Sample Thesis

Anallysis and Deesign of RCC C Box Culvvert using WSM W & LSM M A DISS SERTATION N ENT SUBMIT TTED IN TH HE PARTIA AL FULFILM MENT OF REQUIREM R FOR THE T AWAR RD OF THE DEGREE OF O M MASTER O TECHNO OF OLOGY IN TRA ANSPORTA ATION ENG GINEERING G (Civill Engineering)

BY An nkit Singh (Roll No N – 31407115) Under the t guidancee of Dr. Praaveen Aggarrwal P Professor Civil Enginneering Depaartment N National Insstitute of Tecchnology Kuurukshetra

NATION NAL INSTIITUTE OF TECHNOL LGY KURUKS SHETRA-136119

J June 2016

CERTIFICATE This is to certify that the dissertation entitled “Analysis and Design of RCC Box Culvert using WSM & LSM” in the partial fulfillment of the requirements for the award of the Degree of Master of Technology in Transportation Engineering (Civil Engineering) National Institute of Technology Kurukshetra is an authentic record of my own work carried out during a period of July 2015 to June 2016 under the supervision and guidance of Dr. Praveen Aggarwal, Professor of Civil Engineering Department National Institute of Technology Kurukshetra-136119. The matter presented in this dissertation has not been submitted by me for the award of any other degree of this institute or any other institute.

Ankit Singh Roll No.3140715

This is to certify that the above statement made by the candidate is correct to the best of my knowledge.

Date: Place – Kurukshetra

Dr. Praveen Aggarwal Professor Civil Engineering Department National Institute of Technology Kurukshetra - 136119

(i)

ACKNOWLEDGMENTS I am in debt to a number of people who helped me throughout the course of this dissertation. First of all I would like to thank Dr. Praveen Aggarwal my thesis supervisor for all of the help, hard work and patience that they put into this dissertation. I have learned a lot from them over the last couple of years and I am very lucky to have them as my thesis advisors. I am highly indebted to Dr. S.K. Madan head of the Department of Civil Engineering National Institute of Technology Kurukshetra for his administrative help and all kind of support from department. My thanks are also due the faculty and staff members of Civil Engineering Department for their help and encouragement throughout the dissertation work. Thank you to my parents who have supported me from the beginning. You are truly a blessing in my life and I would not be here without your constant Love and support and also I would like to say thank you to my friends and classmates who helped me every time whenever I needed. Finally I would like to thank my GOD who has blessed me and remained faithful throughout.

Ankit Singh Roll No - 3140715

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TABLE OF CONTENTS CERTIFICATE

[i]

ACKNOWLEDGEMENT

[ii]

TABLE OF CONTENTS

[iii]

LIST OF FIGURES

[vi]

LIST OF TABLES

[viii]

LIST OF SYMBOLS OR ABBREVIATION

[ix]

ABSTRACT

[xi]

CHAPTER - 1 INTRODUCTION 1.1 GENERAL

1

1.2

TOPIC OF RESEARCH AND ITS IMPORTANCE

2

1.3

OBJECTIVES OF THE STUDY

2

1.4

SCOPE OF THE STUDY

2

1.5

PRESENTATION OF THE STUDY

3

CHAPTER - 2 LITERATURE REVIEW 2.1 GENERAL

4

2.2

BOX CULVERT

4

2.3

COMPONENTS OF BOX CULVERT

5

2.3.1

Top Slab

5

2.3.2

Bottom Slab

5

2.3.3

Side Walls

5

2.3.4

Cushion Load (If present)

5

2.4

2.5

LOADS OF BOX CULVERT

5

2.4.1

Concentrated Load

5

2.4.2 Uniform Distributed Load

6

2.4.3

Weight of Side Wall

6

2.4.4

Water Pressure from inside of Box Culvert

6

2.4.5

Earth Pressure on the Vertical Side Wall

6

2.4.6

Uniform Lateral Pressure on the Vertical Side Wall

6

ADVANTAGEOUS OF BOX CULVERT

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7

2.6

APPLICATION OF BOX CULVERT

7

2.7

AN OVERVIEW OF VARIOUS PAPERS

9

CHAPTER 3 STANDARDS SPECIFICATIONS 3.1 GENERAL

12

3.2

IRC LOADINGS

12

3.2.1

IRC Class 70R Loading

12

3.2.2 IRC Class AA Loading

14

3.2.3 IRC Class A and IRC Class B Loading

15

IMPACT EFFECT

16

3.3.1 for IRC Class A or IRC Class B Loading

16

3.3.2 for IRC Class 70R OR IRC Class AA Loading

16

3.4

EFFECTIVE WIDTH OF DISPERSION

16

3.5

EFFECTIVE LEGTH OF LOAD

17

3.6

REDUCTION IN THE LONGITUDINAL EFFECT FOR MORE THAN TWO

3.3

LANE TRAFFIC

17

3.7

WORKING STRESS METHOD (WSM)

18

3.8

LIMIT STATE METHOD (LSM)

21

CHAPTER 4 METHODOLOGY OF THE STUDY 4.1 ANALYSIS & DESIGN CONDITION OF BOX CULVERT

4.2

24

4.1.1

Case-1 Box Empty

24

4.1.2

Case-2 Box Full (With Live Load)

24

4.1.3

Case-3 Box Full (Without Live Load)

25

DESIGN LOAD OF BOX CULVERT

25

4.2.1. Top Slab Dead Load

25

4.2.2

Top Slab Live Load

25

4.2.3

Bottom Slab Dead Load

26

4.2.4

Bottom Slab Live Load

26

4.2.5

Earth Pressure due to Earth-fill on Side Wall [Dead Load]

27

4.2.6

Water Pressure from inside on Side Wall [Dead Load]

27

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4.2.7 Earth Pressure due to Live Load Surcharge on 4.2.8 4.3

Side Wall [Live Load]

28

Critical Load Combination

28

MANUAL ANALYSIS

30

4.3.1

30

Design Load Calculation

4.3.2 Design Moment Calculation

32

4.3.3

34

Distribution Factor

4.3.4 Design Moment

34

4.4

STAAD PRO ANALYSIS

34

4.5

FORMULAS USED FOR DESIGN BY WSM

35

4.6

FORMULAS USED FOR DESIGN BY LSM

36

4.7

SAMPLE PROBLEM

37

CHAPTER – 5 RESULT AND DISCUSSION 5.1 RESULTS OF ANALYSIS BY MS-EXCEL & STAAD PRO

64

5.2

DESIGN BY MS-EXCEL TOOL

64

5.2.1

Effect on Area of Steel in WSM and LSM Approach

64

5.2.2

Saving in Depth of Section in LSM over WSM with Constant Steel Area

5.3

67

DISCUSSION

70

CHAPTER – 6 CONCLUSIONS REFERENCES ANNEXURE 1.

Moment Analysis by STAAD Pro for IRC Class 70R Loading

75

2.

Moment Analysis by STAAD Pro for IRC Class A Loading

80

3.

Developed MS-Excel tool

85

3.1

Design showing saving in Steel with constant Section

88

3.2

Design showing saving in material with constant Area of Steel

92

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LIST OF FIGURES 1.

Figure 2.0 Schematic diagram of a RCC Box Culvert

4

2.

Figure 2.1 Multi-Celled Box

7

3.

Figure 2.2 Box Culvert at Intersection

8

4.

Figure 2.3 Box Culvert below a Railway Track

8

5.

Figure 2.4 Box Culvert at Cross Drainage

8

6.

Figure 3.0 IRC Class 70R Loading

13

7.

Figure 3.1 IRC Class AA Loading

14

8.

Figure 3.2 IRC Class A Loading and IRC Class B Loading

15

9.

Figure 4.0 Box Empty

24

10.

Figure 4.1 Box Full (With Live Load)

24

11.

Figure 4.2 Box Full (Without Live load)

25

12.

Figure 4.3 Top Slab dead load

25

13.

Figure 4.4 Top Slab live load

25

14.

Figure 4.5 Bottom Slab dead load

26

15.

Figure 4.6 Bottom Slab live load

26

16.

Figure 4.7 Side Fill Earth Pressure on Left

27

17.

Figure 4.8 Side Fill Earth Pressure on Right

27

18.

Figure 4.9 Water Pressure on Left

27

19.

Figure 5.0 Water Pressure on Right

27

20.

Figure 5.1 Live Load Surcharge on Left

28

21.

Figure 5.2 Live Load Surcharge on Right

28

22.

Figure 5.3 Critical Load Combination

28

23.

Figure 5.4 Load Combination [Box Full With Live]

29

24.

Figure 5.5 Load Combination [Box Full Without Live Load]

29

25.

Figure 5.6 Soil Base Pressure

31

26.

Figure 5.7 Box Culvert notations

37

27.

Figure 5.8 Wheel imprint of IRC Class 70R Loading

39

28.

Figure 5.9 Wheel imprint of IRC Class A Loading

41

29.

Figure 6.0 Saving in Steel using LSM approach over WSM for Fe415 Steel Grade

65

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30.

Figure 6.1 Saving in Steel using LSM approach over WSM for Fe500 Steel Grade

28.

66

Figure 6.2 Saving in Material using LSM approach over WSM for Fe415 Steel Grade

29.

68

Figure 6.3 Saving in Material using LSM approach over WSM for Fe500 Steel Grade

69

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LIST OF TABLES 1.

Table 3.0 Reduction in the longitudinal effect for more than 2 lane traffic

2.

17

Table 3.1 Permissible Shear Strength of Concrete τc as per Working Stress Method

3.

20

Table 3.2 Permissible Shear Strength of Concrete τc as per Limit State Method

23

4.

Table 4.0 Side Wall Load Calculation

31

5.

Table 4.1 Moment Calculation for Slab

32

6.

Table 4.2 Side Wall Moment Calculation

33

7.

Table 5.0 Design Moments by MS-Excel tool and STAAD.Pro

64

8.

Table 5.1 Saving in Steel using LSM approach over WSM for Fe415 Steel Grade

9.

