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Design of a Box Culvert
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Republic of Iraq
Al-Mansour University College
Civil Engineering department
Research project
Study year
2017-2018
Design of a Box Culvert
This project is in partial fulfillment of the requirements
for a B.Sc. in Civil Engineering
Prepared By
Ali Mahdi Mohammed
Ahmed Nafie Mohammed
Mohammed Abd Al-Amir Hussain
Mutaz Nather Majid
Supervised by
Dr. Ola Adil Qassim
A.D 2018
Baghdad
The Hegira Date:1439
SUPERVISOR’S CERTIFICATE
I certify that the preparation of the project entitled:
Design of a Box Culvert
was prepared under my supervision at Al-Mansour
University College as a partial fulfillment of the requirements
for a B.Sc. Degree in Civil Engineering.
Supervisor’s Signature:
Name:
Date:
COMMITTEE CERTIFICATE
We certify that the project entitled:
Design of a Box
Culvert
was prepared, corrected and defended by the students and in
our opinion, it meets the standards of a graduation project for a
B.Sc. Degree at Al-Mansour University College.
Signature:
(Chairman)
Name:
Date:
Signature:
(Member)
Name:
Date:
Supervisor Signature:
and
(member)
Name:
Date:
Abstract
ABSTRACT
When it is required to construct a road that intersects with a natural stream
flow or a water canal, the major problem shows as how to the keep the stream
flows without threatening the roadway and the passing vehicles due to water
rising when flooding at raining seasons or overflow in the canal. For this purpose,
a culvert is must be constructed in the intersections. A culvert is a structure
designed to allow passing of water through.
It’s required to design a box culvert in Kut-Petera irrigation project at the
intersection of main drain (MD-A) and Al-Dejaili paved road. The design is
carried out on the basis of hydraulics and structure limitations.
The hydraulic design is based on the obtained hydraulic data of the area. The
dimensions of the box culvert were obtained from the hydraulic design. The
designed box culvert is a two cell with a total length of 27m and total width of
3.14m.
The structural design is defined as the stability and safety of the box culvert
from the applied loads. After designing based on the maximum bending moment
and shear value, the required reinforcements are
¨ ∅16 @ 300 mm C*C (EF⁄V) and ∅12 @ 250 mm C*C
(EF⁄H) 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑤𝑎𝑙𝑙𝑠.
¨ ∅12 @ 250 mm C*C at top and bottom for the top and bottom slabs.
Design of Box Culvert
I
List of Contents
Title
Page
I
II
III
IV
V
Abstract
List of Contents.
List of Symbols
List of Tables.
List of Figures.
Chapter One: Introduction
1-1 Introduction
1-2 Aim of the study
1-3 Objectives
1-4 Content
1
2
2
2
Chapter Two: Review of Literature
2-1 General
2-2 Function of Culvert
2-3 Culverts and Bridges
2-3-1 Economic Considerations
2-4 Service Life
2-5 Inlets
2-6 Culvert Hydraulics
2-6-1 Flow Through Culverts
2-7 Types of Flow Control
2-7-1 Inlet Control
2-7-2 Outlet Control
2-8 Headwater
2-9 Culvert Length.
2-10 Box Culvert and Pipe Culvert
2-11 Culvert Failure
2-12 Environmental Impacts
2-13 Velocity Limitation
2-14 Structural Design of Box Culvert
2-14-1 Box Culvert Structural Elements
2-14-2 Applied Load
2-14-3 Structural Design Method
Chapter Three: Theoretical Background
3-1 Introduction
3-2 Hydraulic Design information
3-3 Conveyance condition
3-4 Case 4 formula
3-5 Structural Design Cases
Chapter Four: Results and Discussion
4-1 Hydraulic Design.
4-2 Structural Design.
4-3 Reinforcement Details
Chapter Five: Conclusions and recommendations
5-1 Conclusions.
5-2 Recommendations.
3
4
4
5
6
7
8
8
12
12
13
15
15
16
17
17
18
18
19
19
20
21
23
25
26
29
30
37
52
53
53
References
Appendix
Design of a Box Culvert
II
List of Symbols
Symbol
Definition
B
Drain bed width
D
Span of box culvert section
D/S W. L
Downstream water level
H
Headwater
H`
Critical headwater
∆H
Total head losses
hf
major losses due to friction
hm
minor losses due to entrance and exit
k
Coefficient of losses
n
Manning coefficient
Q
Discharge
S
Longitudinal slope
U/S W. L
Upstream water level
V
Velocity
W
Thickness of box culvert section wall
Design of a Box Culvert
III
List of Tables
Table
No.
Subject
PAGE
NO.
Chapter Two: Review of Literature
(2-1)
Factors influencing culvert design
14
Chapter Four: Results and Discussion
(4-1)
Summary of factored distributed loads
40
(4-2)
Moment distribution table
43
(4-3)
Negative moment at face of support
45
(4-4)
Moments summary
46
(4-5)
Vu at the face of support.
46
(4-6)
Vu at distance d from support face.
47
(4-7)
Reinforcement calculations.
49
(4-8)
ETABS results.
51
Design of a Box Culvert
IV
List of Figures
Figure
No.
PAGE
NO.
Subject
Chapter Two: Literature Review
(2-1)
(2-1)
(2-3)
(2-4)
(2-5)
(2-6)
(2-7)
(2-8)
(2-9)
(2-10)
(2-11)
(2-12)
(2-13)
(2-14)
(2-15)
(2-16)
(2-17)
Box Culvert
Pipe Culvert
Different Cross Sections of Culverts
Bridge Versus Culvert at Same Location
Four Standard Inlet Types
Entrance Condition
Flow in a Culvert
Case 1 of Culvert Flow
Case 2 of Culvert Flow
Case 3 of Culvert Flow
Case 4 of Culvert flow
Case 5 of Culvert Flow
Case 6 of Culvert Flow
Typical Inlet Control Flow Section.
Typical Outlet Control Flow Section.
Roadway Cross Section and Culvert Length.
Small Spatial Requirement of Box Culvert Than Pipes.
3
3
4
5
7
8
8
9
10
10
11
11
12
13
14
15
16
Chapter Three: theoretical background
(3-1)
(3-2)
(3-3)
(3-4)
(3-5)
(3-6)
Sector 3 of the Kut-Petera Irrigation Project
Section of MD-A with Culvert Location
The Profile Between the Stations (5+000 – 11+500) km
Case 4
Total Head Losses
Cross Section of Box Culvert
21
22
24
25
26
27
Chapter Four: Results and Discussion
(4-1)
(4-2)
(4-3)
(4-4)
(4-5)
(4-6)
(4-7)
(4-8)
(4-9)
(4-10)
(4-13)
Main Drain (MD-A) Cross Section
Culvert side view [invert level = main drain (MD-A) level]
Culvert side view when H<H’
Culvert side view with 0.73 m length invert
Culvert side view of a single box when H < H`
Culvert side view with 0.2 m length invert
Section A-A
Factored load distribution
Frame of box culvert
Typical slab reinforcement
Section A-A reinforcement details
Design of a Box Culvert
30
30
31
32
33
34
36
39
41
52
52
V
Chapter One
Introduction
Chapter one
Introduction
Chapter One
Introduction
1-1 Introduction
A hydraulic structure is a structure submerged or partially submerged in any
body of water, which disrupts the natural flow of water. They can be used to
divert, disrupt or completely stop the flow. A hydraulic structure can be built in
rivers, a sea, or any body of water where there is a need for a change in the natural
flow of water.
Culvert is a hydraulic structure that allows water to flow under a road,
railroad, trail, or similar obstruction from one side to the other side. Typically
embedded so as to be surrounded by soil. Culverts can be constructed of a variety
of materials including cast-in-place or precast concrete.
Culverts are commonly used both as cross-drains for ditch relief and to pass
water under a road at natural drainage and stream crossings. A culvert may be a
bridge-like structure designed to allow vehicle or pedestrian traffic to cross over
the waterway while allowing adequate passage for the water. Culverts come in
many sizes and shapes including round, elliptical, and box-like constructions. The
culvert type and shape selection are based on a number of factors including
requirements for hydraulic performance, limitation on upstream water surface
elevation, and roadway embankment height.
The structural design involves consideration of load cases (box empty, full,
surcharge loads etc.) and factors like live load, effective width, braking force,
dispersal of load through fill, impact factor, co-efficient of earth pressure etc. The
structural elements are required to be designed to withstand maximum bending
moment and shear force. Relevant Codes are required to be referred.
Design of Box Culvert
Chapter one
Introduction
1-2 Aim of the project
It is required to design a box shaped culvert on the basis of hydraulics and
structural requirements in Kut-Petera irrigation project at the intersection
between main drain (MD-A) and Al-Dejaili paved road.
1-3 Objectives
The main objectives of this project are summarized as follow: 1. Hydraulically design of a box culvert in Kut-Petera irrigation project at the
intersection between main drain (MD-A) and Al-Dejaili paved road.
2. Determine the total loads acting on the various parts of the box culvert.
3. Suitable structure design for the box culvert.
4. Design reinforcement steel for the culvert.
5. Analysis the structurally designed box culvert using ETABS software.
1-4 Content
This study is divided into the following: • Chapter One: Introduction.
• Chapter Two: Review of Literature.
• Chapter Three: Theoretical Background.
• Chapter Four: Results and Discussion.
• Chapter Five: Conclusion and Recommendations.
