.08
=2.02 m
Load per m width:
=85/2.02
=47.07 KN/m
Shear force = 47.07 (2.2-0.710)/2.2
=28.496 KN
Considering impact factor
=1.25*28.496
=35.62KN

Page | 59
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Shear force due to dead load

Dead load = 6.76 KN/mm2
Shear force = 7.436 KN
Total design shear force = shear force due to (dead load +live load)
=35.62+7.436 =43.06KN
Check for shear :
Nominal shear stressI(τv)=v/bd
=(43.06*103/103*168)
=0.256 N/mm2
For same slab the value of k1and k2 is same
So take,
k=1.2
(τc) =0.404KN/mm2
b. For class A load:
Shear due to live load:

57KN 10.36KN

530
80

500
200

280

2200

FIG. LOAD DISTRIBUTION FOR SHEAR FORCE

CALCULATION OF CLASS A VEHICLE

wheel 1
For continuous slab K=2.6
Effective width of slab = kx(1-x/l)+bw
=2.6*0.53(1-0.53/2.2)+0.25+2*0.08
=1.456m
Load per m width:
=57/1.456
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 Design of RCC Bridge over Bagmati River at Sankhamul
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HCOE/071/BCE

=39.15 KN/m
Shear force = 39.15 (2.2-0.53)/2.2
=29.72 KN
Considering impact factor
=1.25*4
=37.15 KN
wheel2
For continuous slab K=2.6
Effective width of slab = kx(1-x/l)+bw
=2.6*2.14(1-2.14/2.2)+0.25+2*0.08
=.561 m
Load per m width:
=10.36/0.561
=18.44 KN/m
Shear force = 18.44(2.2-2.14)/2.2
=0.5 KN
Considering impact factor
=1.25*0.5
=0.63KN
Shear force due to dead load
Dead load = 6.76 KN/m2
Shear force =7.436 KN
Total design shear force = shear force due to (dead load +live load)
= 37.15 + 0.63 + 7.436
= 45.22KN
Check for shear :
Nominal shear stressI(τv) = v/bd
= (45.22*103/103*168)
= 0.27N/mm2
(τc) = 0.404 N/mm2
Since τc is greater than τv .so, the shear stress are with in permissible limit. Hence
deck slab safe against shear failure.
Design summary of deck slab
overall depth of deck slab= 200 mm
Effective depth of deck slab =168 mm
Provide 12mm∅bars@110mm c/c in short direction.
Provide 10mm∅bars @150mm c/c in longer direction.

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Analysis and Design of Cantilever Slab

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Design of Cantilever Slab

25 × 1.2 × 0.2 ×0.2 ×2 +25 × 0.2 × 0.15 × 1.2 × 14+ 25× 4 × 0.0437
Weight of railing post = 25

= 0.7748 KN @ 1.6 m.
Weight of footpath = 22 × 1.75 × 0.225 = 8.6625 KN @ 0.875 m, (22 assuming wearing
coat.)
Self weight of slab W1 = 25 × 0.15 × 1.75 = 6.5625 KN @ 0.875 m.
W2 = 0.5 ×25 ×0.1 × 1.75 = 2.1875 KN @ 0.583 m.
Moment due to dead load
B.M = 0.7748 ×1.6 +8.6625 × 0.875 +6.5625 × 0.875 +2.1875 ×0.583
=15.84 KNm/m.
Bending moment due to live load
Pedestrian load = 5 KN/m2
1.52
Bending moment = 5 × = 5.630 KNm/m.
2

Total bending moment in longitudinal direction

B.M = 15.84 + 5.63 = 21.47 KNm.
Total bending moment in transverse direction
B.M = 0.3 LL + 0.2 DL = 0.3 ×5.63 + 0.2 ×15.84 = 4.857 KNm
0.28
Q = 0.5 × 10 ×0.28 ×(1 - 3 ) = 1.269
Fck=30MPa
Fy=500MPa
Depth verification
M=Q × b × d2
21.47 × 106 = 1.269 × 1000 × d2
➢ d = 130 mm < 220 mm OK.

Design of Reinforcement
𝐾
m = σst Ast × d × ( 1 - )
3

𝑚 21.47× 106
Ast = 𝐾 = 0.28
𝜎𝑠𝑡 ( 1− )𝑑 240 × ( 1− ) ×220
3 3

Ast = 448.49 mm2 > Ast( min )

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

0.12
As, Ast min = 250 × 1000 × = 300 mm2
100

Provide 10 mm – φ @ 150 mm c/c.

𝜋∗52
Area provided Ast,p = × 1000 = 523.6 mm2 > 447.23 mm2
150

Reinforcement in transverse direction:

d’ = 220 – 5- 4 = 211 mm
4.857×106
Ast = 0.28
240 ×( 1− ) ×211
3

= 105.79 mm2 < 300 mm2

Provided 8mm – φ bar @ 150 mm c/c.
𝜋×42
Ast provide = × 1000
150

= 335.1 mm2 > Ast min OK

Check for shear:
Total shear force minimum
S.F = 0.7748+8.6625+6.5625+2.1875
= 18.1873 KN
Vu 18.1873
Nominal shear stress 𝜏v = 𝑏𝑑 = 1000×220×103

𝜏v =0.083 N/mm2
Shear Strength of Concrete:
523.6
Pt = 220×1000 × 100 =0.0238 and M30 concrete.

𝜏c=0.23N/mm2
𝜏c ‘=1.1×0.23 =0.253N/mm2 > 𝜏v
Hence, design is safe.
Design Summary of Cantilever Slab
overall depth of Cantilever Slab = 250mm
Effective depth of deck slab Cantilever Slab =220 mm from near the support
similarly 150mm , 120 at cantilever end.
Provide 10 mm – φ @ 150 mm c/c. in longitudinal direction.
Provide 8mm – φ bar @ 150 mm c/c. in transverse direction

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Analysis and Design of Longitudinal Girder

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Design for longitudinal girder

Calculation of dead bending moment:
For outer girder:
Effective span = 25 m.
Slab thickness = 200mm.
Width of rib = 300 mm
Spacing of main girder = 1.55 m
B.M due to dead load;
Dead load per m run is estimated as below:
S.N Item Details Weight (KN / m)
1. Wearing Course 1.25 × 0.08 × 22 2.2
2. Deck slab 1.25 × 0.20 × 25 6.25
3. Cantilever slab 1.75 × 0.2 × 25 8.75
4. T – rib 0.3 × 1.55 × 25 11.625
5. Fillets 2 × 0.5 ×0.3 × 0.15 ×25 1.125
6. Cross beams (4 ×2.2 ×1.15 ×0.3 + 2 ×2.2 × 1.15 2.53
25
×0.4 ) × 25 ×0.5
7. Curb 1.75 × 0.25 × 25 9.844

8. Railing post 25 0.528

16 × 0.2 × 0.15 × 1.1 × 25
9. Pipe 4 × 0.0437 0.1748

10. Intersection 2× (0.15 × 0.3 + 0.5 × 0.15 ×0.2) × 25 3.75

bottom extra part
Total 46.78
46.78 ∗ 24.4 ∗ 24.4
Maximum BM = = 3481.86 KNm
8

For inner girder

Effective span = 25 m.
Slab thickness = 200mm.
Width of rib = 300 mm
Spacing of main girder = 2.5 m

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

B.M due to dead load;

Dead load per m run is estimated as below:
S.N Item Details Weight(KN / m)
1. Wearing Course 1.25 × 0.08 × 22 2.2
2. Deck slab 1.25 × 0.20 × 25 6.25
3. Cantilever slab 1.75 × 0.2 × 25 8.75
4. T – rib 0.3 × 1.55 × 25 11.625
5. Fillets 2 × 0.5 ×0.3 × 0.15 ×25 1.125
6. Cross beams (4 ×2.2 ×1.15 ×0.3 + 2 ×2.2 × 1.15 5.06
25
×0.4 ) × 25
7. Intersection 2× (0.15 × 0.3 + 0.5 × 0.15 ×0.2) × 25 3.75
bottom extra part
Total 38.76
38.76 ∗ 24.4 ∗ 24.4
Maximum BM = = 2884.5192 KNm
8

Calculation of live load bending moment:

Calculation of reaction factors:

Reaction factors
Using carbon’s theory, the IRC class AA tracked vehicle loads are arranged for maximum
eccentricity as shown in figure. Reaction factor for outer girder is given by:
𝛴𝑊 𝛴𝐼
Rx = [1 + ( × I ) dx × e]
𝑛 𝛴 𝑑𝑥2

Rx= reaction factor for the girder under consideration

I = MOI of each longitudinal girder
dx= distance of girder under consideration from the central axis of the bridge
W= total concentrate live load
n = number of longitudinal girders
e = eccentricity of live load w. r.t the axis of the bridge
e = 1.1 m.

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

n=4
2𝑊1 4𝐼∗3.75∗1.1
RA = [1 + (2𝐼∗3.752 )+ (2𝐼 ∗ 1.252 ) ] = 0.764 w1
4

As, w1 = 0.5 w
Therefore, RA = 0.764 × 0.5 w = 0.382 w
similarly,
2𝑊1 4𝐼∗1.25∗1.1
RB = [1 + (2𝐼∗3.752 )+ (2𝐼 ∗ 1.252) ]
4

= 0.58w1
= 0.294 w
2𝑊1 4𝐼∗( − 1.25)∗1.1
RC = [1 + (2𝐼∗3.752 )+ (2𝐼 ∗ 1.252) ]
4

= 0.412w1
= 0.206 w
2𝑊1 4𝐼∗(− 3.75 )∗1.1
RD = [1 + (2𝐼∗3.752 )+ (2𝐼 ∗ 1.252 ) ]
4

= 0.236w1
= 0.118 w
Live load BM in girder due to class AA tracked vehicle:
Effective span of girder = 25m
Impact factor (for class AA loading) = 10%
Live load is placed centrally on the span as shown in figure below.