65

Table 5.2 Saving in Steel using LSM approach over WSM for Fe500 Steel Grade

10.

66

Table 5.3 Saving in Material using LSM approach over WSM for Fe415 Steel Grade

11.

68

Table 5.4 Saving in Material using LSM approach over WSM for Fe500 Steel Grade

69

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LIST OF SYMBOLS OR ABBREVIATION IRC

Indian Road Congress

IS

Indian Standards

WSM

Working Stress Method

LSM

Limit State Method

Kn

Kilo Newton

M

Meter

MM

Mili Meter

K

Neutral Axis Factor

J

Lever Arm Factor

R

Moment of Resistance Factor

ℓ

Clear Span

h

Clear Height

L

Effective Span

H

Effective Height

σst

Steel Grade

σcbc

Concrete Grade

Ke.p.

Co-efficient of Earth Pressure at rest

M

Modular Ratio

tw.c.

Thickness of Wearing Course

tcu.

Total Cushion on top (If present)

ttop

Top Slab thickness

tbottom

Bottom Slab thickness

twall

Side Wall thickness

ԃconc

Unit Weight of Concrete

ԃsoil

Unit Weight of Earth-fill

ԃw

Unit Weight of Water

Ф

Angle of internal friction

FEM

Fixed End Moment

τc

Permissible Shear Stress in Concrete

τv

Shear Stress in Concrete

(ix)

d

Effective Depth

D

Total Depth

Ast

Reinforcement Area

Mx

Moment of x Member

MU

Factored Moment of Resistance

V

Shear Force

VU

Factored Shear Force

p%

Percentage of Steel Area

W

Design Load for particular member of Box Culvert

(x)

ABSTRACT As per standard practice bridges (Short Span less than 6M) were designed by IRC: 6 – 2000 & IRC: 21 – 2000. Both the codes were based upon Working Stress Method. But IRC has revised IRC: 6 – 2000 as IRC: 6 – 2014 and published a new code IRC: 112 - 2011 for bridges design. These are based upon the Limit State Method. In the present study using these codes a RCC Box Culvert of 4M span & height is analyzed & designed with WSM approach as well as LSM approach. A MS – Excel sheet is also developed by manual calculation for the same. Results of manual analysis, MS – Excel sheet & Staad Pro are compared for design the problem The Design based on both the approaches WSM & LSM are also compared & a parametric study is carried out by keeping Steel Grade as constant with different Grade of Concrete and finding the % reduction in Steel Reinforcement as well as % reduction in section dimensions due to LSM approach over WSM approach. This study will eventually comment on the design philosophy LSM & WSM regarding the design of RCC Box Culvert and discussed which one will perform better economically as well as structurally. The developed MS – Excel tool is user friendly, error free & fast for convenient-application for the RCC Box Culvert Design.

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CHAPTER – 1 INTRODUCTION 1.1

General A culvert is 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 made from RCC. 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, flat-bottomed, pear-shaped, and box-like constructions. The culvert type and shape selection is based on a number of factors which include requirements for hydraulic performance, limitation on upstream water surface elevation and roadway embankment height. Box culvert is one of the type of culvert that provide passage of traffic movement over an opening without closing of it and consisting a rectangular or square opening whose span and height of side walls is limited to 4m. It is suitable where the bearing capacity of soil is poor or discharge in the cross drainage structure is less. In such situation a box culvert is an ideal structure. The road level can be at top of box culvert or may be at some height due to earth fill or cushion above the box culvert.

1   

1.2

Topic of Research and its Importance The topic “Analysis and Design of RCC Box Culvert using WSM & LSM” has been selected for present study to compare the two design approaches. Box culvert is quite common cross drainage structure. In the present study a MS Excel sheet is developed for the analysis and design of RCC box culvert. With the help of this sheet user shall be better able to understand the design of box culvert by the two design approaches. An easy comparison of material economy is also possible with the developed excel sheet along with faster, error free, user friendly toll for the analysis and design of box culvert using both WSM as well as LSM approach.

1.3

Objectives of the Study Present study “Analysis and Design of RCC Box Culvert using WSM & LSM” aims at collecting information on suitability of LSM approach for design of RCC Box Culvert. In India till 2014 bridge design was based on the working stress method. Relevant IRC codes were IRC: 6 - 2000 & IRC: 21 – 2000. Recently Indian road congress has revised IRC: 6 and published a new code for bridge design. These new codes i.e. IRC: 6 - 2014 & IRC: 112 - 2011 are based on limit state method. The objectives of the study include. 1. To analyzed and design RCC Box Culvert with both WSM and LSM approach 2. To develop MS-Excel sheet for analysis and design of RCC Box Culvert using two approaches 3. To work out material economy by compared the results of two approaches

1.4

Scope of the study The study has been conducted on a RCC Box Culvert up to 4M span. MS – Excel tool is designed as per IRC: 6 – 2000 & IRC: 21 – 2000 and IRC: 6 – 2014 & IRC: 112 – 2011 as applicable for 1-Lane to 8-Lane carriageway. In the developed tool, provisions are made for IRC Class 70R and IRC Class A loading. The results of analysis and design obtained through developed excel sheet are compared and check by manual method and through STAAD Pro. 2 

 

In the present study a box culvert of 4M span on 2-lane road is analyzed and designed, other combinations may also be used. 1.5

Presentation of the study The work undertaken for the dissertation has been presented in six chapters. Chapter – 1 “INTRODUCTION” discusses the introduction of culvert, topic of research and its importance, objectives of study and scope of the study. Chapter – 2 “LITERATURE REVIEW” includes the Box Culvert introduction, Components of Box Culvert, Loads of Box Culvert, advantageous of Box Culvert, its different applications in transportation and overview of various papers. Chapter – 3 “STANDARDS SPECIFICATIONS” includes different standard suggested by IRC Indian Road Congress for analysis & designing of RCC Box Culvert. Some of standards that are cover in the study are as IRC Ladings, Impact Factor, Effective width of dispersion, effective length of load and WSM & LSM design philosophy introduction. Chapter – 4 “METHODOLOGY OF THE STUDY” describes the design load, design condition, basis of manual analysis & STAAD PRO analysis, WSM formulas used for design & LSM formulas used for design and sample problem. Chapter – 5 “RESULT AND DISCUSSION” describes and discusses the results as obtained using developed MS – Excel tool about the design of RCC Box Culvert based on WSM & LSM. This will show us that only changing the required input parameters we will see the whole change in the design philosophy automatically & can comment which one is better economically & structurally. Chapter – 6 “CONCLUSSIONS” In this chapter conclusion and scope for further research is discussed.

3   

CHAPTER – 2 LITERATURE REVIEW 2.1

General Bridges are provided at location of cross drainage structure. Depending upon the span, bridges are classified into three categories (I) Major Bridge (Span > 60M) (II) Minor Bridge (Span 6M to 60M) and (III) Culvert (Span < 6M). Depending upon the shape culverts can further be classified into (I) Slab Culvert (II) Box Culvert and (III) Pipe culvert. Normally Box culverts are provided for span up to 4.0M.

2.2

Box Culvert Box culvert is one of the type of culvert that provide passage of traffic movement over an opening without closing of it and consisting a rectangular or square opening whose span and height of side walls is limited to 4m. It is suitable where the bearing capacity of soil is low and discharge in the cross drainage structure is moderate. In such situation a box culvert is an ideal structure. The road level can be at top of box culvert or may be at some height due to earth fill or cushion above the box culvert (Figure 2.0). Box culverts are economical due to their rigidity and monolithic action and separate foundation are not required since the bottom slab resting directly on the soil, serves as raft slab. For small discharges, single celled box culvert is used and for large discharges, multi celled box culverts can be employed.

4   

Figure 2.0 Schematic diagram of a RCC Box Culvert

2.3

Components of Box Culvert Box Culvert is comprised of top slab, bottom slab and side walls. All three components are rigidly connected to each other so that they can form a monolithic RCC structure. The various parts of Box Culvert are discussed below.

2.3.1

Top Slab Top slab of Box Culvert forms the deck slab which will be in direct contact of moving traffic. Live Load makes the use of this top slab.

2.3.2

Bottom Slab Bottom slab of Box Culvert is in direct contact of soil and resting over it. It is act as a raft foundation over the soil and transmits the load to the earth surface.

2.3.3

Side Walls These are the wall held vertically and are in contact with earth-fill laterally to resist the earth pressure coming from the side fills. This is also resisting the water pressure from inside of Box Culvert if Box is full of water.

2.3.4

Cushion (If Present) If top of box culvert is subjected to some embankment. In this case the top of the top slab are not in direct contact of traffic. The load of this earth fill surcharge or embankment over the top of the top slab is called as cushion load. The cushion height is generally vary 1M to 3M.

2.4

Loads of Box Culvert All the parts of Box Culvert are subjected to the various loads. Their type and nature of action are as under.

2.4.1 Concentrated Load Top slab of box culvert forms the deck slab. We converted the concentrated wheel load into uniformly distributed load calculated by using expression. W=P

I .  

Where W = uniformly distributed load on the slab 5   

P = wheel load as per IRC recommendations beff. = effective width of dispersion ℓeff. = effective length of load I = impact factor as per IRC recommendations 2.4.2

Uniform distributed load The dead load of top slab or deck slab, wearing coat & weight of embankment or cushion (if present) is also considered to be uniformly distributed over the top slab and a uniform soil reaction will developed on the bottom slab.

2.4.3

Weight of Side Wall The weight of two side walls will be acting as a concentrated load and is also assumed to be produced a uniform soil reaction on the bottom slab.

2.4.4

Water pressure from inside of Box Culvert When box culvert is full with water, a water pressure from inside of wall is acting. The pressure distribution on the walls is assumed to be triangular with a maximum pressure intensity given by the expression. p = w h at the base Where w = density of water h = depth of flow

2.4.5

Earth pressure on the vertical Side Wall There is also pressure of side earth fill on the vertical side walls For computing the earth pressure on the side walls of box culvert we make the use of Rankine and Coulomb Theory.