Design of Box Culvert
Chapter Two
Review of Literature
Chapter Two
Review of Literature
Chapter Two
Review of Literature
2-1 General
Creamer (2007) introduced culvert as a structure that allows water to flow
under a road, railroad, trail, or similar obstruction from one side to the other side,
typically embedded so as to be surrounded by soil. A culvert may be constructed
of a variety of materials including cast-in-place or precast concrete (reinforced or
non-reinforced), galvanized steel, aluminum, or plastic, typically high-density
polyethylene. Culverts come in many sizes and shapes including round, elliptical,
flat-bottomed, pear-shaped, and box-like constructions. The culvert type and
shape selection are based on a number of factors including requirements for
hydraulic performance, limitation on upstream water surface elevation, and
roadway profile, flood damage evaluations, construction and maintenance costs,
and estimates of service life.
Figure (2-1). Box Culvert.
Design of Box Culvert
Figure (2-2). Pipe Culvert.
3
Chapter Two
Review of Literature
Figure (2-3). Different cross sections of culverts.
2-2 Function of Culverts
Kilgore, et. al (2012) reported that culverts perform a wide range of
hydraulic and non-hydraulic functions. The most common hydraulic function is
providing cross drainage for a stream channel. Other hydraulic functions include
floodplain relief, where a culvert might be placed in the overbank of a wide
floodplain to provide drainage of the overbank area during large flood events.
Such culverts often have no defined channel upstream or downstream of the
barrel and may be dry for years at a time. Smaller culvert structures often function
to provide ditch relief for drainage ditches along a roadway, diverting some of
the discharge from the ditch. Non-hydraulic functions include crossing structures
for human or animal traffic, such as a pedestrian or trail crossing, cattle crossings,
farm equipment access and crossings designed to facilitate wildlife movement.
2-3 Culverts and Bridges
Creamer (2007) explained that culvert may be a bridge-like structure
designed to allow vehicle or pedestrian traffic to cross over the waterway while
allowing adequate passage for the water. The major benefits of the culvert are: • Decreased traffic interruption time due to roadway flooding.
• Increased driving safety.
Comparing culverts to bridges the designer must determine which type of
structure is best for a particular location, and then decide how to analyze the
Design of Box Culvert
4
Chapter Two
Review of Literature
crossing. For example, in many respects a large box culvert begins to resemble a
small single-span bridge with vertical wall abutments, so culverts are used: • Where bridges are not hydraulically required.
• Where debris and ice potential are tolerable.
• Where more economical than a bridge.
Safety, aesthetic and economic considerations are involved in the choice of a
bridge or culvert.
2-3-1 Economic Considerations
Kilgore, et al. (2012) reported that economic considerations were of primary
importance in deciding between the use of a bridge or a culvert at stream
crossings where either will satisfy hydraulic and structural requirements. The
initial cost for a culvert is usually less than a bridge since the use of increased
headwater at a culvert installation normally permits the use of a smaller opening
– figure (2-4) – compared to a bridge which is normally designed with freeboard
at the design discharge. However, this advantage must be balanced against
possible flood damages associated with increased headwater, especially at higher
discharges.
Figure (2-4). Bridge versus culvert at same location.
Design of Box Culvert
5
Chapter Two
Review of Literature
The major costs are associated with the construction of the roadway embankment
and the culvert itself. The design of a culvert installation should always include
an economic evaluation. A wide spectrum of flood flows with associated
probabilities will occur at the culvert site during its service life. Maintenance of
the facility and flood damage potential must also be factored into the cost
analysis. The benefits of constructing a large capacity culvert to accommodate all
of these events with no detrimental flooding effects are normally outweighed by
the initial construction costs. Thus, an economic analysis of the tradeoffs is
performed with varying degrees of effort and thoroughness. The ideal culvert
selection process minimizes the total annual cost of the installation over the life
of the roadway. The need to compare the cost of available shapes and sizes is well
understood when designing a culvert.
Selecting a culvert material that better withstands corrosion may cost more
initially, but the longer service life will lower total annual cost. The annual cost
includes capital expenditures, maintenance costs, and risks associated with
flooding. Anticipating future maintenance requirements can also save money in
the long run. Maintenance costs for culverts may result from channel erosion at
the inlet and outlet, erosion and deterioration of the culvert invert, sedimentation,
and embankment repair in case of overtopping.
2-4 Service Life
Kilgore, et al. (2012) stated that the desired service life of the culvert should
be considered in the selection process where the service life of the culvert should
match the installation. If the culvert is in a location where replacement would be
impractical, the service life of the culvert should equal the service life of the
roadway. If rehabilitation is feasible, or if it is determined that the roadway will
be rebuilt in a relatively short time, a culvert with a shorter service life should be
selected.
Design of Box Culvert
6
Chapter Two
Review of Literature
2-5 Inlets
Kilgore, et al. (2012) defined a multitude of different inlet configurations
are utilized on culvert barrels. These include both prefabricated and constructedin-place installations. Commonly used inlet configurations include projecting
culvert barrels, cast-in-place concrete headwalls, precast or prefabricated end
sections, and culvert ends mitered to conform to the fill slope – figure (2-5) –.
Hydraulic performance, structural stability, aesthetics, erosion control, and fill
retention are considerations in the selection of various inlet configurations.
Figure (2-5). Four standard inlet types.
The hydraulic capacity of a culvert may be improved by appropriate inlet
selection. The channel is often wider than the culvert barrel, causing a contraction
at the culvert inlet which may be the primary flow control. The provision of a
more gradual flow transition will lessen the energy loss and thus create a more
hydraulically efficient inlet condition – figure (2-6) –. Beveled edges are
therefore more efficient than square edges.
Design of Box Culvert
7
Chapter Two
Review of Literature
Figure (2-6). Entrance Condition.
2-6 Culvert Hydraulics
Kailan (2015) stated that a complete theoretical analysis of culvert
hydraulics based on fundamental equations can be difficult. Flow conditions vary
over time for any given culvert. The barrel of the culvert may flow full or partly
full depending upon upstream and downstream conditions, barrel characteristics,
and inlet geometry.
2-6-1 Flow Through Culverts
Kailan (2015) stated that the inlet will not be submerged if the headwater is
less than a critical value (H), while the outlet is not submerged.
1.2D ≤ H ≤ 1.5D
where D = culvert height
A culvert with a square edge at the top of the entrance will not flow full even if
the inlet is below head water level when the outlet is not submerged.
Separation
Culvert seal
Figure (2-7). Flow in a culvert.
Design of Box Culvert
8
Chapter Two
Review of Literature
For practical purposes, culvert flow may be classified into 6 types of flow within
2 groups.
Group (A)
Free surface flow (inlet and outlet) throughout (neither end submerged).
Case 1
Critical depth at inlet (inlet control).
H < 1.2D
yt < yc
Culverts on supercritical slopes, inlet not submerged, free outlet, control at inlet,
flow is supercritical.
So>Sc
Figure (2-8). Case 1 of culvert flow.
In this case discharge is independent of slope, roughness, length, outlet type,
shape and size of the barrel. It depends entirely on the inlet geometry and the
headwater elevation.
æHö
Q = Bg ç ÷
è 1.5 ø
1.5
1/2
Design of Box Culvert
where B is the width of the box section
9
Chapter Two
Review of Literature
Case 2
Critical depth at outlet (outlet control).
H < 1.2D
yt < yc
Figure (2-9). Case 2 of culvert flow.
Culverts on subcritical or horizontal slope, hence the control section is at the
outlet. Discharge depends on inlet geometry, headwater elev., shape, size of
barrel, roughness, slope and length.
Case 3
Sub critical flow case. Culverts on subcritical slopes, it does not flow full.
H < 1.2D
yt > yc
Figure (2-10). Case 3 of culvert flow.
Design of Box Culvert
10
Chapter Two
Review of Literature
Group (B)
Upstream end of culvert is always submerged.
Case 4
Inlet and outlet are submerged. It is the most economical case, which is usually
used in design. The conduit is flowing full.
H>D
yt > D
Submerged outlet H > 1.2D
full flow
Yt > D
Figure (2-11). Case 4 of culvert flow.
Case 5
Submerged inlet, full flow, free outlet, culverts on mild (subcritical) or
horizontal slopes.
H > 1.2D
yt < D
In this case, the culvert is hydraulically long.
Figure (2-12). Case 5 of culvert flow.
Design of Box Culvert
11
Chapter Two
Review of Literature
Case 6
Partly full flow, submerged inlet, Rapid flow case at entrance, free outlet,
Hydraulically short, control at inlet. Orifice flow.
Figure (2-13). Case 6 of culvert flow.
The flow is analogous to a sluice and the equation of discharge becomes: -
Q = C d .B.D.(2gH )
1/ 2
Cd = 0.42 + 0.05
H
D
For 1.2 <
H
< 4 in meters system
D
2-7 Types of Flow Control
Kilgore, et al. (2012) stated that inlet and outlet control are the two basic
types of flow control defined in the research conducted by the National Bureau
of Standards (NBS) and the Federal Highway Administration (FHWA). The basis
for the classification system was the location of the control section. The
characterization of pressure, subcritical, and supercritical flow regimes played an
important role in determining the location of the control section and thus the type
of control. The hydraulic capacity of a culvert depends upon a different
combination of factors for each type of control.