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

25
TOTAL LOAD
3.6
700KN

12.5 12.5

Wab
l
Unit influence line for
5.35 B.M
5.35
6.25
Fig:Influence line diagram for bending moment for class AA vehicle

Total bending moment = (6.25+5.35) × 0.9 ×700

= 4060 KNm
Including impact factor:
Bending moment= 4060×1.1= 4466KNm
Live load BM in girder class 70R tracked vehicle:

2.5
TOTAL LOAD
4.57
700KN

12.5 12.5

Wab
l
Unit influence line for
5.1075 B.M
5.1075
6.25
Fig:Influence line diagram for bending moment for class 70R vehicle

Total bending moment = (6.25 + 5.1075) × 0.5 × 700

=3975.125 KNm.
BM including impact factor= 4372.64KNm

Page | 69
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Live load BM by class A wheeled vehicle:

𝛴𝑤 𝛴𝐼
Rx = [ 1 + 𝛴𝑑𝑥 2 ∗𝐼 𝑑𝑥 ∗e]
𝑛

as, n = 4, e = 0.7 m
4𝑤 4𝐼
RA = [ 1 + 2 𝐼 ∗ 3.752 + 2𝐼 ∗ 1.252 ∗ 3.75 ∗ 0.7]
4

= 1.336 w
4𝑤 4𝐼
RB = [ 1 + 2 𝐼 ∗ 3.752 + 2𝐼 ∗ 1.252 ∗ 1.25 ∗ 0.7]
4

= 1.112 w
4𝑤 4𝐼
RC = [ 1 − 2 𝐼 ∗ 3.752 + 2𝐼 ∗ 1.252 ∗ 1.25 ∗ 0.7]
4

= 0.888 w L
4𝑤 4𝐼
RD = [ 1 − 2 𝐼 ∗ 3.752 + 2𝐼 ∗ 1.252 ∗ 3.75 ∗ 0.7]
4

= 0.664 w
Reaction factors,
RA = 0.334w
RB = 0.278w
RC = 0.222w RD = 0.166w
Maximum live load BM at mid span i.e. L/2; The below fig shows the ILD
114
114
27
27

68

68

68

7 1.1 3.2 1.2 4.3 3 3 2.2

1.1
2.6
3.5

4.1
4.05

5.65
6.25

FIG. BENDING MOMENT ILD CASE 1 FOR CLASS A

VEHICLE AT L/2

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Load No. Load Value (KN) Ordinate Moment (KNm)

w1 27 3.5 94.5
w2 27 4.05 109.35
W3 114 5.65 644.1
W4 114 6.25 712.5
W5 68 4.1 278.8
W6 68 2.6 176.8
W7 68 1.1 74.8
2090.85
Impact factor for class A vehicle = 0.145
Bending moment including impact factor= 1.145×2090.85 =2394.023KNm
The maximum live load BM at 3L/8
114
114
27
27

68

68

68

68
5075 1100 3200 1200 4300 3000 3000 3000 1125

0.42
1.55
2.67
3.17

3.8
3.86

5.41
5.86

FIG. BENDING MOMENT ILD CASE 2 FOR CLASS A

VEHICLE AT 3L/8

Load No. Load Value (KN) Ordinate Moment (KNm)

w1 27 3.17 85.59
w2 27 3.86 104.22
W3 114 5.86 668.04
W4 114 5.41 616.74
W5 68 3.8 258.4
W6 68 2.67 181.56
W7 68 1.55 105.4
W8 68 0.42 28.56
2048.51

Bending moment including impact factor = 1.145 ×2048.51 = 2345.54 KNm

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

The maximum live load BM at L/4

114
114
27
27

68

68

68

68
1.95 1.1 3.2 1.2 4.3 3.0 3.0 3.0 4.25

1.0625
1.4625

1.8125
2.2875

2.5625
3.3125
4.3875
4.6875

FIG. BENDING MOMENT ILD CASE 2 FOR CLASS A

VEHICLE AT L/4

Load No. Load Value (KN) Ordinate Moment (KNm)

w1 27 1.4625 39.49
w2 27 2.2875 61.76
W3 114 4.6875 534.37
W4 114 4.3875 500.17
W5 68 3.3125 225.25
W6 68 2.5625 174.25
W7 68 1.8125 123.25
W8 68 1.0625 72.25
1730.79
BM at girder A = 1.145×1730.79 = 1981.75KNm

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Live load shear

For estimating the maximum live load shear in the girders, the IRC class AA loads are
placed as shown in fig:

LONGITUDINAL GIRDER
CROSS GIRDER

2.5
5 5

W1=350KN

2.5
B
3.6
W2=350KN

2.5
A
3.6

FIG. POSITION OF IRC CLASS AA

LOADS FOR MAXIMUN SHEAR

Reaction of w2 on girder B = 350 ×0.45 / 2.5

= 63 KN
Reaction of w2 on girder A = 350 × 2.05/ 2.5
= 287 KN
Total load on girder B = 350 + 63 = 413 KN
413 ∗ ( 24.4 – 1.8 )
Maximum reaction in girder B = 24.4

= 382.53 KN
287 ∗ ( 24.4 – 1.8 )
Maximum reaction in girder A = 24.4

= 265.83 KN
Live load = 5 × 1.5 = 7.5 KN/m
24.42
BM = 7.5 × = 558.15 KNm
8
24.4
F = 7.5 × = 91.5 KN
2

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

bending moment due to live

Vehicle type reaction factor
moment load (KNm)
girder Girder
girder A girder B
A B
Class AA tracked 4466 0.382 0.294 1706.012 1313.004
Class 70R tracked 4372.64 0.382 0.294 1670.3485 1285.5562
Class A wheeled 2394.023 0.334 0.278 799.60368 665.53839
Pedestrian load 558.15
Total moment due to live
2264.16 1313.004
load
Moment due to dead load 3481.37 2884.52
Design moment (KNm) 5795.53 4197.52
Design of reinforcement:
Design moment, Mu= 5795.53 KNm
Width of flange, bf = 2500 mm
Width of web, bw = 300m
Depth of flange, Df = 200mm
Use M30 concrete and TMT steel.
fck= 30MPa 𝜎cbc=10MPa
fy=500MPa 𝜎st=240MPa
280⁄ 280⁄
3 3
k= 280⁄ = 280
3+𝜎st ⁄3+240

k=0.28
d= D-110= 1750-110=1640mm
nc=k×d=0.28×1640mm
nc=459.2mm >Df
𝑛𝑐−𝐷𝑓
𝜎c’= 𝜎cbc× ( )
𝑛𝑐
459.2−200
=10× = 5.64MPa
459.2
𝜎𝑐𝑏𝑐+2×𝜎𝑐′ 𝐷𝑓
𝑦̅ = ×
𝜎𝑐𝑏𝑐+𝜎𝑐 ′ 3
10+2×5.64 200
= ×
10+5.64 3

𝑦̅ = 90.72 𝑚𝑚
𝜎𝑐𝑏𝑐+𝜎𝑐 ′ 𝜎𝑐 ′ 𝑛−𝐷𝑓
Mlimiting=bf×Df× ( ) × (𝑑 − 𝑦̅) + 𝑏𝑤 × (𝑛 − 𝐷𝑓) × × (𝑑 − 𝐷𝑓 − )
2 2 3

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

10+5.64 5.64
= 2500×200× ( ) × (1640 − 90.72) + 300 × (1640 − 200) × ×
2 2
459.2−200
(1640 − 200 − )
3

=6356.53 KNm >Mu

Hence, design a singly reinforcement section.
5795.53 × 106
Ast = 0.28 =16240.16 mm2
1640×240×( 1− )
3

Provide 21 -32 φ bars at tension

𝛱
Ast, provided = 21× × 322
4

= 16889.2 mm2
For Girder A
Dead load shear in longitudinal girder, SFD = 46.78×12.2 =570.72 KN
Live load shear in longitudinal girder, SFL = 91.5+265.83 = 357.33 KN
SF total = 570.72 + 357.33 = 928.05 KN
For Girder B
Dead load shear in longitudinal girder, SFD = 38.76×12.2 =472.87 KN
Live load shear in longitudinal girder, SFL = 382.53 KN
SF total = 472.87 + 382.53 = 855.4 KN
Design of shear reinforcement
𝑉 928.08×103
τv = =
𝑏𝑑 300×1640

= 1.88 N/mm2 (< τmax = 2.2 N/mm2)

VC = τC × b ×d
100×8444.6
=1.716 ; fck = 30 MPa
300×1640

τC = 0.4973 N/mm2
VC = 0.4973 × 300 ×1640 = 244.66 KN
Vus = 928.05 – 244.66 = 683.39 KN
Provide 2L – 12 mm φ vertical stirrup @ 120 mm C/C
2× 𝛱×62 ×1640×240
Vus = 120
= 741.92 KN

Vs = VC + Vus = 741.92 + 244.8 = 986.58 KN

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Side face reinforcement

0.1
As = 100 × 300 ×1700 = 510 mm2
510
n = 𝛱× 6 2 = 4.5 ≈ 5

Provide 10-12 mm∅side reinforcement (5 each side)

Design Summary
Overall depth of main girder= 1750mm
Effective depth of main girder =1700mm
Thickness of web= 300mm
Size of ribs= 300mm ×150mm
Provide 21-32mm∅bars at rension
Provide 10-12 mm∅side reinforcement (5 each side)
Provide 2L – 12 mm φ vertical stirrup @ 120 mm C/C

80mm THICK
WEARING COAT

12mm Ø side bar

1750
1550

@200mm c/c
5 each side

21-32mm Ø
300

tension bars
600
FIG.CROSS SECTION OF
LONGITUDINAL GIRDER

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Analysis and Design of Cross Girder

Page | 77
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Design of Cross Girder

Moment & Shear force due to dead load
Weight of slab & wearing coat = 2 × 0.5 × 1.25 × 2.5 × (.08 × 22 + 0.2 × 25)
= 21.125 KN
Self-weight of girder =1.15 × 0.3 × 25 = 8.625 KN/m
2.5×2.5 2.5
Bending moment = 8.625 × + 21.125 ×
8 12

= 11.14 KNm
2.5 21.125
Shear Force = 8.625 × + = 21.34 KN
2 2

Bending moment due to live load

IRC AA Track Vehicle
2.5
B.M = 350 × 1.25 × = 273.44 KNm
4

Shear Force
IRC class AA Track Vehicle
𝟎.𝟒𝟓
(𝟑𝟓𝟎+𝟑𝟓𝟎× )×𝟏.𝟐𝟓
𝟐𝟓
S.F = 𝟐

= 212.5 KN
Design Bending Moment = 273.44 + 11.14= 284.58 KNm
Design Shear Force = 212.5 +21.34= 234.74 KN
Design of Reinforcement
fy = 500 MPa fck =30 MPa
σst = 240 MPa σcbc = 10 MPa
280
3
K= 280 = 0.28
+240
3

1 𝑥
R= 2 × 𝜎𝑐𝑏𝑐 × 12 (1 − 3)
1 0.28
=2 × 10 × 0.28 × (1 − ) = 1.269
3

Moment Carrying Capacity of Section

Mlim = 𝑅 × 𝑏 × 𝑑 2
= 1.269 × 1000 × 12952 = 2128.14 KNm > Mu

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Hence, Design of single reinforcement section.