2.4.6

Uniform lateral pressure on the vertical Side Wall The live load acting on the top slab of box culvert also produces a uniform lateral pressure on the side walls to some extent up to a particular height of side walls.

6   

2.5

Advantageous of Box Culvert

2.5.1

The horizontal & vertical member of box culvert are made up of RCC slab that’s why we can say the box culvert is a monolithic & rigid frame structure and its operation of construction is very simple.

2.5.2

The conventional slab culvert will require the abutment while box culvert has no abutment. In such situation box culvert is an economical & ideal structure.

2.5.3

The superimposed load as well as the dead load of box culvert is distributed uniformly over a wider area because bottom slab works as a raft foundation.

2.5.4

Box culvert makes the use of portion both below and above of top slab. Like above of top slab always use for movement of traffic and below of top slab may be used for traffic & cross drainage structure.

2.5.5

The problem of erosion & scouring of earth fill below a conventional slab culvert is almost completely reduced by the construction of box culvert.

2.6

Application of Box Culvert

2.6.1

If discharge in the drain is considerable then multi celled box culvert can be employed together monolithically (Figure 2.1).

Figure 2.1 Multi-Celled Box Culvert 7   

2.6.2

When a more important road cross to a less important road and

results in an

intersection. It is also used now days at location of intersection for facilitating the cross movement below another road (Figure 2.2).

Figure 2.2 Box Culvert at Intersection Location 2.6.3

In railway engineering also, where a railway line and a cross drainage structure intersect in such situation box culvert is now widely used RCC structure (Figure 2.3).

Figure 2.3 Box Culvert below a Railway Track 2.6.5

In case of cross drainage structure, if discharge is less a box culvert is the single RCC structure that can serve the required purpose if cross movement is to be provided (Figure 2.4).

8   

Figure 2.4 Box Culvert at Cross Drainage Structure

2.6.4

Most of the designers now prefer the box culvert over conventional slab culvert.

2.7

An Overview of various Papers A number of journals and research papers have been published in Indian & International journals as well as conferences on the similar study. These journals and papers are given various results, conclusion, formulas regarding the RCC Box Culvert. In the present study several of concept has been reviewed and used from them. The Literature Review of some of few of Indian & international journal and papers are discussed below: Sinha and Sharma (2009) [1] have done a study in which they analyzed & designed a RCC Box Culvert by manual and computer application. The study told that effective width method mainly applicable for the top slab (particularly for the box without cushion) and the design of box is covered by three load cases. The fourth situation when whole box is submerged under water, provide design moments are less than given by the three load cases hence need not to be considered. This study also told amount of required Steel Reinforcement is confirmed by the required depth of section. Kulkarni and Jirage (2011) [2] have done Comparative Study on Steel Angles as Tension Members Designed by Working Stress Method and Limit State Method. The design of tension member using Angles by Limit state method is economical over the working stress method which values for 12% to 54%. Zhu et al. (2012) [3] have study on optimal design of a Box Culvert under road and find with the reduction in the size of proposed box culvert structure, the self weight of the concrete structure is obviously reduced. Therefore, the requirement for the soil bearing capacity is decreased. As a result, the use of concrete is significantly reduced. As such, the optimal design is much more cost efficient. Solanki and Vakil (2013) [4] have done study on Comparative study for flexure design using IRC 112:2011 & IRC 21:2000. The study guides for flexure design for different combination of grade of concrete & steel. Shreedhar and Shreedhar (2013) [5] have conducted study on Design coefficients for single and two cell box culverts. The study aims on the loads 9 

 

considered for the analysis of box culverts are Dead load, Live load, Soil pressure on side walls, Surcharge due to live load, and Water pressure from inside. These includes Uniform distributed load, Weight of side walls, Water pressure from inside of culvert, Earth pressure on vertical side walls & Uniform lateral load on side walls. Varma (2014) [6] has done study on the working stress method and limit state method & in RCC chimney design and finds on comparison of working stress method and limit state method limit of collapse for chimney of height 70m. Result shows that Limit State method is much more economical than working stress method. Meshram and Pajgade (2014) [7] have done Comparative Study of Water Tank Using Limit State Method and Working Stress Method and obtained result shows that the steel quantity found more for a circular service reservoir design by WSM than that of LSM. The steel quantity found more for a square service reservoir design by WSM than that of LSM. Kolate et al. (2014) [8] have analyzed and design a RCC Box Culvert. The study said that box is designed for maximum moment for its concrete section and reinforcements. It is checked for shear at the critical section and if it exceeds permissible shear stress for the size of section; mix of concrete and percentage of reinforcements, the section has to be increased to bring shear stress within the permissible limit. Tom (2015) [9] has conducted their study on analysis and design of bridge and culvert. The study says that major classifications of vehicles considered as live load for design are Class 70R Wheeled adopted on all roads on which permanent bridges and culverts are constructed and they should also be checked for Class A Loading. Shreedhar (2015) [10] have done Comparative Study of Slab Culvert Design using IRC 112:2011 and IRC 21:2000 and finds in limit state method of design the utilization capacity of limiting moment will increase with increasing span which is up to 65%.

10   

Kumar and Srinivas (2015) [11] have conducted study on analysis and design of box culvert by using computational methods. This study tells that earth can exert pressure as active and passive. Minimum is active and maximum is passive earth pressure and the median is rest. The coefficient of earth pressure is calculated as shown below and the angle of repose is taken as 30⁰. Earth Pressure due to Side earth from lateral direction is calculated as under.   Where

. .

= Unit Weight of Soil

Ke.p. = Earth Pressure Coefficient Height of wall Surcharge is calculated as 1.2m height of soil rest on both sides of the box culvert. Earth Pressure due to Surcharge from top and live load effect on side walls is calculated as under.   Where

. .

1.2

= Unit Weight of Soil

Ke.p. = Earth Pressure Coefficient As per LFRD (Load and Resistance Factor Design) 2013 clause 3.11.5.2-1 earth pressure coefficient is equal to Ke.p. = 1-Sin (Ф). Where Ф = internal friction angle of soil Jha et al. (2015) [12] have done Comparative Study of RCC Slab Bridge by Working Stress (IRC: 21-2000) and Limit State (IRC: 112-2011) and finds the thickness of slab was 500mm for WSM which was reduced to 400mm for both carriageways still there is about 20% saving in amount of concrete and 5-10% saving in amount of reinforcement for LSM i.e. LSM is considerably economical design compared to WSM.

11   

CHAPTER – 3 STATNDARDS SPECIFICATIONS

3.1

General Indian Road Congress has defined various standards for the analysis and design of bridges. Indian Road Congress published various codes of design and revised them with the passage of time. Recently Indian Road Congress revised IRC: 6 2000 as IRC: 6 - 2014 & published a new code for bridge design IRC: 112 – 2011. Both are based on the Limit State method. These two newly published codes replaced the IRC: 6 – 2000 & IRC: 21 – 2000. They were used for bridge design based on the Working Stress Method.

3.2

IRC Loadings There are currently 4 types of IRC loading as per IRC: 6 - 2014 which are considered as Live Load for Bridge design.

3.2.1 IRC Class 70R Loading This loading is recently introduced in IRC: 6 - 2014. It consist the tracked loading as well as wheeled loading. We can say it is the advanced version of IRC Class AA loading (IRC: 6 – 2000). This loading has the highest magnitude in respect of all other IRC loadings. This loading is generally used for construction of bridges in industrial area and military area. The maximum load of a single wheel in case of IRC Class 70R loading is 350Kn. It is different from IRC class AA loading in longitudinal length of load which is 4.57M (Figure 3.0).

12   

Figure 3.0 IR RC Class 700R Loadingg 13   

3..2.2

IRC Class C AA Looading This loading l described by thhe IRC: 6 - 2000 for bridge design based onn the Working Stress Method. M Beffore introduccing of IRC C Class 70R loading thiss had the hiighest magnnitude. Beforre introducinng IRC Classs 70R Loadding this loaading was considered c f design of for o bridges inn Military area, a Industrrial area and for highw ways. In the same mannner of IRC Class 70R loading thee IRC Classs AA loadin ng also had the maximuum load forr single wheeel as 350Knn & longituudinal length h of load as 3.6M 3 (Figurre 3.1).

14   

Figgure 3.1 IRC C Class AA Loading

3..2.3

IRC Class C A and IRC Class B loading Thesee two loadingg is considerred as lighterr loading in comparison to the IRC Class C 70R & IRC Class AA loadingg. These loadding are connsidered for the t bridge design d of rural area or wee can say forr timber briddges. The maximum load of single wheel w for IR RC Class A loading l is 114Kn and foor IRC Class B loading is 68Kn (Fiigure 3.2).

15   

Figure F 3.2 IR RC Class A Loading an nd IRC Class B Loadin ng

3.3

Impact Effect In order to considered the effect of increase in stresses due to the dynamic action. Impact allowance is made as per the IRC codal provision. It is equivalent to the part of live load. It is taken into account to counter act the impact effect due to live load. Impact factor suggested by IRC: 6 - 2014 are follows.

3.3.1 for IRC Class A or IRC Class B Loading I= Where I = impact factor A = constant 4.5 for RCC bridges & 9.0 for steel bridges B = constant 6 for RCC bridges & 13.5 for steel bridges L = effective span of bridge. 3.3.2

for IRC Class 70R or IRC Class AA Loading For RCC bridges designed for tracked vehicle 25% for span up to 5M and linearly reducing to 10% for span of 9M and for spans greater than 9M it is 10% up to a length of 40m. For RCC bridges designed for wheeled vehicle 25% for spans up to 12M and in accordance with the curve for spans exceeds to 12M.