2-7-1 Inlet Control
Kilgore, et al. (2012) observed that inlet control occurs when the culvert
barrel is capable of conveying more flow than the inlet will accept. The control
section of a culvert operating under inlet control is located just inside the
Design of Box Culvert
12
Chapter Two
Review of Literature
entrance. Critical depth occurs at or near this location, and the flow regime
immediately downstream is supercritical. Figure (2-14) shows one typical inlet
control flow condition. Hydraulic characteristics downstream of the inlet control
section do not affect the culvert capacity. The upstream water surface elevation
and the inlet geometry represent the major flow controls. The inlet geometry
includes the inlet shape, inlet cross-sectional area, and the inlet configuration
(Table 2-1).
Figure (2-14). Typical inlet control flow section.
2-7-2 Outlet Control
Kilgore, et al. (2012) observed that outlet control flow occurs when the
culvert barrel is not capable of conveying as much flow as the inlet opening will
accept. The control section for outlet control flow in a culvert is located at the
barrel exit or further downstream. Either subcritical or pressure flow exists in the
culvert barrel under these conditions. Figure (2-15) shows two typical outlet
control flow conditions. All of the geometric and hydraulic characteristics of the
culvert play a role in determining its capacity. These characteristics include all of
the factors governing inlet control, the water surface elevation at the outlet, and
the barrel characteristics (Table 2-1).
Design of Box Culvert
13
Chapter Two
Review of Literature
Figure (2-15). Typical outlet control flow section.
Table (2-1) Factors influencing culvert design.
Factor
Inlet control
Outlet control
Headwater
x
x
Area
Shape
Inlet configuration
x
x
x
x
x
x
Barrel roughness
-
x
Barrel length
-
x
Barrel Slope
Tailwater
x
-
x
x
* For inlet control the area and shape factors relate to the inlet area and shape. For outlet
control, they relate to the barrel area and shape.
Design of Box Culvert
14
Chapter Two
Review of Literature
2-8 Headwater
Kilgore, et al. (2012) noted that energy is required to force flow through a
culvert. This energy takes the form of an increased water surface elevation on the
upstream side of the culvert. The depth of the upstream water surface measured
from the invert at the culvert entrance is generally referred to as headwater depth.
The allowable headwater is the maximum possible headwater, or ponding depth,
at the upstream side of the culvert. Note that this is different from the design
headwater. The design headwater is actual headwater that will occur for the
selected culvert as designed.
2-9 Culvert Length
Creamer (2007) stated that important dimensions and features of the culvert
will become evident when the desired roadway cross section is measured or
established. The dimensions are obtained by superimposing the estimated culvert
barrel on the roadway cross section and the streambed profile, Figure (2-16). This
superposition establishes the inlet and outlet invert elevations.
Figure (2-16) Roadway cross section and culvert length.
Design of Box Culvert
15
Chapter Two
Review of Literature
2-10 Box Culvert and Pipe Culvert
Civil Engineering Portal website (2012) published that in terms of hydraulic
performance, circular section is the best geometrical sections among all.
Therefore, for relative small discharge, precast concrete pipes and ductile iron
pipes are normally used which are circular in shape. But for applications of very
large flow, precast concrete pipes and ductile iron pipes may not be available in
current market. In this condition, cast-in-situ construction has to be employed. It
is beyond doubt that the fabrication of formwork for circular shape is difficult
when compared with normal box culvert structures. However, circular shape is
the most hydraulic efficient structure which means for a given discharge, the area
of flow is minimum. Therefore, it helps to save the cost of extra linings required
for the choice of box culverts.
However, box culverts do possess some advantages. For example, they can cope
with large flow situation where headroom is limited because the height of box
culverts can be reduced while the size of pipe culverts is fixed. Secondly, for
some difficult site conditions, e.g. excavation of structure in rock, for the same
equivalent cross-sectional area, the width of box culverts can be designed to be
smaller than that of pipe culverts and this enhances smaller amount of excavation
and backfilling.
Figure (2-17). Small spatial requirement of box culvert than pipes.
Design of Box Culvert
16
Chapter Two
Review of Literature
2-11 Culvert Failure
Pencol Engineering Consultants (1983) stated that culvert failures can occur
for a wide variety of reasons including maintenance, environmental, and
installation related failures, functional or process failures related to capacity and
volume causing the erosion of the soil around or under them, and structural or
material failures that cause culverts to fail due to collapse or corrosion of the
materials from which they are made.
If the failure is sudden and catastrophic, it can result in injury or loss of life.
Sudden road collapses are often at poorly designed and engineered culvert
crossing sites. Water passing through undersized culverts will scour away the
surrounding soil over time. This can cause a sudden failure during medium-sized
rain events. Accidents due to culvert failure can also occur if a culvert has not
been adequately sized and a flood event overwhelms the culvert or disrupts the
road or railway above it.
Ongoing culvert function without failure depends on proper design and
engineering considerations being given to load and water capacities, surrounding
soil analysis, backfill and bedding compaction, and erosion protection.
Improperly designed backfill support around aluminum or plastic culverts can
result in material collapse or failure from inadequate load support.
2-12 Environmental Impacts
Chanson and Wang (2017) conducted a study about safe and stable stream
crossings can accommodate wildlife and protect stream health while reducing
expensive erosion and structural damage. Undersized and poorly placed culverts
can cause problems for water quality and aquatic organisms. Poorly designed
culverts can degrade water quality via scour and erosion and also restrict aquatic
organisms from being able to move freely between upstream and downstream
habitat. Fish are a common victim in the loss of habitat due to poorly designed
Design of Box Culvert
17
Chapter Two
Review of Literature
crossing structures. Culverts that offer adequate aquatic organism passage reduce
impediments to movement of fish, wildlife and other aquatic life that require
instream passage. These structures are less likely to fail in medium to large scale
rain and snow melt events.
Poorly designed culverts are also more suitable to become jammed with sediment
and debris during medium to large scale rain events. If the culvert cannot pass the
water volume in the stream, the water may overflow over the road embankment.
This may cause significant erosion, washing out the culvert. The embankment
material that is washed away can clog other structures downstream, causing them
to fail as well. It can also damage crops and property
2-13 Velocity Limitation
Pencol Engineering Consultants (1983) considered velocity limitations
include the maximum and the minimum velocities that should be considered
when designing a culvert, the outlet velocity affects the stability of the culvert,
the greater the outlet velocity the greater the need for stability, there is no
specified maximum velocity for reinforced concrete box culverts, but there
should be provision of outer protection when the velocity is an erosion risk.
However, velocity should not be less than 0.5 m/s to prevent sedimentation in the
barrel of the box culvert and should not be more than 1.5 m/s to prevent corrosion
of the box culvert barrel.
2-14 Structural Design of Box Culvert
Bolden, et al. (2016) stated that the culvert design begins when the structure
design unit receives the culvert hydraulic design report. This report shall be used
to contained the culvert length, design fill, and other items that lead to the
completed culvert plans.
Design of Box Culvert
18
Chapter Two
Review of Literature
Pencol Engineering Consultants (1983) defined box culverts are reinforced
concrete closed rigid frames which must support vertical earth and truck loads
and lateral earth pressure. They may be either single or multi-cell based on the
hydraulic requirements.
Garg (2007) reported that box culverts are typically designed similar to
bridges, and the new design concepts for bridges are based on the Load and
Resistance Factor Design (LRFD) which were developed by the AASHTO. Box
culvert’s four sides are built monolithically and also provide haunch at corners to
decrease the water pressure effect. In this type of culvert there is no need of extra
foundation since bottom slab act as mat foundation.
2-14-1 Box Culvert Structural Elements
Kumar and Srinivas (2015) stated that box Culverts consist of top slab,
bottom slab and two vertical side walls. Reinforced concrete rigid frame box
culverts are used for square or rectangular openings. The top of the box section
can be at the road level or can be at a depth below road level with a fill depending
on site conditions.
Pencol Engineering Consultants (1983) assumed the thickness of the box
culvert and later checked in conventional method. However, this may lead to
uneconomical design therefore an attempt is made to evaluate optimum
thicknesses for economical design.
2-14-2 Applied Loads
Kumar and Srinivas (2015) classified loads subjected to box culvert to dead
load and live load. Dead load comprising of self-weight of top and bottom slab
of the culvert and two side walls of the structure which is calculated based on
clear dimensions of the culvert and thickness of the culvert. Super imposed dead
load depends on the typed of the constructed road above the culvert and is
calculated from standards and specifications code of practice. Live load on culvert
Design of Box Culvert
19
Chapter Two
Review of Literature
is vehicular loading. The vehicular live load consists set of wheel loads moving
on top slab of culvert. These loads are distributed through the top slab of the
culvert. Earth can exert pressure as active and passive. Minimum is active and
maximum is passive earth pressure and the median is rest.
Chandrakant and Malgonda (2014) concluded that, since box culvert carries
earth embankment which is subjected to same traffic loads as the road carries and
therefore, it is required for the box culvert to be designed for such loads. The
structural elements are required to be designed to withstand maximum bending
moment and shear force. Analysis of box culvert is carried out for various load
conditions and structural design is suggested for critical cases.
Kim and Yoo (2002) conducted an investigation for deeply buried
structures, the dead weight of soil itself is the main design load and the effect of
live loads is not considered significant. AASHTO LRFD Bridge Design
Specifications stipulate the computation of the design load on the top slab of the
box culvert based primarily the effective density on the concrete box
culverts can be depending on the installation method, trench installation.
2-14-3 Structural Design Method
Oyenuga (2001) stated that a box culvert should be designed as a rigid
structure with moments occurring at the corners using the method of moment
distribution. The analysis carried out for the following cases: • Culvert empty: Full load on top of the slab, surcharge load and
superimposed surcharge load on earth fill.
• Culvert full: Live load surcharge on top slab and no superimposed
surcharge on earth fill.