Now,
Mu = 𝜎𝑠𝑡 × 𝐴𝑠𝑡 × 𝑗 × 𝑑
𝑀𝑢 284.58× 106
𝐴𝑠𝑡 = = 0.28 = 1009.9 𝑚𝑚2
𝜎𝑠𝑡 ×𝑗×𝑑 240×1295×(1− )
3

0.2
𝐴𝑠𝑡,𝑚𝑖𝑛 = × 300 × 1295 = 777 𝑚𝑚2 < 1009.9 𝑚𝑚2
100

Provide 3-25 mm- Φ bar

252
𝐴𝑠𝑡,𝑝 = 3 × × 𝛱 = 1472.62 𝑚𝑚2 > 𝐴𝑠𝑡,𝑟𝑒𝑑𝑢𝑐𝑒𝑑
4

Design of Shear Reinforcement

𝑉𝑢 = 235.2 𝐾𝑁
235.2×103 𝑁
𝜏𝑣 = = 0.605 𝑚𝑚2
300×1295
𝑁
𝜏𝑐,𝑚𝑎𝑥 = 2.2 𝑚𝑚2 > 𝜏𝑣

Provide 2 L- 10 mm – Φ @ 300 mm c/c vertical stirrup

102
𝜎𝑠𝑡 × 𝐴𝑠𝑡 ×𝑑 240×2×𝛱× ×1295
4
𝑉𝑠 = = = 162.73 𝐾𝑁
𝑠𝑝𝑎𝑐𝑖𝑛𝑔 300

𝑉𝑐 = 𝜏𝑐 × 𝑏 × 𝑑
For 𝜏𝑐
𝑓𝑐𝑘 = 30 𝑀𝑃𝑎
100×𝐴𝑠𝑡
= 0.26
𝑏×𝑑

𝜏𝑐 = 0.31 𝑁/𝑚𝑚2
𝑉𝑐 = 0.31 × 300 × 1295 = 120.435 𝐾𝑁
Total Shear, 𝑉𝑡 = 𝑉𝑠 + 𝑉𝑐 = 162.73 + 120.435
= 282.17𝐾𝑁 > 𝑉𝑢 , 𝑂. 𝐾.
Design of side face reinforcement
0.1
𝐴𝑠 = × 300 × 1350 = 486𝑚𝑚2
100
Provide 12 mm – Φ bar
390
Number of bars, n = 𝛱×62 = 3.448 ≈ 4

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Provided 3-12 mm-∅ bar in each side

Provided 2-20mm-∅ in compresion side
Design of side girder
Tension reinforcement
Provided 5-25mm-∅ bar
Provided 3-20mm-∅ bar in compression side
Side face reinforcement
Provided 4-12mm-∅ in each side
Shear reinforcement
Provide 2 L- 10 mm – Φ @ 200 mm c/c vertical stirrup
Design Summary of cross girder
Overall depth of cross girder = 1350mm
Effective depth of cross girder = 1295 mm
Middle Girder
Provide 3-25 mm- Φ bar in tension
Provide 2 L- 10 mm – Φ @ 300 mm c/c vertical stirrup
side face reinforcement
Provided 3-12 mm-∅ bar in each side
Provided 2-20mm-∅ in compresion side
side girder
Tension reinforcement
Provided 5-25mm-∅ bar
Provided 3-20mm-∅ bar in compression side
Side face reinforcement
Provided 4-12mm-∅ in each side
Shear reinforcement
Provide 2 L- 10 mm – Φ @ 200 mm c/c vertical stirrup

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Apendix 2: DESIGN OF SUBSTRUCTURE

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Analysis and Design of Bearing

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Design of Elastomeric Bearing:

Calculation of loading
i) Dead load from super structure on a bearing (DL) = 583.335 KN
ii) Live load on bearing (LL) = 374.25 KN
Total = 957.585 KN
iii) Braking load = 0.2 X (2 x 114 + 4 x 68 + 2 x 27) = 110.8 KN

110.8
Horizontal braking load on bearing (𝐹𝑏𝑟 𝐻 ) = = 27.7 KN
4

Braking loads act at 1.2 m above wearing coat.

Point of application of braking load = (1.2 + 0.08+ 1.75)
= 3.03 m
It includes Vertical reaction on bearing.
Vertical reaction on a bearing due to braking load
110.8 𝑋 3.03
𝐹𝑏𝑟 𝑟 = 24.3 𝑋 2

4. Wind load in transverse direction of bridge

𝑇
𝐹𝑤 = PZ X A X G X C D
Basic wind speed = 47 m/s and terrain with obstruction
A = 1.975 𝑋 25 = 49.375 m2
Increase 25% area for railing post,
Ar = 61.72 m2
P = 190.5 for basic wind speed 33 m/s.
47
Then PZ = 190.5 𝑋 33 = 271.32 N/m2

G = 2 (up to 150m height)

47
VZ = 17.8 𝑋 33 = 25.35 m/s

t = 1.8 m, tvz = 1.8 X 25.35 = 45.63 m2/s > 6m2/s

7
CD = 0.8 for 1.8 = 3.8
𝑇
𝐹𝑤 = 271.32 𝑋 10−3 𝑋 0.8 𝑋 2 𝑋 61.72 = 26.79 KN
Wind load in transverse direction = 26.79 KN
26.79
Wind load in longitudinal direction = = 6.7 KN
4

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

26.79
Wind load in transverse direction of bearing = = 5.95 KN
4
6.7
Wind load in longitudinal direction of bearing = = 1.675 KN
4

Wind load in vertical direction of bridge (FV) = PZ X A X G X CV

A= 11 X 25 = 275 m2
Cv = 0.75 for normal slab
Fv = 271.32 X 10−3 𝑋 275 𝑋 2 𝑋 0.75
= 111.92 KN
111.92
Wind load in vertical direction of bearing = = 27.98 KN
4

5. Seismic load
𝑍 𝐼 𝑆
Seismic load (𝐹𝑠 ℎ ) = (2) 𝑋 (𝑅) 𝑋 ( 𝑔𝑎 ) 𝑋 𝑊

Z = 0.36, I = 1.2, R = 4 (Response reduction factor)

𝑆𝑎
= 2.5, 0 < T <0 0.67 IRC – 6.
𝑔

0.36 1.2
αh = 𝑋 𝑋 2.5 = 0.135
2 4

W = 957.585 KN in longitudinal direction

W = 957.585 + 110.8 = 1068.385 KN in transverse direction.
0.36 1.2
Seismic load in transverse direction of bridge = 𝑋 𝑋 2.5 𝑋 1068.375 = 144.23 KN
2 4
0.36 1.2
Seismic load in longitudinal direction of bridge, = 𝑋 𝑋 2.5 𝑋 957.585 = 129.274
2 4
KN
144.23
Seismic load in transverse direction on a bearing ( 𝐹𝑆 ℎ𝑇 ) = = 36.06 KN
4
129.274
Seismic load in longitudinal direction on a bearing ( 𝐹𝑆 ℎ𝐿 ) = = 32.32 KN
4

vertical reaction due to seismic load on support of bridge (𝐹𝑆 𝑉 ).

CG of load = 1.18 m (From the bearing)
Vertical reaction on bearing when seismic load acts in longitudinal direction
(129.274 𝑋 1.18 ) 1
𝐹𝑆 𝑉𝐿 = 𝑋 (2) = 3.126 KN
24.4
(129.274 𝑋 1.18 ) 1
𝐹𝑆 𝐻𝐿 = 2.5
𝑋 (2) = 30.508 KN

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

6. load due to temperature variation, creep and shrinkage effect

∆ A
Maximum horizontal force on bearing ( 𝐹𝑐𝑠𝑡 ) = ℎ x G x L
𝑜

Strain due to temperature, creep and shrinkage = 5 X 10 – 4

(IRC 83-part II, Cl 916.3.4).
1
Horizontal deformation of bearing (∆) = 5 𝑋 10−4 𝑋 25 𝑋 103 𝑋 2 = 6.25mm,

Shear modulus of Elastomer (G) = 1 N/mm2 > 0.8 N/mm2

< 1.2 N/mm2 (IRC 83-part II, Cl 915.2.1).
Preliminary height of bearing ( ℎ𝑜 ) = 52 mm
Preliminary effective sectional area of bearing (A) = b X l = 320 X 500 = 160,000 mm2
6.25 160000
𝐹𝑐𝑠𝑡 = 𝑋1𝑋 = 9.615 KN
52 2

Calculation of loads on bearing according to combination of loads:

Combination I
Total vertical load = DLsup + LL + 𝐹𝑏𝑟𝑣
= 957.585 + 6.908 = 964.493 KN
Total horizontal load = 𝐹𝑏𝑟𝐻 = 27.7 KN
Combination II
Total vertical load = DL+ LL + 𝐹𝑏𝑟𝑣
= 957.585 + 6.908 = 964.493 KN
Total horizontal load = 𝐹𝑏𝑟𝐻 +𝐹𝑐𝑠𝑡 = 27.7 + 9.615 = 37.315 KN
Combination III
Total vertical load = DL + LL + 𝐹𝑏𝑟𝑣 + 𝐹𝑤 𝑉

= 957.585 + 6.908 + 27.98 = 992.473 KN

Total horizontal load = 𝐹𝑏𝑟𝐻 + 𝐹𝑐𝑠𝑡 + 𝐹𝑤 𝐿 = 37.315 + 1.675 = 38.99 KN
Combination IV
Total vertical load = DL+ 0.2 X LL + 0.5 X 𝐹𝑏𝑟𝑣 + 𝐹𝑠 𝑉𝐿