3.4

Effective width of dispersion The concentrated load on the bridge is not directly taken by the area exactly below the load. It is taken by the some effective area whose dispersion perpendicular to the span direction is known as the effective width of dispersion. Effective width of dispersion is calculated as per IRC clause B3.2 of IRC: 112 2011 only when span is supported on two apposite edges or along four edges when the span length is too more. Effective width of dispersion for one wheel is given by the following expression in the perpendicular direction of traffic movement. beff. = α x (1- [ ]) + bw L

Where beff. = effective width of dispersion 16   

B

α = a constant depends upon [ ] ratio L

B = lane width L = effective span x = distance of center of gravity of load from the nearest support. bw = width of concentrated area of load bw = width of tyre + 2(thickness of wearing course)

3.5

Effective length of load In the same manner of effective width of dispersion the effective length of load for one wheel is given by the following expression along the direction of traffic movement as per IRC clause B3.3 of IRC: 112 – 2011. ℓeff. = length of load + 2(thickness of top slab + thickness of wearing course) ℓeff. = length of load + 2 (ttop + tw.c.) Where ℓeff = effective length of load ttop = top slab thickness tw.c = wearing coat thickness

3.6

Reduction in the longitudinal effect for more than two lane traffic Reduction in longitudinal effect on bridges having more than two traffic lanes due to the low probability that all lanes will be subjected to the characteristic load simultaneously shall be in accordance as per IRC clause 205 of IRC: 6 –

2014

(Table 3.0). Table 3.0 Reduction in the longitudinal effect for more than two lane traffic Number of lanes

Reduction in Longitudinal Effect

Two lanes

No reduction

Three lanes

10% reduction

Four lanes and more than four lanes

20% reduction

17   

3.7

Working Stress Method (WSM) This method is also called as the Modular Ratio Method or Centroidal Axis Method. As we know bridge structure is one of the massive structures and it is subjected to the number of lives that will use in its service period so designing of bridge will be very important for safety purpose. Working Stress Method is also the one of the very first design philosophy for every RCC structure design. The IRC codes for above philosophy were IRC: 6 - 2000 and IRC: 212000. Both based on WSM and for shear criterion IS: 456 – 2000 “Plain and Reinforced Concrete- code of practice (fourth revision)” is also used. Basis of WSM 9 A section prior to loading will be remains same as that of without loading. It means the neutral axis remain straight before bending and after bending. 9 All tensile stresses are taken by only steel and concrete will not take any tensile stresses. 9 In tension area concrete is completely neglected and all tensile stresses are considered to be taken by only steel. 9 This analysis is called as Cracked Section Analysis. A concrete section is considered cracked section if maximum tensile stress developed in concrete is more than the fcr (flexure tensile strength of concrete) and which is very less in comparison to σst value of steel that’s why we neglect the concrete area in tension. 9 The stress strain relation for steel and concrete are straight line within working load. 9 Modular ratio is the ratio of young’s modulus of steel to young’s modulus of concrete or also the ratio of stress in steel to stress in concrete. 9 Un-cracked section- when cracking moment is less than moment that will consider for design of section. i.e. ft< fcr then consider entire area of concrete area M

and stress at any section f = 

 I

Y

9 Cracked section- when cracking moment is more than the moment that will consider for design of section. i.e. ft > fcr then neglect concrete area on tension side and all tensile stresses are taken by steel only.

18   

Formulas used for design by WSM •

Effective Depth required d M

9 d=√

9 Where M = design moment 9 R = moment of resistance factor 9 b = width of section 9 R=

σcbc j k

9 k = neutral axis factor σ

9 k= 

   σ

σ

9 σst = permissible stress in steel 9 j = lever arm factor 9 j = 1•

Area of Steel Reinforcement Ast 9 Ast =

•

M  σ

Check for Shear will be done same as for all parts top slab, bottom slab & side walls

•

Shear Force at effective depth from face of wall V 9 V = 

•

 

 

 

   

 

   

 

Shear Stress τv  

9 τv = •

   

   

 

 

 

   

 

Steel percentage p 9 p=

A  

19   

3.7.1

Permissible Shear Strength of Concrete τc as Per Working Stress Method (Table 3.1). The permissible shear stress in concrete by Working Stress Method is given by clause table 23 of IS: 456 – 2000 are as follows.

Table 3.1 Permissible Shear Strength of Concrete τc as per Working Stress Method Concrete Grade P  

A  

M 15

M2 0

M2 5

M3 0

M35

M4Oandabov e

≤0.15

0.18

0.18

0.19

0.20

0.20

0.20

0.25

0.22

0.22

0.23

0.23

0.23

0.23

0.50

0.29

0.30

0.31

0.31

0.31

0.32

0.75

0.34

0.35

0.36

0.37

0.37

0.38

1.00

0.37

0.39

0.40

0.41

0.42

0.42

1.25

0.40

0.42

0.44

0.45

0.45

0.46

1.50

0.42

0.45

0.46

0.48

0.49

0.49

1.75

0.44

0.47.

0.49

0.50

0.52

0.52

2.00

0.44

0.49

0.51

0.53

0.54

0.55

2.25

0.44

0.51

0.53

0.55

0.56

0.57

2.50

0.44

0.51

0.55

0.57

0.58

0.60

2.75

0.44

0.51

0.56

0.58

0.60

0.62

3.00

0.44

0.51

0.57

0.60

0.62

0.63

>3.00

0.44

0.51

0.57

0.62

0.63

0.60

20   

3.8

Limit State Method (LSM) The earlier design method includes the Working Stress Method (WSM). WSM is based on the SERVICE LOADS. However LSM takes into account the safety at ultimate load and serviceability at service loads. LSM employs different safety factors at ultimate loads and service loads. These multiple safety factors are based on probabilistic approach with separate approaches for each type of failure, type of materials and types of load. Limit State-limit state is the state of “about to collapse” or “impending failure” beyond which, the structure is not of any practical use i.e. either the structure collapses or becomes unserviceable. In LSM two types of limit states are defined which are. 9 Limit State of Collapse- This limit state deals with the strength of the structure in terms of collapse, overturning, sliding, buckling etc. 9 Limit State of Serviceability-This limit state deal with the deformation of the structure to such an extent that the structure becomes unserviceable due to excessive deflection, cracks, vibration, leakage etc. Various limit states of serviceability are: [1] Deflection [2] Excessive vibrations [3] Corrosion [4] Cracking (Do not consider the tensile strength of concrete). This is the currently using design philosophy of Bridge design that has been recently came into existence particularly for RCC bridge design. The IRC codes for above philosophy are IRC: 6 - 2014 and IRC: 112- 2011. Both based on LSM and for shear criterion IS: 456 – 2000 “Plain and Reinforced Concrete- code of practice (fourth revision)” is also used. Basis of LSM 9 Prior to loading a section will always be remain same as without loading. That is neutral axis have no changes itself. 9 The highest strain at last compressed fiber in case of compression bending is 0.0035. 9 Strength of concrete is considered to be 0.67fck and a partial safety factor

mc

=

1.5 also applied to the above value that is 0.45fck is used for design. 21   

9 Strength in tension of concrete is neglected because of all stresses in tension are taking by the steel i.e. cracked section analysis. 9 Partial safety factor of

ms =

1.15 is applied for the steel i.e. design strength value

is 0.87fy of steel. 9 Strain that is maximum in tension at the time of collapse should not be lesser of .

0.002

E

 .

Formulas used for design by LSM •

Effective Depth required d

9 d=√

M

9 Where Mu = factored design moment 9 R = moment of resistance factor 9 b = width of section 9 R = 0.36 fck j k 9 k = Neutral axis factor 9 k=

.

9 fck = characteristics strength of concrete 9 fy = yield strength or characteristics strength of steel 9 j = lever arm factor 9 j = 1- 0.42k •

Area of Steel Reinforcement Ast

9 Ast=   •

M .

Check for Shear will be done same as for all parts top slab, bottom slab & side walls

•

Shear force at effective depth from face of wall Vu

9 Vu = 1.5V =   •

.

 

 

 

 

 

 

 

 

Shear Stress τvu

9 τvu =

 

   

 

 

 

   

 

22   

•

Steel Percentage p A

9 p=

3.8.1

 

Permissible Shear Strength of Concrete τc as Per Limit State Method (Table 3.2) The permissible shear stress in concrete by Working Stress Method is given by clause table 19 of IS: 456 – 2000 are as follows.

Table 3.2 Permissible Shear Strength of Concrete τc as per Limit State Method

p=

Concrete Grade

A  

M 15

M20

M25

M30

M35

M40 and above

≤0.15

0.28

0.28

0.29

0.29

0.29

0.30

0.25

0.35

0.36

0.36

0.37

0.37

0.38

0.50

0.46

0.48

0.49

0.5

0.5

0.51

0.75

0.54

0.56

0.57

0.59

0.59

0.60

1.00

0.6

0.62

0.64

0.66

0.67

0.68

1.25

0.64

0.67

0.70

0.71

0.73

0.74

1.50

0.68

0.72

0.74

0.76

0.78

0.79

1.75

0.71

0.75

0.78

0.8

0.82

0.84

2.00

0.71

0.79

0.82

0.84

0.86

0.88

2.25

0.71

0.81

0.85

0.88

0.90

0.92

2.50

0.71

0.82

0.88

0.91

0.93

0.95

2.75

0.7 1

0.82

0.90

0.94

O.96

0.98

3.00

0.71

0.82

0.92

0.96

0.99

1.01

>3.00

0.71

0.82

0.92

0.96

0.99

1.01

23   

CHAPTER – 4 METHODOLOGY OF THE STUDY 4.1

Analysis & Design Condition of box culvert Box culvert is treated as a Rigid Frame that’s why The Moment Distribution Method is generally adopted for distribution & determination of final moments at the joints of frames or slabs. The box culvert is analysis & designed for following critical loading conditions.

4.1.1

Case-1 Box Empty In such situation box culvert is subjected to the Live Load, Dead Load, Earth Pressure from outside, lateral pressure due to Live Load and No Water Pressure from inside of Box (Figure 4.0).

Figure 4.0 Box Empty

4.1.2

Case-2 Box Full (With Live Load) In such situation box culvert is subjected to the Live Load, Dead Load, earth pressure from outside, lateral pressure due to Live Load and water Pressure from inside of Box (Figure 4.1).