• Culvert full: Live load surcharge on top slab and superimposed surcharge
load on earth fill.
Design of Box Culvert
20
Chapter Three
Theoretical Background
Chapter Three
Theoretical Background
Chapter Three
Theoretical Background
3-1 Introduction
The Kut-Petera irrigation project is of an area of 157,000 donum and
consists of many sectors. Sector 3 is located in Al-Kut side and its area is 22,000
donum. The irrigation network in sector 3, as shown in figure (3-1), has an
irrigation network contains a main cannel which takes water from The Tigers
river then distributes it into branch cannels, as well the drainage network. The
section of main drain (MD-A), shown in figure (3-2), is 35 km in length and
intersected with Al-Dejaili paved road at the station (10 + 660) km where the
culvert is constructed.
Figure (3-1). Sector 3 of the Kut-Petera irrigation project.
Design of Box Culvert
21
Chapter Three
Theoretical Background
Figure (3-2). Section of MD-A with culvert location.
Design of Box Culvert
22
Chapter Three
Theoretical Background
3-2 Hydraulic Design information
The profile shown in figure (3-3) is a section between the stations (5+000 –
11+500) km. At the station (10+660) km is the culvert location and the design
information are obtained from the profile.
Design information of MD-A is: • Discharge (Q) = 1.95 m3/s
• Velocity (V) = 0.297 m/s
• Drain bed width (B) = 3.5 m
• Drain water depth (H) = 1.25 m
• Side slope = 2:1
• Longitudinal slope (S) = 10 cm/km
• Ground level = 12.99 m
• Manning coefficient (n) = 0.015
• Upstream water level (U/S W.L) = 8.56 m
• Downstream water level (D/S W.L) = 8.51 m
• Inlet bed level = 7.31 m
• Outlet bed level = 7.26 m
As for the road, the design information is: • Top level of road = 12.99 m
• Top width of road = 10 m (two lanes each 3 m and two shoulders each 2
m).
• Side slope = 2:1
Finally, the structural design information is: • 𝛾"#$"%&'& = 24 𝐾𝑁/𝑚0
• 𝛾1#23 14'. = 18 𝐾𝑁/𝑚0
Design of Box Culvert
23
Chapter Three
Theoretical Background
Figure (3-3). The profile between the stations (5+000 – 11+500) km.
Design of Box Culvert
24
Chapter Three
Theoretical Background
3-3 Conveyance condition
The used conveyance condition for this culvert design is case 4, as explained in
chapter two, because of the economic benefit. Whereas, the topography of Iraq is
relatively flat, so, to achieve the required slope, it will be a high cost of cut and
fill works. Secondly, Head losses have to be minimized as well keeping the
adequate velocity of the flow, as the high velocity will lead to erosion of the
cannel sides especially it is not filled with concrete and the low velocity will lead
to sedimentation of sediments of the water in the cannel.
Submerged outlet H > 1.2D
full flow
Yt > D
Figure (3-4). Case 4.
Design of Box Culvert
25
Chapter Three
Theoretical Background
3-4 Case 4 formula
The total head losses - showing in figure (3-5) - of the water flowing in the
box culvert is based on the basis of energy losses due to: • Major losses due to friction, and;
• Minor losses due to entrance and exit.
The total head losses equation is: DH = ℎ9 + ℎ; … … (𝑒𝑞. 3 − 1)
Where:
DH = Total head losses
ℎ9 = major losses due to friction
ℎ; = minor losses due to entrance and exit
ℎ; is at the inlet and outlet of the box culvert, therefore,
DH = ℎ9 + ℎ; )2$3&' + ℎ; )#C'3&' … … (𝑒𝑞. 3 − 2)
Figure (3-5). Total head losses.
Design of Box Culvert
26
Chapter Three
Theoretical Background
Regardless the type of flow energy losses, the flow losses equation is: 𝑉G
ℎ= 𝑘𝑥
… … (𝑒𝑞. 3 − 3)
2𝑔
So, the total head losses can be reformatted as: 𝑉G
𝑉G
𝑉G
DH = 𝑘9
+ 𝑘2$3&'
+ 𝑘#C'3&'
2𝑔
2𝑔
2𝑔
DH = (𝑘9 + 𝑘2$3&'
𝑉G
+ 𝑘#C'3&' )
… … (𝑒𝑞. 3 − 4)
2𝑔
Where:
𝑘 = coefficient of losses
Hence, the inlet edge is sharp, 𝑘2$3&' = 0.5 and 𝑘#C'3&' = 1
In order to determine 𝑘9 , the connected canal to the box culvert is an open
channel, so, Manning eq. is used to determine the velocity of the flowing water.
𝑉=
G
O
1
𝑥 𝑅 0 𝑥 𝑆 G … … (𝑒𝑞. 3 − 5)
𝑛
Where:
𝑛 = Manning coefficient of roughness
𝑅 = the hydraulic Radius
𝑆 = the slope of energy line
Figure (3-6). Cross section of
box culvert.
P
R is can be found from the culvert cross section, 𝑅 =
𝑅=
S is the slope of energy line, 𝑆 =
Design of Box Culvert
WX
Y
Q
=
RS
TR
𝐷
… … (𝑒𝑞. 3 − 6)
4
… … (𝑒𝑞. 3 − 7)
27
Chapter Three
Theoretical Background
Therefore,
𝑉=
1
𝐷 G ℎ9 O
𝑥 ( )0 𝑥 ( )G … … (𝑒𝑞. 3 − 8)
𝑛
4
𝐿
G
1 𝐷 0 ℎ9 \.]
𝑉 = 𝑥 G 𝑥 \.]
𝑛
𝐿
40
G
ℎ9 \.] =
𝑉 𝑥 𝑛 𝑥 40 𝑥 𝐿\.]
G
𝐷0
… … (𝑏𝑦 𝑠𝑞𝑢𝑖𝑟𝑖𝑛𝑔 𝑏𝑜𝑡ℎ 𝑠𝑖𝑑𝑒𝑠)
G
ℎ9 =
ℎ9 =
𝑉 G 𝑥 𝑛G 𝑥 40 𝑥 6.35 𝐿
T
……∗
𝐷0
12.7 𝑥 𝑛G 𝑥 𝑔 𝑥 𝑙
T
𝐷0
2𝑔
2𝑔
𝑉G
𝑥
… … (𝑒𝑞. 3 − 9)
2𝑔
From comparing (𝑒𝑞. 3 − 9) to the friction losses eq. j ℎ9 = 𝑘9 𝑥
kS
Gl
m,
It can be noticed that,
𝑘9 =
12.7 𝑥 𝑛G 𝑥 𝑔 𝑥 𝑙
T
𝐷0
… … (𝑒𝑞. 3 − 10)
Sub (𝑒𝑞. 3 − 10) in (𝑒𝑞. 3 − 4)
DH = n
12.7 𝑥 𝑛G 𝑥 𝑔 𝑥 𝑙
T
𝐷0
Design of Box Culvert
+ 𝑘2$3&'
𝑉G
+ 𝑘#C'3&' o
… … (𝑒𝑞. 3 − 11)
2𝑔
28
Chapter Three
Theoretical Background
From the discharge equation,
𝑄 = 𝐴𝑉
𝑉=
𝑄
𝐴
𝑄G
𝑉 = G
𝐴
G
𝑄G
𝑉 = T … … (𝑒𝑞. 3 − 12)
𝐷
G
Thus, the equation for case 4 would be
DH = n
12.7 𝑥 𝑛G 𝑥 𝑔 𝑥 𝑙
T
𝐷0
+ 𝑘2$3&'
𝑄G
1
+ 𝑘#C'3&' o 𝑥 T 𝑥
… … (𝑒𝑞. 3 − 13)
𝐷
2𝑔
3-5 Structural design cases
The design is carried out for 1m length of the box culvert and based on the
obtained dimensions from the hydraulic design. Mainly, the load cases for box
culvert design are: 1. Box empty, live load surcharge on top slab of box and superimposed surcharge
load on earth fill.
2. Box inside full with water, live load surcharge on top slab and superimposed
surcharge load on earth fill.
3. Box inside full with water, no live load surcharge on top slab and superimposed
surcharge on earth fill.
Oyenuga (2001) proven that the first load case gives the higher value of moments,
because when the box culvert inside full with water, the resultant force of
hydrostatic water pressure on the inside and resultant of superimposed surcharge
load on the outside, the sum of the two resultants yields a lesser resultant force
acting on the culvert wall. Therefore, the design will be carried for case 1.
Design of Box Culvert
29
Chapter Four
Results and Discussion
Chapter Four
Results and Discussion
Chapter Four
Results and Discussion
4-1 Hydraulic Design
The culvert equation shown below and the obtained field data – from
Chapter Three - will be used for the hydraulics design of the box culvert.
DH = $
12.7 𝑥 𝑛+ 𝑥 𝑔 𝑥 𝑙
/
𝐷0
+ 𝑘34567
𝑄+
1
+ 𝑘897567 : 𝑥 / 𝑥
… … (𝑒𝑞. 3 − 13)
𝐷
2𝑔
Assume:
• Culvert invert level is equal to the main drain (MD-A) bed level.
• Length of culvert = 27 m.
Figure (4-1). Main drain (MD-A) cross section.
Figure (4-2). Culvert side view [invert level = main drain (MD-A) level].