= 583.335 + 0.2 X 374.25 + 0.5 X 6.908 + 3.126

= 661.639 KN
Total horizontal load = 0.5 𝑋 𝐹𝑏𝑟𝐻 + 𝐹𝑐𝑠𝑡 + 𝐹𝑠 ℎ𝐿

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

= 0.5 X 27.7 + 9.615 + 30.508

= 53.973 KN
Design of Elastomeric pad bearing for combination I (N)
Geometric design is carried out using the guidelines of IRC, [Refer standard plan
dimensions of IRC 83, part II, Cl 916.2, Appendix I]
𝑁𝑚𝑖𝑛 = 𝐷𝐿 = 583.335 𝐾𝑁
𝑁𝑚𝑎𝑥 = 964.493 𝐾𝑁
𝐻𝑚𝑎𝑥 = 27.7 𝐾𝑁
𝑏0 = 320 𝑚𝑚
𝑏 = 308 𝑚𝑚
𝑙0 = 500 𝑚𝑚
𝑙 = 488 𝑚𝑚
ℎ𝑖 = 10 𝑚𝑚
ℎ𝑖
ℎ𝑒 = = 5 𝑚𝑚
2
ℎ𝑠 = 3 𝑚𝑚
𝑛=3
𝑐 = 6 𝑚𝑚
ℎ0 = (𝑛 + 1) ∗ ℎ𝑠 + 𝑛 ∗ ℎ𝑖 + 𝑧 ∗ ℎ𝑒 = 52 𝑚𝑚
ℎ = 𝑛 ∗ ℎ𝑖 + 𝑧 ∗ ℎ𝑒 = 40 𝑚𝑚
Check for Geometry of Bearing
𝑙0 500
i) = 320 = 1.56 ≤ 2 (𝑂. 𝐾. )
𝑏0
𝑏0
ii) ℎ = 40 < = 64 (𝑂. 𝐾. )
5
𝑏0
= 32 (𝑂. 𝐾. )
>
10
𝑙∗𝑏 488∗308
iii) 𝑠 = 2∗ℎ (𝑙+𝑏) = 2∗10∗(488+308) = 9.44 > 6 & < 12 (𝑂. 𝐾. )
𝑖
iv) 𝐵𝑒𝑎𝑟𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑠𝑠 𝑖𝑛 𝑐𝑜𝑛𝑐𝑟𝑒𝑡𝑒 ≤ 𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝑏𝑒𝑎𝑟𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑠𝑠 (𝑂. 𝐾)
𝑁𝑚𝑎𝑥 964.493 ∗ 103
𝐵𝑆 𝑖𝑛 𝑐𝑜𝑛𝑐𝑟𝑒𝑡𝑒 (𝜎𝑚 ) = =
𝑙∗𝑏 488 ∗ 308
𝑁
= 6.417
𝑚𝑚2

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

𝐴1
𝐴𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝐵. 𝑆 = 0.25 ∗ 𝑓𝑐𝑘 ∗ √
𝐴2

320 ∗ 500
= 0.230 ∗ √
308 ∗ 488
𝑁
= 7.74
𝑚𝑚2

2) Structural Design
a) Check for Translation
Design strain in bearing (ᵧ𝑑 ) < 0.7
∆𝑏𝑑
= ᵧ𝑏𝑑 = + 𝜏𝑚𝑑
ℎ
∆𝑏𝑑 5 ∗ 10−4 ∗ 24.4 ∗ 103
=
ℎ 2 ∗ 40
= 0.1525
𝐻 27.7 ∗ 103
𝜏𝑚𝑑 = = = 0.1843
𝐴 ∗ 𝐺 308 ∗ 488 ∗ 1
ᵧ𝑑 = 0.1525 + 0.1843 = 0.337 < 0.7 (𝑂. 𝐾)
b) Check for Rotation
Maximum permissible angle of rotation of a single interval layer of elastomer
corresponding to σm value of 10 N/mm2 is given by,
0.5 𝜎𝑚 × ℎ𝑖 0.5×10× 10
αbi. max = = = 0.00193 radians.
𝑏×𝑠2 308× 9.162

Permissible rotation (αd) =β × n ×αbi. max

Where, β = 0.1, 𝜎𝑚 =0.1 ×6.354 = 0.6354 N/mm2
And n = number of internal elastomer layers = 2
αd = 0.6354 × 2 ×0.00193 = 0.00245 > 0.002 (actual)
(hence safe)
c) Check for friction
Design strain in bearing (ᵧ𝑑 ) ≤ 0.2 + 0.16 𝑚
2𝑁
Normal stress in bearing (𝜎𝑚 ) > 𝑚𝑚2 & ≤ 10 𝑁/𝑚𝑚2

where,
ᵧ𝑑 = 0.337
0.2 + 0.1𝜎𝑚 = 0.2 + 0.1 ∗ 6.417

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

𝑁
= 0.8417 𝑚𝑚2 > ᵧ𝑑 (𝑂. 𝐾. )

d) Check for Shear Stress

𝑁
𝑇𝑜𝑡𝑎𝑙 𝑆ℎ𝑒𝑎𝑟 𝑆𝑡𝑟𝑒𝑠𝑠 ≤ 5
𝑚𝑚2
𝜎𝑚
Shear stress due compression = 1.5 ∗ 𝑠

where, s= shape factor

6.417
= 1.5 ∗
6.11
𝑁
= 1.575
𝑚𝑚2
Shear stress due to horizontal deformation,
𝜏𝑟 = ᵧ𝑟 ∗ 𝑑 = 0.337𝑁/𝑚𝑚2
𝑏 2
Shear Stress due to rotation = 0.5 ∗ (ℎ ) ∗ 𝛼𝑏𝑖
𝑖

308 2
= 0.5 ∗ ( ) ∗ 0.00193
10
= 0.915 𝑁/𝑚𝑚2
Total shear stress = 10575 + 0.337 + 0.915
= 2.827 𝑁/𝑚𝑚2 < 5 𝑁/𝑚𝑚2 (O.K.)
Check for Elastomeric Pad Bearing for combination [𝑁 + 𝑇 + 𝑆]
𝑁𝑚𝑖𝑛 = 𝐷𝐿 = 583.335 𝐾𝑁
𝑁𝑚𝑎𝑥 = 661.639 𝐾𝑁
𝐻 = 53.973 𝐾𝑁
Check for bearing stress in concrete
𝑁𝑚𝑎𝑥
Bearing stress in concrete (𝜎𝑚 ) = 𝑙∗𝑏

661.639 ∗ 103
=
488 ∗ 308
= 4.402 𝑁/𝑚𝑚2 < allowable bearing stress ≈ 7.74 𝑁/𝑚𝑚2 (O.K.)

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Check for bearing translation

∆𝑏𝑑
ᵧ𝑑 = ᵧ𝑏𝑑 = + 𝜏𝑚𝑑
ℎ
∆𝑏𝑑
= 0.1525
ℎ
𝐻 53.973 ∗ 103
𝜏𝑚𝑑 = = = 0.359
𝐴 ∗ 𝐺 488 ∗ 308 ∗ 1
ᵧ𝑑 = 0.1525 + 0.359 = 0.5115 < 0.7 (𝑂. 𝐾. )
Hence, adopt an elastomeric pad bearing of overall dimensions 320mm× 500 mm with a
total thickness of 52 mm having three internal elastomeric layers of 10 mm thickness and
4 steel laminators of thickness 3mm each having bottom & top covers of 5mm.

500

32
52

10

4 x 3 mm thick
5

0
5

FIG. ELASROMETRIC PAD BEARING

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Analysis and Design of Abutment

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Design of abutment cap:

fck= 25MPa
fy= 500MPa

𝜏c=0.25√𝑓𝑐𝑘=0.25√25 =1.25N/mm2

Adopt overall depth of abutment cap, D= 400mm

Effective depth = 400-35= 365mm
𝛽 c=0.5+1 =1.5≤ 1
𝛽 c=1
𝜏c = 𝛽 c× 𝜏c=1.25
𝜏uv= 𝜏c×B0×d =1.25×(2×(500+320) +4×d) ×365
=1.25×(2×820+4×365) ×365
=1414.38KN
1414.38
𝜏uv= =942.92KN>938KN (OK)
1.5

Design of reinforcement:
Longitudinal direction:
Area of steel =1% of BD
=0.01×400×1000=4000mm2
As one side =2000mm2
Adopt 20-mm-∅bar
2000
Number of bar n=𝜋×102=6.36≈7

Provide 8-20mm∅bar at each side.

Transverse direction of abutment:
Ast=1% of BD
=0.01×400×9000=36000mm2
At each side Ast=18000mm2
Adopt 16mm∅bars.
16000
Number of bars= 𝜋×82 =79.577≈80nos.

The traverse direction bars are provided in the term of the stirrups.

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

In addition, two layers of mesh reinforcement; each consisting 8mm∅@75mm c/c in both
direction on at6 20mm and other 100 mm from the top of cap are provided directly under
the bearing.
Check for stability of abutment
Description of item unit Force (KN) Lever arm Moment (KNm)
S.N. Component name wirdth height
of work weight Vertical Horizontal (m) Resisting Overturning
Dead load from
1 232 2.84 658.88
superstructure
Self weight
W1 1*5*1.2*25 1 5 1.2 25 150 2.5 375
W2 1*0.8*4.4*25 1 0.8 4.4 25 88 2.8 246.4
W3 1*1*0.4*25 1 1 0.4 25 10 2.9 29
W4 1*0.3*1.6*25 1 0.3 1.6 25 12 3.25 39
2
W5 0.5*0.4*4.4*25 0.5 0.4 4.4 25 22 2.267 49.874
vertical loab due to live load 1*1*1.2*18 1 1 1.2 18 21.6 4.1 88.56

vertical loab due to

1*1*0.2*25 1 1 0.2 25 5 4.1 20.5
surcharge
3 Weight of earth on heel 1.8*6.6*18 1 1.8 6.6 18 213.84 4.1 876.744
Live load from super
4 120 2.85 342
structure
5 Active earth pressure 0.5*0.3*7.8*7.8*18 0.3 7.8 7.8 9 164.268 3.276 538.142
Earth pressure due to
6 0.3*0.2*7.8*25 0.3 0.2 7.8 25 11.700 3.9 45.630
surcharge
Earth pressure due to live
7 0.3*1.2*7.8*18 0.3 1.2 7.8 25 70.200 3.9 273.780
load
braking force 20% * veh weight 11.11 2.84 31.5524
8
braking force 20% * veh weight 22.22 6 133.32
earthquake load
Dead load from
0.15*232 0.15 232 34.8 6 208.8
superstructure
Self weight
9 W1 0.15*5*1.2*-25 0.15 5 1.2 25 22.5 0.6 13.5
W2 0.15*0.8*4.4*25 0.15 0.8 4.6 25 13.8 3.5 48.3
W3 0.15*1*0.4*25 0.15 1 0.4 25 1.5 6 9
W4 0.15*0.3*1.6*25 0.15 0.3 1.6 25 1.8 6.9 12.42
W5 0.15*0.2*4.4*25 0.15 0.2 4.6 25 3.45 2.667 9.201
Sum 885.55 346.238 2757.51 1292.09