Figure 4.1 Box Full (With Live Load)

24   

4.1.3

Case-3 Box Full (Without Live Load) It is the advanced case of Box Full. Where there is no live load on the top slab it will also come in the category of Box Full. In this case we don’t provide such strength to the top slab because it is not subjected to any Live Load (Figure 4.2). Figure 4.2 Box Full (Without Live load)

4.2

Design Load of Box Culvert For Top Slab Load Top slab load consists of top slab dead load, top slab live load and their nature & direction of action. The nature & direction of action are as follows.

4.2.1

Top Slab dead load This load is coming from up word direction due to dead load of top slab and dead load of wearing coat. It is acting as uniformly distributed load (Figure 4.3).

Figure 4.3 Top Slab dead load 4.2.2

Top Slab live load This load is also coming from up word direction due to live load. In actual Live load is the wheel load. This is a concentrated load but with the help effective width of dispersion & effective length of load this concentrated load is converted into the uniformly distributed load as top slab dead load (Figure 4.4).

Figure 4.4 Top Slab live load

25   

For Bottom Slab Load In the same manner of top slab the bottom slab load also subjected to bottom slab dead load and bottom slab live load and their nature & direction of action. The nature & direction of bottom slab load are as follows. 4.2.3

Bottom Slab dead load This load is coming on the bottom slab due to dead load of top slab and dead load of side wall. It is acting as the uniformly distributed load as shown (Figure 4.5).

Figure 4.5 Bottom Slab dead load

4.2.4

Bottom Slab live load This load is coming on bottom slab due to the live load of top slab. In actual it is fraction of live load of top slab that will have to be bear by the bottom slab (Figure 4.6).

Figure 4.6 Bottom Slab live load

For Side Wall Load There are two side wall in a box culvert which are left side wall and right side wall & both walls is always be in direct contact of earth fill from the outer side and earth fill exert the soil pressure on the side walls varying in triangular pattern. If the box culvert is in full condition of water in such situation water also exerts the pressure on the side walls from inside. The water pressure also varies in the triangular pattern. Along with the earth fill pressure from outside & water 26   

pressure from inside of box culvert, the soil base pressure is also associated with box culvert. It is acting from the bottom of bottom slab in the up word vertical direction. It also assumes that the live load on the top slab is too exerting the pressure on the side wall equivalent to a particular height of side wall and it is varying in uniform pattern along the height of side wall. These all pressure may be simultaneously acting on the box culvert or may be individually depending upon the design condition of box culvert. The pressure distribution pattern and pressure acting direction of possible condition of box culvert are as follows. 4.2.5

[Dead Load] Earth pressure due to earth fill on Side Wall The pressure distribution due to earth fill on side walls of Box Culvert is shown as below: (Figure 4.7 and 4.8)

Figure 4.7 Side Fill Earth Pressure on Left

4.2.6

Figure 4.8 Side Fill Earth Pressure on Right

[Dead Load] Water Pressure from inside on Side Wall The pressure distribution due to Water Pressure from inside of Box Culvert is shown as below: (Figure 4.9 and 5.0)

27   

Figure 4.9 Water Pressure on Left

Figure 5.0 Water Pressure on Right

4.2.7

[Live Load] Earth Pressure due to Live Load Surcharge on Side Wall The pressure distribution due to Live Load Surcharge on side walls of Box Culvert is shown as below: (Figure 5.1 and 5.2)

Figure 5.1 Live Load Surcharge on Left 4.2.8

Figure 5.2 Live Load Surcharge on Right

Load Combination Mainly there are three possible load combination (I) Box Empty (II) Box Full (With Live load) and (III) Box Full (Without Live load). Out of these three load combination the (I) Box Empty is most critical because in Box Empty there will no counter acting bending moment from inside of box and results in the highest design bending moment and worst condition for analysis and design of Box Culvert. The box empty is also one of the widely used conditions of Box Culvert like below a railway line and intersection also. The schematic diagrams of all critical load combination of Box Culvert are as below.

4.2.8.1 Critical Load Combination Box Empty case forms the critical load combination for Box Culvert Analysis & Designing is shown as below: (Figure 5.3)

28   

Figure 5.3 Critical Load Combination

4.2.8.2 Load Combination [Box Full With Live Load] The Load Combination belonging to Box Full with Live Load is shown as below: (Figure 5.4)

Figure 5.4 Load Combination [Box Full With Live Load]

4.2.8.3 Load Combination [Box Full Without Live Load] The Load Combination belonging to Box Full without Live Load is shown as below: (Figure 5.5)

Figure 5.5 Load Combination [Box Full Without Live Load] 29   

4.3

Manual Analysis For calculating the moment we have to calculate the various design loads due to which the moments are developing. In order to calculating the moment for all design conditions of box culvert we have to first calculate the design Loads. The different design loads for analysis & designing of a RCC box culvert are as follows.

4.3.1 Design Load Calculation 4.3.1.1 Top Slab dead load calculation Top Slab dead load = dead load of top slab + dead load of wearing coat Dead load of top slab = thickness of top slab concrete density for top slab (24 Kn/M3) Dead load of wearing coat = thickness of wearing coat concrete density for wearing coat (22 Kn/M3)

4.3.1.2 Top Slab live load calculation Top Slab live load = live load defined by IRC: 6 – 2014 as per effective width of dispersion (IRC: 112 – 2011) and effective length of load (IRC: 112 – 2011) including impact factor (IRC: 6 – 2014) Total load of top slab = top slab dead load + top slab live load

4.3.1.3 Bottom Slab dead load calculation Bottom slab dead load= dead load of top slab on bottom slab + dead load on bottom slab from side walls Dead load on bottom slab from side walls = 2 dead load of one side wall on bottom slab DLS.W. = [

H

   

 

     

   

   

   

 

     

 

]

Where DLS.W. = Dead load of one side wall on bottom slab

30   

4.3.1.4 Bottom Slab live load calculation  

BSLL= [

 

 

f

 

   

 IRC:  

   

 

 

 

   

   

 

]

Where BSLL = Bottom Slab live load Total load of bottom slab= bottom slab dead load + bottom slab live load 4.3.1.5 Side wall load calculation The expressions used for calculation of Side Walls are tabulated below: (Table 4.0) Table 4.0 Side Wall Load Calculation Load

Load

Type

Cases

Case-1 Box Empty

[Live Load] Earth Pressure at base due to Live Load Surcharge

1.2×

[Dead Load] Earth Pressure at base due to Earth fill

H×

[Dead Load] Water Pressure at base from inside Where

soil

soil×Ke.p.

soil

× Ke.p.

X

Case-2 Box Full (With Live Load)

1.2×

H×

Case-3 Box Full (Without Live Load)

X

soil×Ke.p.

soil

× Ke.p.

water×h

H×

soil ×

Ke.p.

water×h

= unit weight of soil

Ke.p = earth pressure coefficient h = height of water level

H = Total height of Side Wall

4.3.1.6 Bottom Slab base reaction It is base reaction from bottom slab due to all up word superimposed and dead load of box culvert. Its role is important for checking the bearing capacity of soil and in ensuring that Our RCC structure will be held on

Figure 5.6 Soil Base Pressure 31 

 

earth will serve the required purpose safely or not. Bottom slab reaction is comes out by the help following load calculation (Figure 5.6). Bottom slab base reaction = dead load base reaction + live load base reaction Dead load base reaction = dead load of top slab, bottom slab and side wall Live load base reaction = live load of bottom slab without impact effect 4.3.2

Design Moment Calculation After calculating the design loads we will calculate the fixed end moments. These fixed end moments will be distributed at all junctions of Box Culvert. For this we calculate the fixed end moment at all corner of box culvert manually and these Moments are distributed by the Moment Distribution Method because box culvert is a Rigid Frame structure. The expressions that are used for calculating the fixed end moments for box Culvert are as follows.

4.3.2.1 Moment Calculation for Slab The expressions used for Moment calculation of Slab are tabulated below: (Table 4.1)

Table 4.1 Moment Calculation for Slab Load

Slab

Type

Type

Dead Load Moment Live Load Moment

Top Slab Moment Calculation

Bottom Slab Moment Calculation

12

12

12

12

Where W = Dead Load or Live Load as the case may be L = Effective Span

32   

4.3.2.2 Side Wall Moment Calculation The expressions used for Moment calculation of Side Walls are tabulated below: (Table 4.2)

Table 4.2 Side Wall Moment Calculation

Case-1 Box Empty

Case-2 Box Full (With Live Load)

Case-3 Box Full (Without Live Load)

Live Load Moment at top corner of Side Wall

WL 12

WL 12

X

Dead Load Moment at top corner of Side Wall Earth

WL 30

WL 30

WL 30

Dead Load Moment at top corner of Side Wall Water

X

WL 30

WL 30

Live Load Moment at base corner of Side Wall

WL 12

WL 12

X

Dead Load Moment at base corner of Side Wall Earth

WL 20

WL 20

WL 20

Dead Load Moment at base corner of Side Wall Water

X

WL 20

WL 20

Load

Load

Type

Cases

Where W = Dead Load or Live Load as the case may be. L = Effective Span

33   

4.3.2.4 Braking Force Moment Calculation The concern of braking force or braking force moment depends upon the designer. If the designer wants to take this then he can take for safer side of design otherwise if does not want to take then he can’t. Because impact allowance has already made in the design that’s why we can leave the braking force moment. It is taken under consideration for dealing with more safer and practical situation as in field. It is calculated as per

IRC clause 211.2 of IRC: 6 – 2014.

Braking force = 20% for first load train + 10% for second load train Effective braking force =  Braking force moment = 4.3.3

 

       

   

   

   

     

 

WL

Distribution Factor For manual analysis we consider the distribution factor on an average as 0.5 for distribution of moment by moment distribution method.