Design of Box Culvert
30
Chapter Four
Results and Discussion
v First attempt
DH = U/S W.L – D/S W.L
DH = 8.56 – 8.51
DH = 0.05 m
0.05 = $
12.7 𝑥 (0.015)+ 𝑥 9.81 𝑥 27
/
𝐷0
1.95+
1
+ 0.5 + 1: 𝑥
𝑥
𝐷/
2𝑥9.81
By using trial and error
D = 1.65 m
To ensure the flow conveyance of the culvert is case 4;
J.+K
J.LK
G
H
≥ 1.2
= 0.75 < 1.2
Which means the inlet will not be submerged because the value of the headwater
(H) is less than the critical value (H`) which is indicated by the relation
– 1.2D ≤ H` ≤ 1.5D – where (D) is culvert height, while the outlet will not be
submerged neither. In this situation, an invert with a slope of 5:1 must be used to
solve this issue.
Figure (4-3) Culvert side view when H<H’.
Design of Box Culvert
31
Chapter Four
Results and Discussion
To calculate the required invert: Hcal = 1.2 x D
Hcal= 1.2 x 1.65
Hcal = 1.98 m
Invert = Hcal. – Hact
Invert = 1.98 – 1.25
Invert = 0.73 m
Invert with 0.73 m length is hard to execute because the main drain (MD-A) level
is already below the ground, so to reach the invert level (I.L), excavation would
be very hard to achieve. Thus, the culvert is divided into two boxes, each takes
half of the discharge.
Figure (4-4). Culvert side view with 0.73 m length invert.
Design of Box Culvert
32
Chapter Four
Results and Discussion
v Second attempt
The design for a single box culvert:
𝑄=
1.95
= 0.975 𝑚0/𝑠
2
0.05 = $
12.7 𝑥 (0.015)+ 𝑥 9.81 𝑥 27
/
𝐷0
0.975+
1
+ 0.5 + 1: 𝑥
𝑥
𝐷/
2𝑥9.81
By using trial and error
D = 1.2 m
For case 4,
J.+K
J.+
G
H
≥ 1.2
= 1.04 < 1.2; the headwater (H) is less than the critical value (H`).
Figure (4-5). Culvert side view of a single box when H < H`.
Design of Box Culvert
33
Chapter Four
Results and Discussion
To calculate the required invert: Hcal = 1.2 x D
Hcal = 1.2 * 1.2
Hcal = 1.44 m
Invert = Hcal. – Hact
Invert = 1.44 – 1.25
Invert = 0.2 m; which can be considered to be executable.
For case 4,
GR34S6T7
H
≥ 1.2
1.25 + 0.2
= 1.2 ∴ 𝑜𝑘
1.2
Invert level = main drain (MD-A) level – Invert length
= 7.31 – 0.2 = 7.11 m
Top culvert level = Invert level + D
= 7.11 + 1.2 = 8.31 m
Figure (4-6). Culvert side view with 0.2 m length invert.
Design of Box Culvert
34
Chapter Four
Results and Discussion
According to the Design Manual for Irrigation and Drainage by Pencol
Engineering Consultants (1983), the thicknesses of the box culvert were assumed
to be based on table (11.5), as showing below.
The total discharge of the main drain (MD-A) is 1.95 𝑚0 /𝑠. So, the assumed
design thickness for top slab, walls and bottom slab is 0.25 m.
For checking the assumption of culvert length;
Bottom level of road = top culvert level + top slab thickness
8.31 + 0.25 = 8.56 m
Height of road = 12.99 - 8.56 = 4.43 m
L = Top width of road + (Height of road x Horizontal slope of road)
L = 10 + [(4.43 x 2) x 2] = 27 m
The calculated length is equal to the assumed length = 27 m ∴ 𝑜𝑘
Design of Box Culvert
35
Chapter Four
Results and Discussion
Figure (4-7). Section A-A.
The velocity (V) of a single box must be, less than 1.5 m/s to prevent corrosion
of the unfilled cannel and more than 0.5 m/s to prevent sedimentation of water
sediments. To check for the flow velocity (V) of a single box:
𝑄 = 𝑉𝐴
𝑄
𝐴
0.975
𝑉=
(1.2)+
𝑉=
𝑉 = 0.67 m/s ∴ 𝑜𝑘
Design of Box Culvert
36
Chapter Four
Results and Discussion
4-2 Structural Design
v Loads
Loads were calculated and factored according to AASHTO LRFD Bridge
Design Specifications 4th Edition (2007). Distribution of wheel live load is
neglected due to the article: “For single-span culverts, the effects of live load may be neglected where the
depth of fill is more than 2400 mm and exceeds the span length; for multiple span
culverts, the effects may be neglected where the depth of fill exceeds the distance
between faces of end walls.”.
– article (3.6.1.2.6)
Since the designed box culvert is multiple span;
Fill depth = 4.43m > distance between end walls faces = 2.65m
Therefore, distribution of wheel load is neglected.
Load factors are obtained from table 3.4.1-2 of AASHTO LRFD, as showing
below.
Design of Box Culvert
37
Chapter Four
Results and Discussion
Ø Top slab: 𝑆𝑒𝑙𝑓 − 𝑤𝑒𝑖𝑔ℎ𝑡 = 24 𝑥 0.25 = 6 𝐾𝑁 ⁄𝑚+⁄𝑚
𝐵𝑎𝑐𝑘𝑓𝑖𝑙𝑙 𝑙𝑜𝑎𝑑 = 4.43 𝑥 18 = 79.74 𝐾𝑁 ⁄𝑚+⁄𝑚
𝐹𝑎𝑐𝑡𝑜𝑟𝑒𝑑 𝑡𝑜𝑡𝑎𝑙 𝑙𝑜𝑎𝑑 = 6 𝑥 1.25 + 79.74 𝑥 1.35 = 115.15 𝐾𝑁 ⁄𝑚+⁄𝑚
Ø Exterior side walls: To calculate lateral earth pressure (EH), Mohr’s equation is used to calculate Ka.
∅
30
1
l = 𝑡𝑎𝑛+ j45 −
l=
2
2
3
1
𝐸G = 𝐾i 𝑥 𝛾o 𝑥 𝐻 = 𝑥 18 𝑥 1.45 = 8.7 𝐾𝑁 ⁄𝑚+⁄𝑚
3
𝐾i = 𝑡𝑎𝑛+ j45 −
“Where a uniform surcharge is present, a constant horizontal earth pressure shall
be added to the basic earth pressure. This constant earth pressure may be taken
as:
∆𝑝 = 𝑘o 𝑞o
(3.11.6.1-1)
Where:
∆𝑝 = Constant horizontal earth pressure due to uniform surcharge (KPa).
𝑘o = coefficient of earth pressure due to surcharge. For active earth pressure
conditions, ks shall be taken as ka.
𝑞o = uniform surcharge applied to the upper surface of the active earth wedge
(KPa)”.
– article (3.11.6)
1
𝑥 79.74 = 26.58 𝐾𝑁 ⁄𝑚+⁄𝑚
3
𝐹𝑎𝑐𝑡𝑜𝑟𝑒𝑑 𝐸G )s8778t = (26.58 + 8.7) 𝑥 1.5 = 52.92 𝐾𝑁 ⁄𝑚+⁄𝑚
∆𝑝 =
𝐹𝑎𝑐𝑡𝑜𝑟𝑒𝑑 𝐸G )78u = 26.58 𝑥 1.5 = 39.87 𝐾𝑁 ⁄𝑚+⁄𝑚
Design of Box Culvert
38
Chapter Four
Results and Discussion
Ø Bottom slab: 𝐹𝑎𝑐𝑡𝑜𝑟𝑒𝑑 𝑆𝑒𝑙𝑓 − 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑤𝑎𝑙𝑙𝑠 =
3 𝑥 24 𝑥 1.2 𝑥 0.25 𝑥 1.25
3.15
= 8.57 𝐾𝑁 ⁄𝑚+⁄𝑚
𝐹𝑎𝑐𝑡𝑜𝑟𝑒𝑑 𝑙𝑜𝑎𝑑 𝑓𝑟𝑜𝑚 𝑡𝑜𝑝 𝑠𝑙𝑎𝑏 = 115.15 𝐾𝑁 ⁄𝑚+⁄𝑚
𝑇𝑜𝑡𝑡𝑎𝑙 𝑙𝑜𝑎𝑑𝑠 = 115.15 + 8.57 = 123.72 𝐾𝑁 ⁄𝑚+⁄𝑚
The calculated loads can be considered as linear loads since the designed is
carried for 1m length of the box culvert.
Figure (4-8). Factored load distribution.
Design of Box Culvert
39
Chapter Four
Results and Discussion
Table (4-1). Summary of factored distributed loads.
Member
Top
Slab
Load source
Load
factor
Area load
(kN/m2/m)
Self-weight
1.25
7.5
Backfill
1.35
Total linear
load (kN/m2/m)
115.15
115.15
107.65
Top
Exterior Lateral
side
earth
walls
pressure
Total area
load
(kN/m2/m)
39.87
1.5
Bottom
Self-weight of
walls
52.92
1.25
8.57
Bottom
slab
123.72
Total top slab
loads
Design of Box Culvert
-
123.72
115.15
40
Chapter Four
Results and Discussion
v Reinforced concrete design
Moment calculated according to Building Code Requirements for Structural
Concrete (ACI 318M-14) and Commentary (ACI 318RM-14).
Figure (4-9). Frame of box culvert.
o Fixed end moment (F.E.M.)