Σmr = 2757.51 KNm

Σm0 = 1292.09 KNm
ΣV = 885.55 KN
ΣH = 346.24 KN
Σm 2757.21
FOS against overtuning = Σm𝑟 = 1292.09
0

= 2.13>2 OK
µ ΣV 0.6∗885.55
FOS against sliding = =
ΣH 346.24

= 1.53>1.5 OK
Σm𝑟 − Σm𝑜 2757.51−1292.09
𝑥= = = 1.687 m
ΣV 885.55

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

𝐵 5 𝐵
e = 2 − 𝑥 = 2 − 1.667 = 0.813 < 6 ok
𝛴𝑉 6𝑒
σheel = (1- )
𝐵 𝐵
885.55 6∗0.813
= (1- ) =0.7 KNm
5 5
𝛴𝑉 6𝑒
σtoe = (1+ )
𝐵 𝐵
885.55 6∗0.813
= (1+ ) = 349.98KNm
5 5

Foundation of abutment:
The bending moment is maximum at the face of abutment.
22 2
BM= 212.77× + (349.98-212.77) × 0.5 ×2 × 2 × 3 = 614.05 KNm
2

Depth verification
Fy= 500MPa
𝜎abc=6.67MPa
𝜎st= 240MPa
280/3
k= 280 = 0.28
+240
3

1
R= 2 × 𝜎abc × j × k

R = 0.8466

𝑚 614.05×106
d= √𝑅×𝑏=√0.8466×1000= 851.66mm < 1125 mm (OK)

D= 1200 mm
d= 1200-65-20/2 = 1125 mm
Ast,max=4% of B × D =0.04×1000×1200=4800mm2
Ast, min=0.12%of B×D=0.0012×1000×1200=1440mm2

Design of longitudinal reinforcement:

𝑀𝑢 614.05 ∗ 10^6
Ast= 𝑘 = 0.28
𝜎𝑠𝑡∗𝑑∗(1− ) 240 ∗ 1125 ∗ (1− 3 )
3

=2508.37mm2 >Astmin
<Astmax (OK)

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Provide 20mm∅ bars @105mm c/c

𝜋∗102
Ast provides= ∗ 1000
105

=2991.99mm2 >Ast required (OK)

Design of transverse reinforcement:
Provide 20 mm∅ bars @215mm c/c
𝜋∗102
Ast provided= ∗ 1000
215

= 1461.2mm2 >Ast min (OK)

Check for one-way shear:
One-way shear is maximum at d- distance from the face.
V= 292.3×0.875+0.5×0.875×(354.15 – 292.3) =282.82 KN
𝑉 282.82∗103
𝜏v=𝑏𝑑= 1000∗1125 = 0.21 N/mm2
2094
Pt = 1125∗1000 × 100 = 0.224

fck= 20MPa
𝜏c=0.212 N/mm2> 𝜏v (OK)
Design of top bar
1.8 1 1.8
BM = 0.7 × 1.8 × + 2 × (91.94-0.7)*1.8 × – 213.84× 0.9 – 26.6 × 0.9 – 1.8 × 1.2 ×1
2 3
×25 × 0.9
= - 214.59KNm
Top reinforcement is required.
214.59∗10 6
Ast = 0.28 = 876.59 < Ast , min
240∗1125∗(1− )
3

Provide 20 mm − 𝜑 𝑏𝑎𝑟 @215 mm C/C in both direction

𝜋∗10^2
Ast provided= ∗ 1000
215

= 1461.2mm2 >Ast min (OK)

Curtailment of reinforcement:
25∗0.58∗500
𝑙𝑑 = =0.755m ≈0.8m
4∗1.2∗1.6

Mu=232.8KNm

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Ast, required=947.72mm2
Provide 20mm∅bar @210mm c/c
Ast, provided=1491.62mm2

Design of dirt wall:

Assume the wall is cantilever slab.
Earth pressure due to surcharge= (0.2×25+1.2×18)×0.3×1.6 = 14.19 KN
Active earth pressure= 0.5×Ka× 𝛾 ×H2
=0.5×0.3×18×1.62
= 7.68 KN
Seismic load due to weight of dirt wall= 0.15×0.3×1.6×25×1 =1.8KN
1.6
BM= 1.8×0.8+14.19×0.8+7.68× 3

= 16.88 KNm
R=0.8466
Depth verification

𝑀𝑢 16.88 ∗106
D=√𝑅∗𝑏=√0.8466∗1000

d= 141.2mm <210mm (OK)

Ast = 0.12 % × b × D
= 0.12 % × 300 ×1000 = 360 mm2
𝑚𝑢
Ast = 𝑘
𝜎𝑠𝑡 ∗𝑑∗(1− )
3

16.88 ∗106
= 0.28
240∗270∗( 1− )
3

= 287.3 mm2 < Ast, min

Provide 10 mm – φ bar @ 200 mm c/c at both side of dirt wall in both direction
Ast ,p = 392.7 mm2 > Ast , min.
Check for shear
Shear force= V =1.8+14.19+7.68 = 33.22 KN

Page | 95
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

𝑣 33.22∗103
τv = 𝑏∗𝑑 = = 0.123 N/mm2 < τc ,max
1000∗270

As for M20 and Fe500 steel , τc, max = 0.18 N/mm2

Use M20 concrete and 500MPa steel
Pt = 0.145 %
τc = 0.18 N/ mm2 > τv (No shear reinforcement required.)

Design of steam wall

Description of item of Force (KN) Moment (KNm)
S.N. component name Lever arm (m)
work Vertical Horizontal Resisting Overturning
Dead load from
1 232 0.24 55.68
superstructure
Self weight 0
W2 1*0.8*4.4*25 88 0.2 17.6
2 W3 1*1*0.4*25 10 0.3 3
W4 1*0.3*1.6*25 12 0.65 7.8
W5 0.5*0.4*4.4*25 22 0.33 7.26
Active earth
3 0.5 *0.33*6.2*6.2*18 103.788 2.6 269.849
pressure
Earth pressure due
4 0.33*0.2*6.2*25 9.300 3.1 28.830
to surcharge
Earth pressure due
5 0.33*1.2*6.2*18 40.176 3.1 124.546
to live load
earthquake load 0
Dead load from
0.15*232 34.8 4.8 167.04
superstructure
Self weight 0
6
W2 0.15*0.8*4.4*25 13.2 2.2 29.04
W3 0.15*1*0.4*25 1.5 4.6 6.9
W4 0.15*0.3*1.6*25 1.8 5.7 10.26
W5 0.5*4.4*0.4*1*25 3.3 1.467 4.8411
sum 364 207.864 84.08 648.566
with live load
Live load from super
7 120 0.24 28.8
structure
braking force 25 % * veh load 11.11 0.24 2.6664
8
braking force 25 % * veh load 22.22 4.3 95.546
sum 495.11 230.08 115.55 744.112

Page | 96
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Net moment = 628.565 KNm

ΣV = 495.11 KN
S.F = ΣH =230.08 KN

𝑀𝑢 628.565∗106
d = √𝑄∗𝑏=√0.8466∗1000 = 861.66mm < 1125mm OK

𝑀𝑢
Ast = 𝐾
𝑄∗𝑑(1− )
3

628.565∗106
= 0.28
240 ∗1125∗(1− )
3

= 2567.67 mm2 > Ast, min

As, Ast, min = 0.12 % × 1200 × 1000 = 1440 mm2
Provide 20mm – φ bar @ 120 mm c/c
Ast, provided = 2617.99 mm2 in vertical direction
Provide 20mm – φ bar @ 215 mm c/c in horizontal direction.
𝜋∗10^2
Ast provided= ∗ 1000
215

= 1461.2mm2 >Ast min (OK)

In horizontal direction

Reinforcement at compression side

Provide 20 mm –φ bar @ 215 mm C/C in both direction
𝜋∗10^2
Ast provided= ∗ 1000
215

= 1461.2mm2 >Ast min (OK)

Check for shear
Shear force= V =248.25 KN
𝑣 230.08∗103
τv = 𝑏∗𝑑 = = 0.204N/mm2 < τc ,max
1000∗1125

As for M20 and Fe500 steel , τc, max = 1.8 N/mm2

Pt = 0.25 % ,
τc = 0.22 N/mm2 > τv

Page | 97
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

No shear reinforcement is required.

Check for development length:
25∗0.58∗500
𝑙𝑑 = =0.755m ≈0.8m
4∗1.2∗1.6

Curtailment of reinforcement:
From above 2.4m above the top of footing
Mu=260.55KNm
Ast, min=0.12*10*990= 1188mm2
260.55∗106
Ast, required= 28 = 1308.61mm2
240∗915∗(1− )
3

Provide 200mm∅bar @240mm c/c

Ast, provided=1308.99mm2

Page | 98
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Analysis and Design of Pier and Pier Foundation

Page | 99
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Design of Pier and Pier Cap:

i. Dead load from super structure (without wearing coat) from abutment design =
3843.92 KN
ii. Dead load of wearing coat = 330 KN
iii. Live load (From class A wheeled vehicle)
Vehicle in any one span = 776 KN
Vehicle in both span = 1013.3 KN
Pedestrian load = 5 ∗ 1.5 ∗ 25 ∗ 2 = 375 𝐾𝑁
iv. Braking load
Horizontal braking load = 100 KN
Vertical braking load = 11.11 KN
v. Wind load
Wind load in transverse direction
𝐹𝑤𝑇 = P2 × A ×G ×CD
A = 1.975 ×25 = 52.375 m2
Increase 25% area for railing post
AT = 1.25 × 42.375 = 61.72 m2
Height of bridge = 5.5 m from bed level
Basic wind velocity, Vb = 47 m/s
P = 190.5 for basic wind speed 33 m/s

47
Then PZ= 190.5 × 33 = 271.32 N/m2
G = 2 (up to 150 m height)
47
Vz = 17.8 × 33 = 25.35 m/s
t = 1.8 m. t vz = 1.8 × 25.35 = 45.63 m2 /s > 6 m2 /s
7
CD = 0.8 For 1.8 = 3.8
FwT = 271.32 ×10 – 3 × 0.8 ×2 ×61.72 = 26.79 KN