4.3.4

Design Moment Design Moment = Final Moment after distribution OR Design Moment = Final Moment after distribution + Braking Force Moment

4.4

STAAD.Pro Analysis STAAD.Pro is a structural analysis and design computer program originally developed by Research Engineers International at Yorba Linda, CA in year 1997. In late 2005, Research Engineers International was bought by Bentley Systems. An older version called Staad-III for windows is used by Iowa State University for educational purposes for civil and structural engineers. Initially it was used for DOS-Window system. The commercial version STAAD.Pro is one of the most widely used structural analysis and

design software. It supports several

steel, concrete and timber design codes. It can make use of various forms of analysis from the traditional 1st order static analysis, 2nd order p-delta analysis,

geometric

non

linear

analysis

or

34   

a buckling analysis. It can also make use of various forms of dynamic analysis from modal extraction to time history and response spectrum analysis. In recent years it has become part of integrated structural analysis and design solutions mainly using an exposed API called Open STAAD to access and drive the program using a VB macro system included in the application or other by including Open STAAD functionality in applications that themselves include suitable programmable macro systems. 4.5

Formulas used for design by WSM •

Effective Depth required d M

9 d=√

9 Where M = design moment 9 R = moment of resistance factor 9 b = width of section 9 R=

σcbc j k

9 k = neutral axis factor σ

9 k= 

   σ

σ

9 σst = permissible stress in steel 9 j = lever arm factor 9 j = 1•

Area of Steel Reinforcement Ast 9 Ast =

•

M  σ

Check for Shear will be done same as for all parts top slab, bottom slab & side walls

•

Shear Force at effective depth from face of wall V 9 V = 

•

 

   

 

 

   

 

   

 

Shear Stress τv 9 τv =

 

   

 

 

 

   

 

35   

•

Steel percentage p A

9 p=

4.6

 

Formulas used for design by LSM •

Effective Depth required d

9 d=√

M

9 Where Mu = factored design moment 9 R = moment of resistance factor 9 b = width of section 9 R = 0.36 fck j k 9 k = Neutral axis factor 9 k=

.

9 fck = characteristics strength of concrete 9 fy = yield strength or characteristics strength of steel 9 j = lever arm factor 9 j = 1- 0.42k •

Area of Steel Reinforcement Ast

9 Ast=   •

M .

Check for Shear will be done same as for all parts top slab, bottom slab & side walls

•

Shear force at effective depth from face of wall Vu

9 Vu = 1.5V =   •

 

 

 

 

 

 

 

 

Shear Stress τvu  

9 τvu = •

.

   

 

 

 

   

 

Steel Percentage p

9 p=

A  

36   

4.7 Sample Problem ‐ve  A    

Clear Span

+ve B

ttop ‐ve 

+ve 

 

Clear height

   

twall 

twall tbottom

   

+ve 

‐ve 

D 

+ve 

‐ve

C

   

  Input parameters

Figure 5.7 Box Culvert notations

Clear span ℓ = 4M Clear height h = 4M Top slab thickness ttop = 0.5M Bottom slab thickness tbottom = 0.5M Side wall thickness twall = 0.5M Unit weight of concrete conc. = 24 Kn/M3 Unit weight of soil soil = 18 Kn/M3 Unit weight of water water = 10 Kn/M3 Co efficient of earth pressure Ke.p. = 0.5 Total cushion on top (If present) tcu. = 0M Thickness of wearing course tw.c. = 0.08M Carriage way width B = 2 Lane 7.5M Concrete grade = M35 Steel grade = Fe415 Modular ration for bridge as per IRC: 6 – 2000 m = 10 Live load IRC Class 70R Loading IRC Class A Loading All dimensions in M and force in Kn.

  37   

WSM design parameters Permissible flexural compressive stress in concrete for M35 concrete as per IRC: 21

–

2000 σcbc = 11.67 N/MM2 Permissible stress in steel in tension for Fe415 grade as per IRC: 21 – 2000 σst = 200 N/MM2 Neutral axis factor σ

k=

σ

   σ

.

=

.

 

 

= 0.37

Lever arm factor j = 1- = 1-

.

= 0.88

Moment of resistance factor q=

σcbc j k = *11.67*0.88*0.37 = 1.89

LSM design parameters Characteristics strength of concrete for M35 fck = 35 N/MM2 Yield strength of steel for Fe415 fy = 415 N/MM2 Neutral axis factor k=

.

=

.

= 0.48

Lever arm factor j = 1 – 0.42 k = 1 – 0.42*0.48 = 0.80 Moment of resistance factor q = 0.36 fck j k = 0.36*35*0.80*0.48 = 4.82

        38   

Analysis Load calculation for all members 1. Top slab load calculation Self weight of Top Slab = ttop  Concrete density for ttop (24 Kn/M3) = 0.5*24 = 12 Kn/M2 Self weight of wearing course = tw.c.   Concrete density for t w.c. (22 Kn/M3) = 0.08*22 = 1.76 Kn/M2 Adopt minimum of 2 Kn/M2 weight of wearing course as per MOST specifications = 2 Kn/M2 Total dead load of top slab = self weight of top slab + self weight of wearing course = 12 + 2 = 14 Kn/M2 Live load of top slab IRC Class 70R Loading  

 

   

L = 4.5M 

               

350Kn

350Kn

1.22M  Leff. = 5.73M 

 

0.85M

0.85M

     

7.5M  C=1.2M

     

beff. = 4.27M 

beff. =  2.9M 

Figure 5.8 Wheel imprint of IRC Class 70R Loading 39   

Effective span L = clear span + thickness of side wall = 4+0.5 = 4.5M Dispersal of load in span direction as per IRC: 112 - 2011 ℓeff. = length of load + 2 (ttop + tw.c.) = 4.57 + 2*(0.5+0.08) = 5.73M Also in case of IRC Class 70R Loading dispersal of train of load Leff. = 4.5M It should not more than the effective span L so Leff = 4.5M Dispersal of load traverse to span direction as per IRC: 112 - 2011 X

beff. = α x (1- [ ] ) + bw L

Where beff. = effective width of dispersion B

Α = A constant depends upon [ ] ratio L

B = Lane width L = Effective Span X = Distance of center of gravity of load from the nearest support. bw = Width of concentrated area of load bw = Width of tyre + 2(tcu.) B L

=

. .  

= 1.67 so α = 2.91 from IRC: 112 - 2011 

.

X =    = 2.25   bw = 0.84 + 2(0.08) = 1M  beff. = 2.91*2.25 (1 – 

. .

 ) + 1 = 4.27M 

Also dispersal of train of load Beff. = 2.135 + 0.42 + 1.22 + 0.42 + 2.135 = 6.33M  It should not more than the effective span B so Beff. = 6.33M  Live load of top slab = 

.

.

 Kn/M2 = 

.

.

*

. .

. .

 = 15.16 Kn/M2 

Impact for IRC Class 70R Loading as per IRC: 112 – 2011 25% for Span up to 5M  So Live Load with Impact effect = 1.25*15.16 = 18.95 Kn/M2  Total load of top slab = Dead load of top slab + Live load of top slab   Total load of top slab for IRC Class 70R Loading = 14 + 18.95 = 32.95 Kn/M2  Live load of top slab IRC Class A Loading  

40   

7.5M

57Kn 

57Kn

57Kn 

57Kn 

57Kn

57Kn 

 

L = 4.5M 

    

57Kn 

C=0.1 5m 

 

57Kn 

57Kn 

57Kn 

57Kn 

   

57Kn 

0.5 M 

1.3 M

0.5 M

1.2 M

0.5 M

1.3 M

0.5 M 

Figure 5.9 Wheel imprint of IRC Class A Loading Effective Span L = Clear span + Thickness of side wall = 4+0.5 = 4.5M Dispersal of load in span direction as per IRC: 112 - 2011 ℓeff. = Length of Load + 2 (ttop + tw.c.) = 0.25 + 2*(0.5+0.08) = 1.41M Also dispersal of train of load Leff. = 0.705 + 1.2 + 3.2 + 0.705 = 5.81M It should not more than the effective span L so Leff = 4.5M Dispersal of load traverse to span direction as per IRC: 112 - 2011 X

beff. = α x (1- [ ]) + bw L

Where beff. = Effective width of dispersion B

Α = A constant depends upon [ ] ratio L

B = Lane width L = Effective Span X = Distance of center of gravity of load from the nearest support. bw = Width of concentrated area of load bw = Width of tyre + 2(tcu.) B L

=

. .  

= 1.67 so α = 2.91 from IRC: 112 - 2011

X = 0.05 bw = 0.5 + 2*0.08 = 0.66M beff. = 2.91*0.05 (1 –

. .

) + 0.66 = 0.80M

Also dispersal of train of load Beff. = 0.40 + 0.25 + 1.3 + 0.5 + 1.2 + 0.5 + 1.3 + 0.25 + 0.40 = 6.10M It should not more than the effective span B so Beff. = 6.10M Live load of top slab =

.

.

Kn/M2 =

.

.

*

. .

. .

= 14.95 Kn/M2 41 

 

Impact for IRC Class A Loading as per IRC: 112 – 2011 I= Where I = impact factor A = constant 4.5 for RCC bridges & 9.0 for steel bridges B = constant 6 for RCC bridges & 13.5 for steel bridges L = effective span of bridge. I=

.

= 0.43

.

So live load with impact effect = 1.43*14.95 = 21.38 Kn/M2 Total load of top slab = dead load of top slab + live load of top slab Total load of top slab for IRC Class A Loading = 14 + 21.38 = 35.38 Kn/M2 2. Bottom slab load calculation Dead Load on bottom slab = Dead load of top slab + 2 Dead load of one side wall on bottom slab Dead load of top slab = 14 Kn/M2 Dead load of one side wall on bottom slab DLS.W. =

 H

   

 W L

T

   

 

   

 W

 W

 W

 

 B

   C

 

 

Load dispersion of side wall = Effective span + Thickness of bottom slab = 4.5 + 0.5 = 5M DLS.W. =

 

.

 

= 19.2 Kn/M2

Dead load on bottom slab = 14 + 19.2 = 33.2 Kn/M2 Live load of bottom slab BSLL = Live load of top slab without Impact effect IRC Class 70R Loading =

L

 L

E

  .

.

.

=

.

 

f

   

 IRC     C

   

 I T

 

     

 W

= 9.56 Kn/M2

.