𝑤𝑙+
𝐹. 𝐸. 𝑀.@z{ = 𝐹. 𝐸. 𝑀.@{z = 𝐹. 𝐸. 𝑀.@{| = 𝐹. 𝐸. 𝑀.@|{ =
12
115.15 𝑥 (1.45)+
=
= 20.18 𝐾𝑁. 𝑚/𝑚
12
𝑤𝑙+
𝐹. 𝐸. 𝑀.@H} = 𝐹. 𝐸. 𝑀.@}H = 𝐹. 𝐸. 𝑀.@}~ = 𝐹. 𝐸. 𝑀.@~} =
12
123.72 𝑥 (1.45)+
=
= 21.67 𝐾𝑁. 𝑚/𝑚
12
𝑊J 𝑙+ (𝑊+ − 𝑊J )𝑙+
𝐹. 𝐸. 𝑀.@zH = 𝐹. 𝐸. 𝑀.@|} =
+
12
30
39.87 𝑥 (1.45)+ (52.92 − 39.87)𝑥 (1.45)+
=
+
= 8.11 𝐾𝑁. 𝑚/𝑚
12
30
Design of Box Culvert
41
Chapter Four
Results and Discussion
𝑊J𝑙+ (𝑊+ − 𝑊J )𝑙+
𝐹. 𝐸. 𝑀.@Hz = 𝐹. 𝐸. 𝑀.@~| =
+
12
20
39.87 𝑥 (1.45)+ (52.92 − 39.87)𝑥 (1.45)+
=
+
= 8.67 𝐾𝑁. 𝑚/𝑚
12
20
𝐹. 𝐸. 𝑀.@{} = 𝐹. 𝐸. 𝑀.@}{ = 0
o Distribution factor
4𝐸𝐼
𝑙
𝐾𝐾@ t6ts6T
=
Σ𝐾@ t6ts6T
𝐾@ t6ts6T =
𝐾@ •8347
Since, all members have the same modules of elasticity (E) and the dimensions
are equal which makes the moment of inertia equal for all. Hence, the distribution
factor for all joints is equal.
𝐾@ •8347 = 0.5
Design of Box Culvert
42
Chapter Four
Results and Discussion
o Moment distribution calculation
Table (4-2). Moment distribution table.
Design of Box Culvert
43
Chapter Four
Results and Discussion
o Mid-span moments
R
𝑀z{
=
R
𝑀{|
𝑤𝑙+
𝑀Jƒ + 𝑀+ƒ
=
− j
l
8
2
115.15 𝑥 (1.45)+
11.99 + 24.08
=
−j
l = +12.2 𝐾𝑁. 𝑚/𝑚
8
2
R
𝑀H}
=
R
𝑀}~
𝑤𝑙+
𝑀Jƒ + 𝑀+ƒ
=
− j
l
8
2
123.72 𝑥 (1.45)+
13.07 + 25.77
=
−j
l
8
2
= +13.1 𝐾𝑁. 𝑚/𝑚
R
𝑀zH
=
R
𝑀|~
𝑤+ 𝑙+
𝑀Jƒ + 𝑀+ƒ
== „
+ [0.128 𝑥 (𝑤+ − 𝑤J )𝑥 𝑙] ‡ − j
l
8
2
39.87 𝑥 (1.45)+
11.99 + 13.07
= ˆ
+ [0.128 𝑥 (52.92 − 39.87) 𝑥 1.45]‰ − j
l
8
2
= +0.37 𝐾𝑁. 𝑚/𝑚
R
𝑀{}
= 0
o Negative moments at face of support
“For slabs built integrally with supports, Mu at the support shall be permitted
to be calculated at the face of support”.
Design of Box Culvert
– ACI 7.4.2.1
44
Chapter Four
Results and Discussion
𝑉 𝑥 𝑏 𝑤𝑙 (0.5𝑏)+
= 𝑀 −
+
;
2
2
𝑤𝑙
𝑀J + 𝑀+
𝑉=
± j
l
2
𝑙
ƒ
𝑀@o9uu8T7
Ši‹6
ƒ
Where;
𝑀ƒ = negative moment at the center of support.
𝑉 = modified shear value due to the difference of negative moments.
𝑏 = width of support.
𝑀J & 𝑀+ = moments of a member’s supports based on the sum of moment
distribution table.
Table (4-3). Negative moment at face of support.
Member
AB
BC
DE
EF
AD
CF
Joint
A
B
B
C
D
E
E
F
A
D
C
F
Design of Box Culvert
𝑴ƒ
11.99
24.08
24.08
11.99
13.07
25.77
25.77
-13.07
11.99
13.07
11.99
13.07
𝑽𝒖 @𝒔𝒖𝒑𝒑𝒐𝒓𝒕 𝒇𝒂𝒄𝒆
75.15
91.81
91.81
75.15
80.94
98.46
98.46
80.94
31.31
35.96
31.31
35.96
𝑴ƒ
@𝒔𝒖𝒑𝒑𝒐𝒓𝒕 𝒇𝒂𝒄𝒆
-3.50
-13.50
-13.50
-3.50
-3.92
-14.86
-14.86
-3.92
-8.43
-8.96
-8.43
-8.96
45
Chapter Four
Results and Discussion
o Moments summary
Table (4-4). Moments summary.
Member
Joint
AB = BC
DE = EF
AD = CF
moment
(KN.m/m)
A=C
-3.5
B
-13.5
D=F
-3.92
E
-14.86
A=C
-8.43
D=F
-9.05
(KN.m/m)
+12.2
+13.1
+0.37
B
BE = EB
Mid – Span
Support moment
0
E
o Shear checking
“For slabs built integrally with supports, Vu at the support shall be permitted to
be calculated at the face of support”.
– ACI 7.4.3.1
›𝑽𝒖 @𝒔𝒖𝒑𝒑𝒐𝒓𝒕 𝒇𝒂𝒄𝒆 œ are obtained from table (4-3).
Table (4-5). Vu at the face of support.
Member
AB = AC
DE = EF
AD = CF
Joint
A=C
B
D=F
E
A=C
D=F
𝑽𝒖 @𝒔𝒖𝒑𝒑𝒐𝒓𝒕 𝒇𝒂𝒄𝒆
𝑲𝑵/𝒎
75.15
91.81
80.94
98.46
31.31
35.96
Design of Box Culvert
46
Chapter Four
Results and Discussion
“Sections between the face of support and a critical section located d from the
face of support for nonprestressed slabs or h/2 from the face of support for
prestressed slabs shall be permitted to be designed for Vu at that critical section
if (a) through (c) are satisfied:
(a) Support reaction, in direction of applied shear, intro-duces compression
into the end region of the slab.
(b) Loads are applied at or near the top surface of the slab.
(c) No concentrated load occurs between the face of support and critical
section.”
– ACI 7.4.3.2
Hence, (a) through (c) are satisfied, Vu shall be calculated at the critical section
which is at distance equal to (d) from the face of support.
Concrete cover shall be taken as 75mm for all member because the structure is
exposed to ground permanently as specified in (ACI – Table 20.6.1.3.1).
∅siT
2
12
= 250 − 75 −
= 169 𝑚𝑚
2
𝑑 = ℎ − 𝑐𝑜𝑣𝑒𝑟 −
𝑉9 @¡ ŠT8t o9uu8T7 Ši‹6 = 𝑉9 @o9uu8T7 Ši‹6 − 𝑤9 𝑑
Table (4-6). Vu at distance d from support face.
Member
Joint
𝑽𝒖 @𝒅 𝒇𝒓𝒐𝒎 𝒔𝒖𝒑𝒑𝒐𝒓𝒕 𝒇𝒂𝒄𝒆
𝑲𝑵/𝒎
AB = AC
A
B
55.68
72.35
DE = EF
D
E
60.03
77.55
AD = CF
A
D
24.57
33.75
Max 𝑉9 is at joint E = 77.55 KN/m
Design of Box Culvert
47
Chapter Four
Results and Discussion
Checking the shear capacity of the concrete cross section: -
𝑉4 = 0.17𝜆¤𝑓‹` 𝑏¦ 𝑑
𝐴𝐶𝐼 (22.5.5.1)
Where:
𝜆 = modification factor according to the type of concrete. In case of
normal concrete, it equals 1 as specified in (ACI – Table 19.2.4.2).
𝑓‹` = concrete compressive strength.
𝑏¦ = width of the concrete section
𝑉4 = 0.17 𝑥 1 𝑥 √25 𝑥 1000 𝑥 169 𝑥 10ƒ0 = 143.65 𝐾𝑁/𝑚
The reduction factor (∅) for shear is specified as 0.75 in (ACI – Table 21.2.1).
∅𝑉‹ = 0.75𝑉4 = 0.75 𝑥 143.65 = 107.74 𝐾𝑁/𝑚
∅𝑉‹ = 107.74 > 𝑉9 = 77.55 ∴ 𝑜𝑘
o Flexural reinforcement
The following procedure is obtained from ACI (Chapter 22 – Sectional Strength).
𝑅9 =
𝑀9
,
∅𝑏𝑑 +
𝑚=
𝑓¬
0.85 𝑓‹`
𝜌=
1
2𝑅9 𝑚
®1 − ¯1 −
°
𝑚
𝑓¬
∅ = 0.9
𝐴o = 𝜌𝑏𝑑
Design of Box Culvert
48
Chapter Four
Results and Discussion
Table (4-7). Reinforcement calculations.