Wind load in transverse direction = 26.79 KN

26.79
Wind load in longitudinal direction = 4 = 6.7 KN
Wind load in vertical direction (FV) = PZ × A × G ×CV
A = 11×25 = 275 m2
CV = 0.75 for normal slab
Fv = 271.32 ×10 – 3 × 275 × 2 × 0.75
= 111.92 KN
vi. Load due to water current
Transverse direction = 52 × k × (V × cos 𝛳)2 ×A
A= 1.8 ×4.32 = 7.776 m2
K = 0.66 for circular pier
V = 3 m /s
Fwc = 52 × 0.66 × (3 × cos 20)2 × 7.776 × 10 – 2 = 21.2 KN
Longitudinal direction = 52 × 0.66× (3 × sin 20)2 × 7.776 × 10 – 2 = 2.8 KN

Page | 100
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

vii. Load due to hydrodynamic force

Fhyd = c × αh ×w
𝑍 𝐼 𝑆
αh = 2 ∗ 𝑅 ∗ 𝑔𝑎
From IRC – 6
Z= 0.36 for zone V
I = 1.2 important factor of structure
R = 4 response reduction factor
S/g = 2.5 0 < T < 0.67 IRC – 6
0.36 1.2
αh = ∗ ∗ 2.5 = 0.135
2 4
𝐻
C = 0.8 ; = 7.77
𝑅
Fhyd =0.8 × 0.135 × 107.95 = 11.66 KN

vii. Buoyancy force

Fby = γw × Vsub
= 9.81 × Π × 0.9 2 × 4.32
= 107.95 KN

viii. Dead load of sub – structure

Self-weight:
Self-weight of pier cap = 1 × 9 × 1.4 ×25 + 2 × 0.5 × 3.55 ×1.4 ×0.5 ×25 + 1.9 ×
0.5 × 1.4 ×25
= 315 + 62.125 +33.25
= 410.375 KN
𝑑2
Self-weight of pier (WP) = 𝜋 × ×l×γ
4
= 𝜋 × 0.92 × 7 ×25
= 445.321 KN
Total load of sub structure = 410.375 + 445.321 = 855.696 KN
ix. seismic load sues to super structure = αh ×w
= 0.15 × (3843.92 + 330) = 626.09 KN
x. seismic load due to sub – structure
Wspc = 0.15 × 410.375 = 61.56 KN
Wsp = 0.15 × 445.321 = 66.8 KN
315∗0.5+62.125∗1.167+33.25∗1.25
𝑋= = 0.662 m from bearing level.
410.375

Let braking load is shared among the two supports,

Horizontal Braking load = 100 𝐾𝑁
Vertical Braking load = 100 𝐾𝑁

Page | 101
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

750

1400 800
1

9000

FIG: Plan - Pier Cap

750 2500
500

1000
1500

Face of pier stem

(Critical section of cap for BM and SF)

S.F.= (1.35 ∗ 1921.96 + 1.75 ∗ 330) + 1.5 ∗ 1388.3 + 50 ∗ 1.15 + 3.886 ∗ 1.4 ∗ 1 ∗
25 + 0.5 ∗ 3.886 ∗ 1.4 ∗ 25
= 2594.646 + 577.5 + 2082.45 + 57.5
= 5312.096 + 136 + 34
= 5482.096 𝐾𝑁
At the face of first beam,
𝑆. 𝐹 = 5312.096 + 3.5 ∗ 1.4 ∗ 1 ∗ 25 + .486 ∗ 1.4 ∗ 0.5 ∗ 3.5 ∗ 25
= 5312.096 + 122.5 + 29.77
= 5464.366 𝐾𝑁

Page | 102
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

𝐵. 𝑀 = 1.35 ∗ 960.98 ∗ (0.614 + 3.114) + 1.75 ∗ 82.5 ∗ (0.6114 + 3.114) + 1.5

∗ 347.075 ∗ (0.614 + 3.114) + 1.15 ∗ 25 ∗ (0.3114 + 3.114) + 136
3.886 3.886
∗ + 34 +
2 3
= 7422.67 + 308.29
= 7730.96 𝐾𝑁𝑚
Depth Verification
𝑥𝑢,𝑚𝑎𝑥 𝑥𝑢,𝑚𝑎𝑥
𝑀 = 0.36 ∗ 𝑓𝑐𝑘 ∗ ∗ (1 − 0.42 ∗ ) ∗ 𝑏 ∗ 𝑑2
𝑑 𝑑

= 0.36 ∗ 0.46 ∗ (1 − 0.42 ∗ 0.46) ∗ 𝑓𝑐𝑘 ∗ 𝑏 ∗ 𝑑 2

= 0.1336 ∗ 𝑓𝑐𝑘 ∗ 𝑏 ∗ 𝑑 2
𝑀
𝑑 = √0.1336∗𝑓 2
𝑐𝑘 ∗𝑏∗𝑑

7730.96∗106
= √0.1336∗25∗1400

= 1285.82 𝑚𝑚 < 1460 𝑚𝑚 (𝑂𝐾)

Design of Reinforcement
𝐴𝑠𝑡 ∗ 𝑓𝑦
𝑀𝑢 = 0.87 ∗ 𝑓𝑦 ∗ 𝐴𝑠𝑡 ∗ 𝑑 ∗ (1 − )
𝑏 ∗ 𝑑 ∗ 𝑓𝑐𝑘
𝐴𝑠𝑡 ∗ 500
𝑜𝑟, 7730.96 ∗ 106 = 0.87 ∗ 500 ∗ 𝐴𝑠𝑡 ∗ (1455 −
1400 ∗ 25
𝐴𝑠𝑡 = 14125 𝑚𝑚2 < 𝐴𝑠𝑡,𝑚𝑎𝑥

> 𝐴𝑠𝑡,𝑚𝑖𝑛
0.85 ∗ 1400 ∗ 1455
𝐴𝑠𝑡,𝑚𝑖𝑛 = = 3462.9 𝑚𝑚2
500
𝐴𝑠𝑡,𝑚𝑎𝑥 = 0.04 ∗ 1400 ∗ 1000 = 56000 𝑚𝑚2
Provide 23-28 mm-Φ bars
𝐴𝑠𝑡,𝑝𝑟𝑜𝑣𝑖𝑑𝑒𝑑 = 23 ∗ 𝛱 ∗ 142 = 14162.3 𝑚𝑚2 > 𝐴𝑠𝑡,𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 (𝑂. 𝐾. )
1400 − 40 ∗ 2
𝑆𝑝𝑎𝑐𝑖𝑛𝑔 = = 60 𝑚𝑚
22
14162.3
𝑝𝑡 = ∗ 100 = 0.7 % ; 𝑓𝑐𝑘 = 25 𝑀𝑃𝑎
1400 ∗ 1447
𝜏𝑚𝑎𝑥 = 3.1 𝑁/𝑚𝑚2

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

𝜏𝑐 = 0.544 𝑁/𝑚𝑚2
𝛽 = 8°
𝑀𝑢
𝑉𝑢 + ∗ 𝑡𝑎𝑛𝛽
𝜏𝑣 = 𝑑
𝑏∗𝑑
7730.96
5482.096 −
= 1.46 ∗ tan(80°)
1.4 ∗ 1460
= 2.32 𝑁/𝑚𝑚2
At the face,
𝑀𝑢 = 7217.82 𝐾𝑁𝑚
𝑀𝑢
𝑉𝑢 + ∗ 𝑡𝑎𝑛𝛽
𝜏𝑣 = 𝑑
𝑏∗𝑑
1217.82
5482.096 − 1.442 ∗ tan(80°)
=
1.4 ∗ 1442
𝑁
= 2.36 < 𝜏𝑐,𝑚𝑎𝑥
𝑚𝑚2
Hence, shear force is maximum at the face of bearing.
𝑉𝑐 = 𝜏𝑐 ∗ 𝑏 ∗ 𝑑
= 0.554 ∗ 1400 ∗ 1442
= 1118.415 𝐾𝑁
𝑉𝑢𝑠 = 𝑉𝑢 − 𝑉𝑐
= 5464.366 − 1118.415
= 4345.951 KN
0.87 ∗ 𝑓𝑦 ∗ 𝐴𝑠𝑣 ∗ 𝑑
𝑉𝑢𝑠 =
𝑠𝑝𝑎𝑐𝑖𝑛𝑔
Provide 6L- 12 mm – Φ vertical stirrup @ 95 mm c/c
4 ∗ 0.87 ∗ 500 ∗ 𝛱 ∗ 62 ∗ 1442
𝑉𝑢𝑠 =
100
= 4480.58 𝐾𝑁
𝑉𝑢′ = 𝑉𝑐 + 𝑉𝑢𝑠
= 4480.583 + 1118.415

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

= 5598.998𝐾𝑁 > 𝑉𝑢 (𝑂. 𝐾. )

Design of side face reinforcement,

0.1
𝐴𝑠𝑡 = ∗ 1400 ∗ 1500 = 2100 𝑚𝑚2
100
Provide 16 mm- Φ bar
2100
Number of bars = 𝛱∗82 = 10.44 ≈ 12

Provide 6- 16 mm – Φ bar in each side.