.

     

.

IRC Class A Loading =

L

 L

E

 

   

.

=

.

.

. .

.

 

.

f

     

 IRC     C

   

 I T

 

     

 W

= 9.07 Kn/M2

42   

Adopt live load of bottom slab = 9.56 Kn/M2 So total load on bottom slab = 9.56 + 33.2 = 42.76 Kn/M2 3. Side wall load calculation Earth pressure due to Live Load Surcharge equivalent to 1.2M height is considered. (Kn/M2) Load

Load

Type

Cases

Case-1 Box Empty

[Live Load] Earth pressure at base due to Live Load

1.2×

soil×Ke.p.=

1.2*18*0.5 = 10.8

Case-2 Box Full (With Live Load) 1.2×

Case-3 Box Full (Without Live Load)

soil×Ke.p. =

X

1.2*18*0.5 = 10.8

Surcharge [Dead Load] Earth pressure at base due to Earth fill

H×

soil

× Ke.p. =

5*18*0.5 = 45

[Dead Load] Water pressure at base

X

H×

soil

× Ke.p. =

H×

soil

× Ke.p. =

5*18*0.5 = 45

5*18*0.5 = 45

water×h

water×h

= 10*4 =

40

= 10*4 =

40

from inside Check for Base pressure Dead load base pressure = Dead load from top slab + Dead load of side walls on bottom slab + Dead load of bottom slab = 14 + 19.2 + 0.5*24 = 45.2 Kn/M2 Live load base pressure = Live load of bottom slab = 9.56 Kn/M2 Base pressure = 45.2 + 9.56 = 54.76 Kn/M2 In both case base pressure is less than the 150 Kn/M2 so our RCC structure is Safe.         43   

Moment calculation for all members 1. Top slab and bottom slab moment calculation (Kn-M)         

Slab Type

 

Load

 

Type  

 

Top Slab Moment Calculation

Bottom Slab Moment Calculation

IRC Class 70R Loading

IRC Class A Loading

.

.

Dead Load Moment

=

23.63

IRC Class 70R Loading .

=

23.63

.

IRC Class A Loading .

=

56.03

.

=

56.03

               

Live load Moment

Total Load Moment

.

.

=

.

.

=

.

.

=

.

.

31.98

36.08

16.13

16.13

55.61

59.71

72.16

72.16

=

                        44   

2. Side wall moment calculation (Kn-M)

Load

Load

Type

Cases

Case-2

Case-3

Case-1

Box Full

Box Full

Box

(With

(Without

Empty

Live

Live

Load)

Load)

.

Live Load Moment at top corner of Side Wall

.

WL

= 18.23

= 18.23

.

.

=

30.38

Live Load Moment at base corner of Side Wall  

.

.

=

.

.

=

27

27

21.61

3.38

.

=

.

X

WL

Dead Load Moment at base corner of Side Wall Earth  

48.61

.

30.38

X

WL

Total Load Moment at top corner of Side Wall

=

30.38

Dead Load Moment at top corner of Side Wall Water  

.

X

Dead Load Moment at top corner of Side Wall Earth  

.

WL

WL

= 18.23

= 18.23

.

.

=

45.56

Dead Load Moment at base corner of Side Wall Water  

WL

Total Load Moment at base corner of Side Wall

.

=

45.56

45.56

.

.

X

63.79

=

=

40.5

40.5

23.29

5.06

=

45   

Among all above cases of side walls the Case – 1 Box Empty is the critical case because of non availability of any counteracting moment due to absent of water. Moments for distribution may be drawn: for IRC Class 70R Loading

for IRC Class A Loading

MAB = MBA = 55.61

MAB = MBA = 59.71

MDC = MCD = 72.16

MDC = MCD = 72.16

MAD = MBC = 48.61

MAD = MBC = 48.61

MDA = MCB = 63.79

MDA = MCB = 63.79

IRC Class 70R Loading A

D

B

C

AB

AD

DA

DC

BA

BC

CB

CD

-55.60

48.61

-63.79

72.16

55.60

-48.60

63.79

-72.16

3.50

3.50

-4.19

-4.19

-3.50

-3.50

4.19

4.19

-1.75

-2.09

1.75

2.09

1.75

2.09

-1.75

-2.09

1.92

1.92

-1.92

-1.92

-1.92

-1.92

1.92

1.92

-51.93

51.93

-68.15

68.15

51.93

-51.93

68.15

-68.15

     

     

 

IRC Class A Loading   A

D

B

C

 

AB

AD

DA

DC

BA

BC

CB

CD

-59.71

48.60

-63.79

72.16

59.71

-48.60

63.79

-72.16

5.52

5.52

-4.18

-4.18

-5.52

-5.52

4.18

4.18

-2.76

-2.09

2.76

2.09

2.76

2.09

-2.76

-2.09

 

2.43 

2.43 

‐2.43 

‐2.43 

‐2.43

‐2.43

2.43

2.43

 

‐54.45 

54.45 

‐67.64 

67.64 

54.45

‐54.45

67.64

‐67.64

 

   

   

46   

3. Braking force moment calculation as per IRC: 112 - 2011 Braking force = 20% for first load train + 10% for second load train For IRC Class 70R Loading .

= 0.2*[

.

] + 0.1*[

. .

] = 82.46 Kn

Effective braking force =

 

       

 

       

 

Moment due to braking force =

WL

.

=

 

=

.

. .

.

= 58.62 Kn/M2

= 131.90 Kn-M

Moment due to braking force will quarterly distributed at all corner of box culvert. = 32.97 Kn-M For IRC Class 70R Loading .

= 0.2*[

.

] + 0.1*[

. .

.

] + 2*0.05*[

] = 44.15 Kn

.

Effective braking force =

 

       

 

       

Moment due to braking force =

 

=

  WL

=

.

.

.

. .

= 82.56 Kn/M2

= 73.26 Kn-M

Moment due to braking force will quarterly distributed at all corner of box culvert. = 18.31 Kn-M Design moment = distributed moment + moment due to braking force for IRC Class 70R Loading

for IRC Class A Loading

MAB = MBA = 84.90

MAB = MBA = 72.76

MDC = MCD = 101.12

MDC = MCD = 85.95

MAD = MBC = 84.90

MAD = MBC = 72.76

MDA = MCB = 101.12

MDA = MCB = 85.95

47   

Design IRC Class 70R Loading WSM design approach with constant depth of section 1. Top slab M

Effective depth required d = √ d=√

.

= 212.17MM

.

Let us provide 20MM Ф bars @ 40MM clear cover so effective depth provided d=450MM Area of steel =

M  σ

.

=

= 1071.96MM2

.

Shear force at effective depth from face of wall V=

T

  .

V=

    .

 

 

 

 

.

= 59.30Kn

 

 

Shear Stress τv =

   

 

 

 

   

  A

Steel percentage p =

.

=

 

=

.  

= 0.13 N/MM2

= 0.24

Permissible Shear Strength of Concrete τc corresponding to p = 0.23 N/MM2 Since τv < τc hence design is safe. 2. Bottom slab M

Effective depth required d = √ d=√

.

= 231.30MM

.

Let us provide 20MM Ф bars @ 40MM clear cover so effective depth provided d = 450MM Area of steel =

M  σ

.

=

= 1276.76MM2

.

Shear force at effective depth from face of wall V= V=

T

  .

    .

  .

 

Shear Stress τv = Steel percentage p =

 

 

 

= 76.97Kn  

   

 

   

A  

=

  .

   

=

.  

= 0.17 N/MM2

= 0.28

Permissible Shear Strength of Concrete τc corresponding to p = 0.24 N/MM2 48   

Since τv < τc hence design is safe. Since moments at junctions of side wall are same as that of top slab and bottom slab. Hence same reinforcement is to be continued for side wall. Check for shear for side walls RA = reaction at point A  

=

   

 

   

 

 

 

 

+

 

M

 

   

 

   

 f

 

   

 

 

 

=

   

.

.

.

+

*

* = 58.05Kn

RD = reaction at point D RD

 

=

M

   

 

   

 

 

 

  .

    .

 

+

   

   

 f

 

   

 

 

 

=

   

.

+

* = 91.8Kn

Pressure at ttop from face A = Pressure at ttop from face A = Effective

height

   

*

 

of

. .

*0.25 = 2.5 Kn/M2 *4.25 = 42.5 Kn/M2

side

wall

   

=

clear

height

of

side

wall

+

 

dwall = 4 + 0.5 = 4.5M Effective depth for side wall = effective depth for bottom slab = 450MM Shear force at effective depth from face A VA = RA –

.

* dwall – 10.8* dwall = 58.08 -

.

* 0.450 – 10.8*0450 = 52.63Kn

Shear force at effective depth from face D VD = RD –

.

.

* dwall – 10.8* dwall = 91.8-

Maximum shear stress τv =

 

   

* 0.450 – 10.8* 0.450 = 67.25Kn

 

   

 

   

 

.  

= 0.15

N/MM2 Permissible Shear Strength of Concrete τc corresponding to p = 0.24 N/MM2 Since τv < τc hence design is safe.

49   

IRC Class 70R Loading LSM design approach with constant depth of section 3. Top slab Effective depth required d = √ d=√

.

.

M

= 162.54MM

.

Let us provide 20MM Ф bars @ 40MM clear cover so effective depth provided d = 450MM M

Area of steel =

.

=

.

.

.

= 979.78MM2

.

Shear force at effective depth from face of wall Vu = Vu =

T

 

.

    .

 

.

  .

 

= 88.95Kn  

Shear Stress τvu =

 

     

 

 

 

   

  A

Steel percentage p =

.

=

 

=

.

= 0.20 N/MM2

 

= 0.22

Permissible Shear Strength of Concrete τc corresponding to p = 0.34 N/MM2 Since τvu < τc hence design is safe. 4. Bottom slab Effective depth required d = √ d=√

.

.

M

= 177.39MM

.

Let us provide 20MM Ф bars @ 40MM clear cover so effective depth provided d = 450MM M

Area of steel =

=

.

.

.

.