Member
Joint
A=C
Mid-Span
B
D=F
Mid-Span
E
A=C
Mid-Span
D
AB =
BC
DE =
EF
AD =
CD
𝑴𝒖
𝑹𝒖
(𝑲𝑵. 𝒎/𝒎) (𝑴𝑷𝒂/𝒎)
-3.50
12.20
-13.50
-3.92
13.10
-14.86
-8.43
0.37
-9.05
1.39E-01
4.86E-01
5.38E-01
1.56E-01
5.22E-01
5.92E-01
3.36E-01
1.47E-02
3.61E-01
𝒎
𝝆 𝒄𝒂𝒍𝒄𝒖𝒍𝒂𝒕𝒆𝒅
19.76
19.76
19.76
19.76
19.76
19.76
19.76
19.76
19.76
3.331E-04
1.171E-03
1.297E-03
3.732E-04
1.258E-03
1.430E-03
8.061E-04
3.511E-05
8.659E-04
It’s clear that the value of 𝜌 is very small due to the small value of the applied
moment (𝑀9 ). Therefore, 𝐴o t34 specified by (ACI – Table 7.6.1.1) must be used.
𝐴o t34 =
0.0018𝑥420
𝐴µ ≥ 0.0014𝐴µ
𝑓¬
𝐴o t34 =
0.0018𝑥420
(1000 ∗ 250) ≥ 0.0014𝐴µ
420
𝐴o t34 = 450 ≥ 350
+
𝐴o t34 = 450 𝑚𝑚 ·𝑚
𝑀𝑎𝑥 𝑠𝑝𝑎𝑐𝑖𝑛𝑔 (𝑆ti¸ ) = 3ℎ ≤ 450𝑚𝑚
– 𝐴𝐶𝐼 (7.7.2.3)
= 3𝑥250 ≤ 450𝑚𝑚
= 750 ≤ 450𝑚𝑚
𝑆ti¸ = 450 𝑚𝑚⁄𝑚
+
Use ∅12 @ 250 𝑚𝑚 𝐶·𝐶 , which will provide 𝐴o = 482 𝑚𝑚 ·𝑚 > 𝐴o t34
Therefore, the reinforcement for flexural is, ∅12 @ 250 𝑚𝑚 𝐶·𝐶
Design of Box Culvert
49
Chapter Four
Results and Discussion
o Shrinkage and temperature reinforcement
The required area of steel for shrinkage and temperature is specified by (ACI –
Table 24.4.3.2) as: 𝐴o t34 =
0.0018𝑥420
𝐴𝑔 ≥ 0.0014𝐴𝑔
𝑓¬
Which is equal to the flexural area of steel. Therefore: +
𝐴o t34 = 450 𝑚𝑚 ·𝑚
𝑀𝑎𝑥 𝑠𝑝𝑎𝑐𝑖𝑛𝑔 (𝑆ti¸ ) = 5ℎ ≤ 450𝑚𝑚
– 𝐴𝐶𝐼 (7.7.6.2.1)
= 5𝑥250 ≤ 450𝑚𝑚
= 1250 ≤ 450𝑚𝑚
𝑆ti¸ = 450 𝑚𝑚⁄𝑚
+
Use ∅12 @ 250 𝑚𝑚 𝐶·𝐶 , which will provide 𝐴o = 482 𝑚𝑚 ·𝑚 > 𝐴o t34
Therefore, the reinforcement for shrinkage and temperature is, ∅12 @ 250 𝑚𝑚
Design of Box Culvert
50
Chapter Four
Results and Discussion
v Analysis using ETABS software
One of the main objectives of selecting a numerical model is to reduce the
infinite degrees of freedom system to a limited degree of freedom, which will
represent the significant physical behavior of the system. The theoretical study
presented in this chapter consists of idealization of the physical system under
consideration to make it amenable to treat numerically followed by selection of
proper numerical technique and mathematical formulation of the specific
problems.
The box culvert was analyzed using ETABS software and the obtained
results are as following: Table (4-8). ETABS results.
Reinforcement/𝒎
Walls
Top slab
Floor slab
Flexural
Shrinkage and
temperature
∅𝟏𝟔 @ 𝟑𝟎𝟎 mm (EF/V)
∅𝟏𝟐 @ 𝟐𝟓𝟎 𝒎𝒎
∅𝟏𝟐 @ 𝟐𝟓𝟎 𝒎𝒎
∅𝟏𝟐 @ 𝟐𝟓𝟎 𝒎𝒎 (EF/H) ∅𝟏𝟐 @ 𝟐𝟓𝟎 𝒎𝒎
∅𝟏𝟐 @ 𝟐𝟓𝟎 𝒎𝒎
Therefore, the obtained results resemble the calculated results. The results in table
(4-8) is used as the designed reinforcement.
Design of Box Culvert
51
Chapter Four
Results and Discussion
4-3 Reinforcement Details
Figure (4-10). Typical slab reinforcement.
Figure (4-11). Section A-A reinforcement details.
Design of Box Culvert
52
Chapter Five
Conclusions and Recommendations
Chapter Five
Conclusions & Recommendations
Chapter Five
Conclusions & Recommendations
5-1 Conclusions
The dimensions of box culvert were obtained from the hydraulic design. The
box culvert designed as a two cells culvert with a total length of 27 m and total
width of 3.15 m. The span for each cell is 1.2 m measured from face of the
supports. The invert of the box culvert is 0.2m downward from the bottom of the
main drain (MD-A). Conveyance condition case 4 gave the minimum head losses
as required.
The box culvert structural elements are top slab, floor slab, two exterior side
walls and one interior wall. The box culvert structural design carried out for the
maximum bending moment and shear force in each structural element.
The design was analyzed by ETABS software which gave a resemble results to
the hand calculated results. The used reinforcements are: ¨ ∅16 @ 300 𝑚𝑚 𝐶*𝐶 (𝐸𝐹 ⁄𝑉 ) 𝑎𝑛𝑑 ∅12 @ 250 𝑚𝑚 𝐶*𝐶 (𝐸𝐹 ⁄𝐻 )
for
the walls.
¨ ∅12 @ 250 𝑚𝑚 𝐶*𝐶 𝑎𝑡 𝑡𝑜𝑝 𝑎𝑛𝑑 𝑏𝑜𝑡𝑡𝑜𝑚 for top and floor slabs.
5-2 Recommendations
For inlet and outlet transition, the suggestion is to use rocks as a transition
for both the inlet and outlet due to the ease of execution. However, a suitable
design is recommended for choosing the adequate transition.
Using ETABS software for the design is helpful and saves a lot of time. However,
results must be checked for some criteria such as the minimum reinforcement
ratio (𝜌<=> ) which is specified by the design code.
Design of Box Culvert
53
References
References
1. American Association of State Highway and Transportation Officials, (2007).
“AASHTO LRFD Bridge Design Specifications SI Units 4th Edition”.
American Association of State Highway and Transportation Officials, 444
North Capitol Street, New York. Pp 1590.
2. American Concrete Institute, (2014). “Building Code Requirements for
Structural Concrete (ACI318M-14) and Commentary (ACI 318RM-14)”.
American Concrete Institute, P.O. Box 9094, Farmington Hills, Michigan. PP
519.
3. Bolden, J., Carroll, T., Muller, D., Snoke, D., (2016). “Structural Management
Unit Manual”. North Carolina Department of Transportation (NCDOT), North
Carolina. PP 180.
4. Chandrakant, L. A. and Malgonda, P. V. (2014), “Finite element analysis of
box culvert”, International Journal of Advanced Technology in Engineering
and Science, Volume No.02, Issue No. 06.
5. Civil Engineering Portal, (2012). “What are the differences in applications
between
pipe
culverts
and
box
culverts?”,
URL:
http://www.engineeringcivil.com/what-are-the-differences-in-applicationsbetween-pipe-culverts-and-box-culverts.html, Last visit was on 4/11/2017.
6. Creamer, P. A., (2007). “Culvert Hydraulics: Basic Principle”, Professional
Development Series (PDF), CONTECH Bridge Solutions Inc., Ohio.
Design of Box Culvert
7. Garg, A. K., (2007). “Experimental and Finite Element Based Investigations of
Shear Behavior of Reinforced Concrete Box Culverts”, PhD Dissertation,
Department of Civil Engineering, The University of Texas at Arlington.
8. Kailan, A. L. (2015). “Hydraulic structures”, Water Resources Engineering
lectures, Chapter 5, Department of Civil Engineering, Al-Mansour University
College, Iraq.
9. Kilgore, R. T., Morris, J. L., Schall, J. D., Thompson, P. L. and Zerges, S. M.
(2012). “Hydraulic Design of Highway Culverts Third Edition”. Federal
Highway Administration (FHWA), Washington, D.C. PP 326.
10. Kumar, Y. V., Srinivas, C. (2015). “Analysis and Design of Box Culvert by
Using Computational Methods”, International Journal of Engineering and
Science Research, 5(7): 850-861.
11. Kim, K. and Yoo, C. (2002), “Design loading for deeply buried box culverts”,
Highway Research Center Auburn University, Auburn University, Alabama.
12. Oyenuga, V. O. (2001), “Fundamentals of Reinforced Concrete Design”.
Agros Limited, Lagos, Nigeria. PP415.
13. Pencol Engineering Consultants. (1983). “Design Manual for Irrigation and
Drainage”, Ministry of Irrigation, Iraq. PP 530.
14. Wikipedia,
The
Free
Encyclopedia.
(2004).
“Culverts”,
https://en.wikipedia.org/wiki/Culvert, Last visit was on 27/12/2017.
Design of Box Culvert
URL:
Appendix
Top slab shear values by ETABS.
Top slab bending moments by ETABS.
Top slab reinforcement by ETABS.