Analysis and design of pier cap:
cae I
basic combination of loads:
distance Mux
eccentrcity Muy
load(KN) from bottom Pu(KN) (KN- Hx(KN) Hy (KN)
(KN-m)
(m) x (m) y(m) m)
DLss 3843.92 1.35 5189.292 0
DLwc 330 1.75 577.5 0
FbrH 100 1 8.5 850 100
FbrV 11.11 1.15 12.7765 0
FwL 6.7 1.5 8.5 85.425 10.05
Wpier 855.696 1.35 1155.19 0
FwcT 21.2 1 4.867 0 103.18 21.2
FwcL 2.8 1 4.867 13.628 2.8
Fbuoy -107.95 0.15 -16.1925 0
total (without LL) 6918.566 949.05 103.18 112.85 21.2
LL' 779 1.5 0.335 1168.5 391.45
total (with LL') 8087.066 1340.5 103.18 112.85 21.2
LL'' 1013.3 1.5 0 1519.95 0
total (with LL'') 8438.516 949.05 103.18 112.85 21.2

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

cae I
Sesmic combination of loads:
distance eccentrcity Mux Muy
load(KN) Pu(KN) Hx(KN) Hy (KN)
from x (m) y(m) (KN- (KN-m)
DLss 3843.92 1 3843.92 0
DLwc 330 1 330 0
FbrH 100 0.2 8.5 170 20
FbrV 11.11 0.2 2.222 0
Fs L 626.09 1 8.5 5321.8 626.09
Fs VL 22.54 1 22.54 0
L(stem)
Fs(sub) 66.8 1 3.5 233.8 66.8
Fs(sub) L (cap) 61.56 7.838 0
em)FhydL 6.7 1 3.65 24.455 6.7
Wpier 855.696 1 855.696 0
FwcT 21.2 1 4.867 0 103.18 21.2
FwcL 2.8 1 4.867 13.628 2.8
Fbuoy -107.95 0.15 -16.193 0
total (without LL) 5038.19 5763.6 103.18 722.39 21.2
LL' 779 0.2 0.335 155.8 52.193
total (with LL') 5193.99 5815.8 103.18 722.39 21.2
LL'' 1013.3 0.2 0 202.66 0
total (with LL'') 5240.85 5763.6 103.18 722.39 21.2

Page | 106
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

cae II
basic combination of loads:
distance eccentrcity Mux Muy
load(KN) from Pu(KN) Hx(KN) Hy(KN)
(KN-m) (KN-m)
bottom x (m) y(m)
DLss 3843.9 1.35 5189.292 0
DLwc 330 1.75 577.5 0
FbrH 100 1 8.5 850 100
FbrV 11.11 1.15 12.7765 0
FwT 26.79 1.5 8.5 341.57 40.185
Wpier 855.7 1.35 1155.19 0
FwcT 21.2 1 4.867 0 103.18 21.2
FwcL 2.8 1 4.867 13.628 2.8
Fbuoy -107.95 0.15 -16.1925 0
total (without LL) 6918.566 1205.2 103.18 142.985 21.2
LL' 779 1.5 0.335 1168.5 391.45
total (with LL') 8087.066 1596.6 103.18 142.985 21.2
LL'' 1013.3 1.5 0 1519.95 0
total (with LL'') 8438.516 1205.2 103.18 142.985 21.2

cae II
sesmic combination of loads:
distanc eccentrcity Mux Muy
load(KN) e from Pu(KN) Hx(KN) Hy (KN)
(KN-m) (KN-m)
bottom x (m) y(m)
DLss 3843.92 1 3843.92 0
DLwc 330 1 330 0
FbrH 100 0.2 8.5 170 20
FbrV 11.11 0.2 2.222 0
Fs T 626.09 1 8.5 5321.77 626.09
Fs VT 22.54 1 22.54 0
T(stem)
Fs(sub) 66.8 3.5
T(cap)
Fs(sub) 61.56 1 7.838 482.507 61.56
FhydT 6.7 1 3.65 24.455 6.7
Wpier 855.696 1 855.696 0
FwcT 21.2 1 4.867 0 103.1804 21.2
FwcL 2.8 1 4.867 13.6276 2.8
Fbuoy -107.95 0.15 -16.193 0
total (without LL) 5038.19 6012.35 103.1804 717.15 21.2
LL' 779 0.2 0.335 155.8 52.193
total (with LL') 5193.99 6064.55 103.1804 717.15 21.2
LL'' 1013.3 0.2 0 202.66 0
total (with LL'') 5240.85 6012.35 103.1804 717.15 21.2

Page | 107
 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Check for Pier

𝑙0 = 1000 𝑚𝑚
𝑙𝑒𝑓𝑓 = 1.2 ∗ 1000 = 800 𝑚𝑚

𝐷𝑒𝑓𝑓 = 1800 − 70 = 1730 𝑚𝑚

𝑙𝑒𝑓𝑓 4 ∗ 8400
= = 19.42 > 12 & < 50
𝐷𝑒𝑓𝑓 1730
4
Hence, column is short column.
Minimum Eccentricity
0 𝑙 𝐷
𝑒𝑚𝑖𝑛 = 500 + 30

7000 1800
= +
500 30
= 74 𝑚𝑚 > 20 𝑚𝑚
< 0.05 ∗ 1800 = 90 𝑚𝑚 ( 𝑂. 𝐾. )
𝑀𝑢𝑥 = 6012.35 𝐾𝑁𝑚
𝑀𝑢𝑦 = 103.84 𝐾𝑁𝑚

𝑃𝑢 = 5193.98 𝐾𝑁𝑚
𝑀𝑒,𝑚𝑖𝑛 = 𝑃 ∗ 𝑒𝑚𝑖𝑛 = 0.074 ∗ 5193.98 = 384.35 𝐾𝑁𝑚
Design Moment
𝑀𝑢𝑥 = 6012.35 𝐾𝑁𝑚
𝑀𝑢𝑦 = 384.35 𝐾𝑁𝑚

Assume, 𝑑 ′ = 70 𝑚𝑚
𝑝 % = 0.8%
𝑑′
= 0.038 ≈ 0.05
𝐷
From SP-16 code,
Chart 59
𝑑′ 𝑝 0.8
= 0.05 = = 0.04
𝐷 𝑓𝑐𝑘 20

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

𝑃𝑢 5193.98 ∗ 103
= = 0.08
𝑓𝑐𝑘 ∗ 𝐷2 20 ∗ 18002
𝑀𝑢1
= 0.065
𝑓𝑐𝑘 ∗ 𝐷3
𝑀𝑢1 = 0.065 ∗ 20 ∗ 18003
= 7581.6 𝐾𝑁𝑚
𝑃𝑢𝑧 = 0.4 ∗ 𝑓𝑐𝑘 ∗ 𝐴𝑐 + 0.75 ∗ 𝑓𝑦 ∗ 𝐴𝑠𝑐

= (0.4 ∗ 20 ∗ 0.992 + 0.75 ∗ 500 ∗ .008) ∗ 𝛱 ∗ 9002

= 27828.73 𝐾𝑁
𝑃𝑢 5193.986
= = 0.186 ≥ 0.2
𝑃𝑢𝑧 27828.73
𝑃𝑢
= 0.2
𝑃𝑢𝑧
𝑃𝑢
𝛼𝑛 = 0.667 + 1.667
𝑃𝑢𝑧
𝛼𝑛 = 1

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Sheet for check of design of the pier;

moment due design moment

minimum Pu/Puz Pu/FckD 3
Pu(max) Mux Muy to minimum Puz Pu/Puz αn 2 Mu1/FckD Mu1 check
eccenricity adopted
eccentricirty Mux Muy
Without loading 6918.57 949.053 103.18 0.074 511.974 949.05 511.97 27828.73 0.249 0.249 1.081 0.107 0.064 7464.96 0.163
basic one way loading 8087.07 1340.5 103.18 0.074 598.443 1340.50 598.44 27828.73 0.291 0.291 1.151 0.125 0.068 7931.52 0.180
two way loading 8438.52 949.053 103.18 0.074 624.450 949.05 624.45 27828.73 0.303 0.303 1.172 0.130 0.068 7931.52 0.134
case I
Without loading 5038.19 5763.65 103.18 0.074 372.826 5763.65 372.83 27828.73 0.181 0.200 1.000 0.078 0.065 7581.60 0.809
one way loading 5193.99 5815.84 103.18 0.074 384.355 5815.84 384.35 27828.73 0.187 0.200 1.000 0.080 0.065 7581.60 0.818
sesmic two way loading 5240.85 5763.65 103.18 0.074 387.823 5763.65 387.82 27828.73 0.188 0.200 1.000 0.081 0.065 7581.60 0.811
Without loading 6918.57 1205.2 103.18 0.074 511.974 1205.20 511.97 27828.73 0.249 0.249 1.081 0.107 0.064 7464.96 0.194
one way loading 8087.07 1596.65 103.18 0.074 598.443 1596.65 598.44 27828.73 0.291 0.291 1.151 0.125 0.068 7931.52 0.209
basic two way loading 8438.52 1205.2 103.18 0.074 624.450 1205.20 624.45 27828.73 0.303 0.303 1.172 0.130 0.068 7931.52 0.161
case II
Without loading 5038.19 6012.35 103.18 0.074 372.826 6012.35 372.83 27828.73 0.181 0.200 1.000 0.078 0.065 7581.60 0.842
one way loading 5193.99 6064.55 103.18 0.074 384.355 6064.55 384.35 27828.73 0.187 0.200 1.000 0.080 0.065 7581.60 0.851
sesmic two way loading 5240.85 6012.35 103.18 0.074 387.823 6012.35 387.82 27828.73 0.188 0.200 1.000 0.081 0.065 7581.60 0.844

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Check
𝑀𝑢𝑥 𝛼 𝑀𝑢𝑦 𝛼
( ) 𝑛 +( ) 𝑛≤1
𝑀𝑢1 𝑀𝑢1
6012.35 1 384.35 1
( ) +( ) ≤1
7581.6 7581.6
0.85 ≤ 1 (𝑂. 𝐾. )

Hence, Design is safe.(long table in landscape)

Design of Reinforcement
𝜋 ∗ 1.82
𝐴𝑠𝑐 = 0.8% 𝑜𝑓
4
0.8 𝜋 ∗ 1.82
= ∗
100 4
= 20357.52 𝑚𝑚2
Provide 25 mm – Φ bar
20357.52
𝑛= = 41.47 ≈ 42
𝜋 ∗ 12.52
Provide 42nos – 25 mm-Φ bar
Design of Lateral tie
Provide 12 mm- Φ bar @ 200 mm c/c
0.75 ∗ 1800 = 1350 𝑚𝑚
16 ∗ 28 = 448 𝑚𝑚 ≤ 300 𝑚𝑚

42-25 mm Ø bars
Ø1
80
0

12 mm dia @ 200 c/c

FIG. SECTION OF PIER

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Design of Pier Foundation

Case-II
Basic Combination: - Vehicles are loaded on two spans
𝑃𝑢 = 8438.52 𝐾𝑁
𝑀𝑢𝑥 = 1205.2 𝐾𝑁𝑚
𝑀𝑢𝑦 = 372.83 𝐾𝑁𝑚