Bottom slab shear values by ETABS.
Bottom slab bending moments by ETABS.
Bottom slab reinforcement by ETABS.
Exterior wall moments by ETABS.
Exterior wall shear values by ETABS.
12 @ 250 mm
16 @ 300 mm
Typical wall reinforcement by ETABS.
Typical wall reinforcement layout by ETABS.
12 @ 250 mm
16 @ 300 mm
Section A-A of wall reinforcement.
3d reinforcement cage by ETABS.
Box culvert moments by ETABS.
Box culvert resultant shear by ETABS.
Box culvert displacement value by ETABS.
‫اﻟﺨﻼﺻﺔ‬
‫ﻋﻨﺪﻣﺎ ﯾﻜﻮن ﻣﻄﻠﻮب ان ﯾﺸﯿﺪ طﺮﯾﻖ ﯾﺘﻘﺎطﻊ ﻣﻊ ﺟﺮﯾﺎن اﻟﻤﯿﺎه ﻓﻲ ﻣﺠﺮى طﺒﯿﻌﻲ او ﻗﻨﺎة ﻣﺎﺋﯿﺔ‪،‬‬
‫ﺗﻜﻮن اﻟﻤﺸﻜﻠﺔ اﻟﺮﺋﯿﺴﯿﺔ ﻓﻲ ﻛﯿﻔﯿﺔ اﻟﺤﻔﺎظ ﻋﻠﻰ ﺟﺮﯾﺎن اﻟﻤﯿﺎه دون أي ﯾﺸﻜﻞ أي ﺧﻄﻮرة ﻋﻠﻰ اﻟﻄﺮﯾﻖ‬
‫او اﻟﻤﺮﻛﺒﺎت اﻟﻲ ﺗﻤﺮ ﻋﻠﻰ اﻟﻄﺮﯾﻖ ﺑﺴﺒﺐ ارﺗﻔﺎع ﻣﻨﺴﻮب اﻟﻤﯿﺎه ﻋﻨﺪ ﺣﺪوث ﻓﯿﻀﺎن ﻓﻲ ﻣﻮﺳﻢ‬
‫اﻻﻣﻄﺎر او ﻛﻤﯿﺔ اﻟﺘﺼﺎرﯾﻒ ﻓﻲ اﻟﻘﻨﺎة ﺗﻜﻮن أﻛﺒﺮ ﻣﻦ اﻟﻤﺼﻤﻤﺔ ﻟﺘﺤﻤﻠﮭﺎ‪ .‬ﻟﮭﺬا اﻟﻐﺮض‪ ،‬ﯾﺠﺐ ﺗﻨﻔﯿﺬ‬
‫ﻗﻨﻄﺮة ﻋﻨﺪ ﻣﻜﺎن اﻟﺘﻘﺎطﻊ‪ .‬اﻟﻘﻨﻄﺮة ھﻲ ﻣﻨﺸﺂ ﻣﺼﻤﻢ ﻟﯿﺴﻤﺢ ﺑﻤﺮور اﻟﻤﯿﺎه ﻣﻦ ﺧﻼﻟﮭﺎ‪ .‬ﯾﻨﻄﻠﺐ اﻟﺘﺼﻤﯿﻢ‬
‫دراﺳﺔ ﻣﻦ اﻟﻨﻮاﺣﻲ اﻟﮭﯿﺪروﻟﻮﺟﯿﺔ‪ ،‬اﻻﻧﺸﺎﺋﯿﺔ وطﺒﯿﻌﺔ اﻷرض‪.‬‬
‫اﻟﻤﻄﻠﻮب ھﻮ ﺗﺼﻤﯿﻢ ﻗﻨﻄﺮة ﺻﻨﺪوﻗﺔ ﻓﻲ ﻣﺸﺮوع ﻛﻮت ‪ -‬ﺑﺘﯿﺮه ﻹرواﺋﻲ ﻋﻨﺪ ﺗﻘﺎطﻊ اﻟﻤﺒﺰل‬
‫اﻟﺮﺋﯿﺴﻲ )م‪.‬ر – أ( ﻣﻊ طﺮﯾﻖ اﻟﺪﺟﯿﻠﻲ اﻟﻤﻌﺒﺪ‪ .‬اﻟﺘﺼﻤﯿﻢ ﺳﯿﻜﻮن ﻋﻠﻰ اﻷﺳﺲ اﻟﮭﯿﺪروﻟﻮﺟﯿﺔ‬
‫واﻻﻧﺸﺎﺋﯿﺔ‪.‬‬
‫اﻟﺘﺼﻤﯿﻢ اﻟﮭﯿﺪروﻟﻮﺟﻲ ﺳﯿﻜﻮن ﻋﻠﻰ أﺳﺎس اﻟﻤﻌﻠﻮﻣﺎت اﻟﮭﯿﺪروﻟﻮﺟﯿﺔ اﻟﻤﺴﺘﺤﻠﺔ ﻟﻠﻤﻨﻄﻘﺔ‪ .‬اﺑﻌﺎد‬
‫اﻟﻘﻨﻄﺮة اﻟﺼﻨﺪوﻗﯿﺔ ﯾﺘﻢ ﺣﺴﺎﺑﮭﺎ ﻣﻦ ﺧﻼل اﻟﺘﺼﻤﯿﻢ اﻟﮭﯿﺪروﻟﻮﺟﻲ‪ .‬اﻟﻘﻨﻄﺮة اﻟﺼﻨﺪوﻗﯿﺔ اﻟﺘﻲ ﺗﺼﻢ‬
‫ﺣﺴﺎﺑﮭﺎ ھﻲ ذات ﺧﻠﯿﺘﯿﻦ ﻣﻊ طﻮل ﻛﻠﻲ ﯾﺴﺎوي ‪٢٧‬م وﻋﺮض ﻛﻠﻲ ‪٣.١٤‬م‪.‬‬
‫ﯾﻌﺮف اﻟﺘﺼﻤﯿﻢ اﻻﻧﺸﺎﺋﻲ ﻋﻠﻰ اﻧﮫ اﺳﺘﻘﺮارﯾﮫ واﻣﺎن اﻟﻤﻨﺸﺄ ﻣﻦ اﻻﺣﻤﺎل اﻟﻤﺴﻠﻄﺔ‪ .‬ﺑﻌﺪ اﻟﺘﺼﻤﯿﻢ‬
‫ﻋﻠﻰ وﻓﻖ اﻗﺼﻰ ﻋﺰم اﻧﺤﺎء وﻗﻮى ﻗﺺ‪ ،‬ﺗﻢ ﺣﺴﺎب ﺣﺪﯾﺪ اﻟﺘﺴﻠﯿﺢ اﻟﻤﻄﻠﻮب ﺣﯿﺚ ﺳﯿﺴﺘﺨﺪم ق‪ ١٦‬ﻣﻠﻢ‬
‫ﻛﻞ ‪ ٣٠٠‬ﻣﻠﻢ م‪/‬م )ﻟﻜﻞ وﺟﮫ ﻋﺎﻣﻮدي( و ق‪ ١٢‬ﻣﻠﻢ ﻛﻞ ‪ ٢٥٠‬ﻣﻠﻢ م‪/‬م )ﻟﻜﻞ وﺟﮫ اﻓﻘﻲ( ﻟﻠﺠﺪران و‬
‫ق‪ ١٢‬ﻣﻠﻢ م‪/‬م ﻓﻲ اﻷﻋﻠﻰ و اﻷﺳﻔﻞ ﻟﻜﻞ ﻣﻦ اﻟﺴﻘﻒ اﻟﻌﻠﻮي و اﻟﺴﻔﻠﻲ‪.‬‬
‫ﺟﻤﮭﻮرﯾﺔ اﻟﻌﺮاق‬
‫ﻛﻠﯿﺔ اﻟﻤﻨﺼﻮر اﻟﺠﺎﻣﻌﺔ‬
‫ﻗﺴﻢ اﻟﮭﻨﺪﺳﺔ اﻟﻤﺪﻧﯿﺔ‬
‫ﻣﺸﺮوع ﺗﺨﺮج‬
‫اﻟﻌﺎم اﻟﺪراﺳﻲ‬
‫‪2017-2018‬‬
‫ﺗﺼﻤﯿﻢ ﻗﻨﻄﺮة ﺻﻨﺪوﻗﯿﺔ‬
‫ھﺬا اﻟﻤﺸﺮوع ھﻮ ﺟﺰء ﻣﻦ ﻣﺘﻄﻠﺒﺎت اﻟﺤﺼﻮل ﻋﻠﻰ ﺷﮭﺎدة اﻟﺒﻜﺎﻟﻮرﯾﻮس ﻓﻲ‬
‫اﻟﮭﻨﺪﺳﺔ اﻟﻤﺪﻧﯿﺔ‬
‫اﻋﺪاد‬
‫ﻋﻠﻲ ﻣﮭﺪي ﻣﺤﻤﺪ‬
‫اﺣﻤﺪ ﻧﺎﻓﻊ ﻣﺤﻤﺪ‬
‫ﻣﺤﻤﺪ ﻋﺒﺪ اﻷﻣﯿﺮ ﺣﺴﯿﻦ‬
‫ﻣﻌﺘﺰ ﻧﺬﯾﺮ ﻣﺎﺟﺪ‬
‫اﺷﺮاف‬
‫د‪ .‬ﻋﻼ ﻋﺎدل ﻗﺎﺳﻢ‬
‫‪ 2018‬م‬
‫ﺑﻐﺪاد‬
‫ھـ ‪1439‬‬
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