Assume the size of footing is 7.2m×7.2m×1.25m

𝑀𝑢𝑥 1205.2 𝐵
Eccentricity 𝑒 = = 8438.52 = 0.14 < = 1.2 𝑚 (𝑂. 𝐾. )
𝑃𝑢 6

𝑃𝑢 8438.52
Direct stress (𝜎𝑑 ) = =
𝐴 7.2∗7.2

𝜎𝑑 = 162.78 𝐾𝑁/𝑚2
𝑃𝑢 ∗𝑒∗6 8438.56∗6∗0.12
Bending Stress (𝜎𝑏 ) = =
𝑙3 7.23

𝐾𝑁
𝜎𝑏 = 19.37
𝑚2
Total Stress 𝜎𝑚𝑎𝑥/𝑚𝑖𝑛 = 𝜎𝑑 ± 𝜎𝑏

𝜎𝑚𝑎𝑥 = 𝜎𝑑 + 𝜎𝑏
= 162.78 + 19.37
= 182.15 𝐾𝑁/𝑚2
𝜎𝑚𝑖𝑛 = 162.78 − 19.37
= 143.4 𝐾𝑁/𝑚2
1) Check for Bending Moment
Bending moment is maximum at the face of the column
2.96362 1 2.9636
𝐵. 𝑀 = {166.2 ∗ + ∗ (182.15 − 166.2) ∗ 2.9636 ∗ 2 ∗ } ∗ 7.2
2 2 3
= 5591.35 𝐾𝑁𝑚

Depth Verification
𝐵. 𝑀 = 0.36 ∗ 𝑓𝑐𝑘 ∗ 𝑏 ∗ 𝑥𝑢 ∗ (𝑑 − 0.42 ∗ 𝑥𝑢,𝑙𝑖𝑚 )
𝑜𝑟, 5591.35 ∗ 106 = 0.36 ∗ 20 ∗ 7200 ∗ 0.46 ∗ (1 − 0.42 ∗ 0.46) ∗ 𝑑 2
𝑜𝑟, 5591.35 ∗ 106 = 2.672 ∗ 𝑏 ∗ 𝑑2
5591.35 ∗ 106
𝑑=√ = 539.1𝑚𝑚 < 1175 𝑚𝑚 (𝑂. 𝐾. )
2.672 ∗ 103 ∗ 7.2

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𝐷 = 𝑑 + 75 = 1175 + 75 = 1250 𝑚𝑚

1272

7200
1272

7200
4604 2964

143.4
166.2 182.15

FIG: Check for Bending Moment

Design of Reinforcement
0.12
𝐴𝑠𝑡,𝑚𝑖𝑛 = ∗ 1250 ∗ 72000
100
= 10800 𝑚𝑚2
𝑓𝑦 ∗ 𝐴𝑠𝑡
𝐵. 𝑀. = 0.87 ∗ 𝑓𝑦 ∗ 𝐴𝑠𝑡 ∗ (𝑑 − )
𝑏 ∗ 𝑓𝑐𝑘
500 ∗ 𝐴𝑠𝑡
5591.35 ∗ 106 = 0.87 ∗ 500 ∗ 𝐴𝑠𝑡 ∗ (1175 − )
20 ∗ 7200
Solving, we get
𝐴𝑠𝑡 = 11307.82 𝑚𝑚2 > 𝐴𝑠𝑡,𝑚𝑖𝑛 (𝑂. 𝐾. )
𝑐
𝑃𝑟𝑜𝑣𝑖𝑑𝑒 20 𝑚𝑚 − 𝛷 𝑏𝑎𝑟 @ 175 𝑚𝑚 𝑖𝑛 𝑏𝑜𝑡ℎ 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛
𝑐
2
𝛱 ∗ 10
𝐴𝑠𝑡,𝑝𝑟𝑜𝑣𝑖𝑑𝑒𝑑 = ∗ 7200
200
= 11309.73𝑚𝑚2 > 𝐴𝑠𝑡,𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 (𝑂. 𝐾. )

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2) Check for one-way shear

One-way shear is critical at a distance d from the face of the column
𝑉𝑢 = {172.53 + 0.5 ∗ (182.75 − 175.53)} ∗ 1.7886 ∗ 7.2
= 2283.78 𝐾𝑁

𝑉𝑢 2283.78 𝑁
𝜏𝑣 = = = 0.27
𝑏 ∗ 𝑑 7.2 ∗ 1175 𝑚𝑚2

1272

7200
1272

1175

1789
7200

143.4
172.53
182.15

FIG: Check for One Way Shear

From IRC (456:2000) Table 19

𝑓𝑐𝑘 = 20 𝑀𝑃𝑎
𝐴𝑠𝑡 100 ∗ 11309.73
𝑝% = 100 ∗ = = 0.14%
𝑏∗𝐷 7200 ∗ 1125
𝑁
𝜏𝑐 = 0.28 > 𝜏𝑣 (𝑂. 𝐾. )
𝑚𝑚2

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 Design of RCC Bridge over Bagmati River at Sankhamul
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HCOE/071/BCE

3) Check for Two Way Shear

The two-way shear is critical for d/2 distance from the face of column
Figure
𝑑′ = 1800 + 1175 = 2975 𝑚𝑚
𝛱
𝑉𝑢 = 162.78 ∗ (7.22 − ∗ 2.9752 )
4
= 162.78 ∗ 44.89 = 7306.99 𝐾𝑁
𝑉𝑢
𝜏𝑣 =
𝑏∗𝑑
𝑏0 = 𝛱 ∗ 𝑑 ′ =∗ 2.975 = 9.346 𝑚

𝜏𝑐 = 0.25 ∗ √𝑓𝑐𝑘

= 0.25 ∗ √20
𝑁
= 1.118
𝑚𝑚2

Ø2975
7200
1800

7200
FIG: Check for Two Way Shear

𝑆ℎ𝑜𝑟𝑡𝑒𝑟 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛 𝑜𝑓 𝑃𝑖𝑒𝑟

𝛽𝑐 =
𝐿𝑜𝑛𝑔𝑒𝑟 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛 𝑜𝑓 𝑃𝑖𝑒𝑟
1.8
= =1
1.8
𝑘𝑐 = (0.5 + 𝛽) ≤ 1

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= (0.5 + 1) = 1.5 ≤ 1
𝑘𝑐 = 1
𝑁
𝜏𝑐′ = 𝑘𝑐 ∗ 𝜏𝑐 = 1.118
𝑚𝑚2
7306.99
𝜏𝑣 =
9.346 ∗ 1175
= 0.665 < 𝜏𝑐′ (𝑂. 𝐾. )
Hence, design is safe.
Top reinforcement
Provide 20 mm-Φ bar@ 200 mm c/c
𝛱 ∗ 102
𝐴𝑠𝑡,𝑝𝑟𝑜𝑣𝑖𝑑𝑒𝑑 = ∗ 7200 = 11309.7 𝑚𝑚2 > 𝐴𝑠𝑡,𝑚𝑖𝑛 (𝑂. 𝐾. )
200
Check for Development Length
∅𝜎𝑠
Ld=4𝜏𝑏𝑑
25×0.58×500
= 4×1.2×1.6

=944mm

20 mm dia. @ 200 mm c/c

both ways

20 mm dia. @ 200 mm c/c

both ways
7200
FIG: Reinforcement details along Section of pier

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Apendix 3: ESTIMATION OF QUANTITY

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Estimation of Quantity of Concrete

S.N Description of works No. Length (m) Breadth(m) Height(m) Quantity(m3) Remarks

Super Structure
1 Deck slab 4 25 7.5 0.2 150
2 Cantilever slab 2 25 1.75 0.2 17.5
3 Kerb(Footpath) 8 25 1.75 0.225 78.75
4 Railing post
End 24 0.2 0.2 1.2 1.152 Approach &
Iintermediate 60 0.2 0.15 1.2 2.16 Deck slab

5 Cross Girder 0
End girder 24 2.5 0.4 1.35 32.4
Intermediate 48 2.5 0.3 1.35 48.6
6 Main Girder 0
Web 12 25 0.3 1.75 157.5
Fillet 24 25 0.3 0.15 27
I end (Triangle) 24 25 0.15 0.2 18
I end (Rectangular) 24 25 0.15 0.3 27
Total 560.062 M30 concrete
7 Approach slab 2 3.5 11 0.3 23.1
Sub structure
8 Pier Cap
3 9 1.4 1 37.8
3 1.9 1.4 0.5 3.99
6 3.55 1.4 0.5 7.455 V = (1/2)*l*b*h
9 Abutment cap 2 9 1.1 0.4 7.92
Total 80.265 M25 concrete

10 Pier Stem 3 7 Π* 1.8 *1.8 213.84

11 Abutment
Dirt wall 2 9 0.3 1.5 8.1
Stem wall 2 9 1 4.4 79.2
Fillet (Triangle) 2 9 0.1 0.1 0.09 V = (1/2)*l*b*h
12 Foundation
Abutment 2 9 5 1.2 108
Pier 3 7.2 7.2 1.2 186.624
Total 595.854 M20 concrete

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Estimation of Quantity of Steel

SN Particulars Description Quantity (Kg)

1 Railing Pipe (4*8*25 + 2*8*3.5)*2.88 2465.28

2 Railing Post 84 * 4 *1.2 *10 * 10/162.2 248.58
6
3 Cantilever slab (335.1+523.6) *8*1.75*25*7850/10 2359.28
4 Footpath 2 *(0.12/100)*78.75 *7850 1483.65
5 Deck slab (904.78+523.6)*4*7.5*25*7850/106 8409.59
6 Main girder (Π/4)*12*25*(21*322+10*122+2*202)*7850/106 43917.2
7 Cross girder
End girder (Π/4)*(5*252+3*202+8*122)*2.5*24*7850/106 2020.06
Intermediate girder 2 2 2 6 2618.31
(Π/4)*(3*25 +2*20 +6*12 )*2.5*48*7850/10
8 Abutment
Abutment cap ((Π/4)*2*(16*9*202+2*56*1.1*202)*7850/106 1339.61
6
Dirt wall 392.7 * 4 *1.5 * 9 7850 /10 332.93
Stem wall 6 3989.53
(2856+3*1461.2)*9 *4.4* 7850 * 2/10
9 Pier
Pier cap 3*(Π/4) *(23*282+12*162+6*162) * 9 *7850/106 3768.77
Pier stem 2 6 4126.95
3*(Π/4)*42*25 *8.5*7850/10
10 Foundation
Pier 3*(12925.4*2+2*11309.7)*7.2*7850/106 8218.61
Abutment 6 4576.71
2*(2094.4+3*1461.2)*5*9*7850/10
11 Approach slab (0.2/100)*23.1*7850*2 725.34

Total Steel ; Rebar 90600.4

90.6 tons

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

SITE PHOTOGRAPH

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Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

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Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

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 Design of RCC Bridge over Bagmati River at Sankhamul
Kathmandu- Lalitpur
HCOE/071/BCE

Apendix 4: DRAWINGS AND DETAILING

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