= 1166.96MM2

.

Shear force at effective depth from face of wall Vu = Vu =

T .

 

    .

 

.  

Shear Stress τvu = Steel percentage p =

 

 

 

.

= 115.46Kn  

   

 

 

 

   

  A  

=

.

=

.  

= 0.26 N/MM2

= 0.26

Permissible Shear Strength of Concrete τc corresponding to p = 0.38 N/MM2 Since τvu < τc hence design is safe. 50   

Since moments at junctions of side wall are same as that of top slab and bottom slab. Hence same reinforcement is to be continued for side wall. Check for shear for side walls RA = reaction at point A  

=

   

 

   

 

 

 

M

 

   

 

   

 f

 

   

 

 

 

=

   

 

+

 

.

.

.

+

*

* = 58.05Kn

RD = reaction at point D RD

 

=

M

   

 

   

 

 

 

 

   

 

   

 f

 

   

 

 

 

=

.

.

.

+

Pressure at ttop from face A =

   

 

+

*

* = 91.8Kn

Pressure at ttop from face A =

Effective

   

 

height

of

 

. .

*0.25 = 2.5 Kn/M2 *4.25 = 42.5 Kn/M2

side

wall

   

=

clear

height

of

side

wall

+

 

dwall = 4 + 0.5 = 4.5M Effective depth for side wall = effective depth for bottom slab = 450MM Shear force at effective depth from face A VuA = [RA –

.

* dwall – 10.8* dwall = 58.08 -

.

* 0.450 – 10.8*0450]*1.5 = 78.95Kn

Shear force at effective depth from face D VuD = [RD –

.

.

* dwall – 10.8* dwall = 91.8-

* 0.450 – 10.8* 0.450]*1.5 =

100.88Kn Maximum shear stress τvu =

 

   

 

   

 

   

 

.  

= 0.22

N/MM2 Permissible Shear Strength of Concrete τc corresponding to p = 0.38 N/MM2 Since τvu < τc hence design is safe.

51   

IRC Class A Loading WSM design approach with constant depth of section 5. Top slab M

Effective depth required d = √ d=√

.

= 196.20MM

.

Let us provide 20MM Ф bars @ 40MM clear cover so effective depth provided d = 450MM Area of steel =

M  σ

.

=

= 918.69MM2

.

Shear force at effective depth from face of wall V=

T

  .

V=

    .

 

 

 

 

.

= 63.61Kn

 

 

Shear Stress τv =

   

 

 

 

   

  A

Steel percentage p =

.

=

 

=

.  

= 0.14 N/MM2

= 0.20

Permissible Shear Strength of Concrete τc corresponding to p = 0.22 N/MM2 Since τv < τc hence design is safe. 6. Bottom slab M

Effective depth required d = √ d=√

.

= 213.47MM

.

Let us provide 20MM Ф bars @ 40MM clear cover so effective depth provided d = 450MM Area of steel =

M  σ

.

=

= 1085.22MM2

.

Shear force at effective depth from face of wall V= V=

T

  .

    .

  .

 

Shear Stress τv = Steel percentage p =

 

 

 

= 76.97Kn  

   

 

 

 

   

  A  

=

.

=

.  

= 0.17 N/MM2

= 0.24

Permissible Shear Strength of Concrete τc corresponding to p = 0.23 N/MM2 Since τv < τc hence design is safe. 52   

Since moments at junctions of side wall are same as that of top slab and bottom slab. Hence same reinforcement is to be continued for side wall. Check for shear for side walls RA = reaction at point A  

=

   

 

   

 

 

 

M

 

   

 

   

 f

 

   

 

 

 

=

   

 

+

 

.

.

.

+

*

* = 58.05Kn

RD = reaction at point D RD

 

=

M

   

 

   

 

 

 

 

   

 

   

 f

 

   

 

 

 

=

.

.

   

 

+

 

.

+

* = 91.8Kn

Pressure at ttop from face A = Pressure at ttop from face A = Effective

height

   

*

 

of

. .

*0.25 = 2.5 Kn/M2 *4.25 = 42.5 Kn/M2

side

wall

   

=

clear

height

of

side

wall

+

 

dwall = 4 + 0.5 = 4.5M Effective depth for side wall = effective depth for bottom slab = 450MM Shear force at effective depth from face A VA = RA –

.

* dwall – 10.8* dwall = 58.08 -

.

* 0.450 – 10.8*0450 = 52.63Kn

Shear force at effective depth from face D VD = RD –

.

.

* dwall – 10.8* dwall = 91.8-

Maximum shear stress τv =

 

   

* 0.450 – 10.8* 0.450 = 67.25Kn

 

   

 

   

 

.  

= 0.15

N/MM2 Permissible Shear Strength of Concrete τc corresponding to p = 0.23 N/MM2 Since τv < τc hence design is safe.

53   

IRC Class A Loading LSM design approach with constant depth of section 7. Top slab Effective depth required d = √ d=√

.

.

M

= 150.45MM

.

Let us provide 20MM Ф bars @ 40MM clear cover so effective depth provided d = 450MM M

Area of steel =

.

=

.

.

.

= 839.68MM2

.

Shear force at effective depth from face of wall Vu = Vu =

T

 

.

    .

 

.

  .

 

= 95.42Kn  

Shear Stress τvu =

 

     

 

 

 

   

  A

Steel percentage p =

.

=

 

=

.

= 0.21 N/MM2

 

= 0.19

Permissible Shear Strength of Concrete τc corresponding to p = 0.32 N/MM2 Since τvu < τc hence design is safe. 8. Bottom slab Effective depth required d = √ d=√

.

.

M

= 163.51MM

.

Let us provide 20MM Ф bars @ 40MM clear cover so effective depth provided d = 450MM M

Area of steel =

=

.

.

.

.

= 991.89MM2

.

Shear force at effective depth from face of wall Vu = Vu =

T .

 

    .

 

.  

Shear Stress τvu = Steel percentage p =

 

 

 

.

= 115.46Kn  

   

 

 

 

   

  A  

=

.

=

.  

= 0.26 N/MM2

= 0.22

Permissible Shear Strength of Concrete τc corresponding to p = 0.35 N/MM2 Since τvu < τc hence design is safe. 54   

Since moments at junctions of side wall are same as that of top slab and bottom slab. Hence same reinforcement is to be continued for side wall. Check for shear for side walls RA = reaction at point A  

=

   

 

   

 

 

 

M

 

   

 

   

 f

 

   

 

 

 

=

   

 

+

 

.

.

.

+

*

* = 58.05Kn

RD = reaction at point D RD

 

=

M

   

 

   

 

 

 

 

   

 

   

 f

 

   

 

 

 

=

.

.

.

+

Pressure at ttop from face A =

   

 

+

*

* = 91.8Kn

Pressure at ttop from face A =

Effective

   

 

height

of

 

. .

*0.25 = 2.5 Kn/M2 *4.25 = 42.5 Kn/M2

side

wall

   

=

clear

height

of

side

wall

+

 

dwall = 4 + 0.5 = 4.5M Effective depth for side wall = effective depth for bottom slab = 450MM Shear force at effective depth from face A VuA = [RA –

.

* dwall – 10.8* dwall = 58.08 -

.

* 0.450 – 10.8*0450]*1.5 = 78.95Kn

Shear force at effective depth from face D VuD = [RD –

.

.

* dwall – 10.8* dwall = 91.8-

* 0.450 – 10.8* 0.450]*1.5 =

100.88Kn Maximum shear stress τvu =

 

   

 

   

 

   

 

.  

= 0.22

N/MM2 Permissible Shear Strength of Concrete τc corresponding to p = 0.35 N/MM2 Since τvu < τc hence design is safe.

55   

IRC Class 70R Loading WSM design approach with constant steel area 9. Top slab Let us provide area of steel = 1000MM2 Effective depth required d = √ d=√

.

M

= 212.17MM

.

Effective depth provided as per area of steel  =

M  σ

.

=

A

= 482.39MM > 212.17MM OK

.

Shear force at effective depth from face of wall V=

T

 

   

.

V=

.

 

 

 

 

.

= 58.26Kn

 

 

Shear Stress τv =

   

 

A

Steel percentage p =

 

 

   

 

=

 

=

.  

= 0.12 N/MM2

= 0.21

Permissible Shear Strength of Concrete τc corresponding to p = 0.22 N/MM2 Since τv < τc hence design is safe. 10. Bottom slab Let us provide area of steel = 1200MM2 Effective depth required d = √ d=√

.

M

= 231.30MM

.

Effective depth provided as per area of steel  =

M  σ

.

=

A

= 478.78MM > 231.30MM OK

.

Shear force at effective depth from face of wall V= V=

T

  .

    .

  .

 

Shear Stress τv = Steel percentage p =

 

 

 

= 75.77Kn  

   

 

 

 

   

 

A  

=

=

.  

= 0.16 N/MM2

= 0.25

Permissible Shear Strength of Concrete τc corresponding to p = 0.23 N/MM2 Since τv < τc hence design is safe. 56   

Since moments at junctions of side wall are same as that of top slab and bottom slab. Hence same reinforcement is to be continued for side wall. Check for shear for side walls RA = reaction at point A  

=

   

 

   

 

 

 

M

 

   

 

   

 f

 

   

 

 

 

=

   

 

+

 

.

.

.

+

*

* = 58.05Kn

RD = reaction at point D RD

 

=

M

   

 

   

 

 

 

 

   

 

   

 f

 

   

 

 

 

=

.

.

   

 

+

 

.

+

* = 91.8Kn

Pressure at ttop from face A = Pressure at ttop from face A = Effective

height

   

*

 

of

. .

*0.25 = 2.5 Kn/M2 *4.25 = 42.5 Kn/M2

side

wall

   

=

clear

height

of

side

wall

+

 

dwall = 4 + 0.5 = 4.5M Effective depth for side wall = effective depth for bottom slab = 450MM Shear force at effective depth from face A VA = RA –

.

* dwall – 10.8* dwall = 58.08 -

.

* 0.478 – 10.8*0.478 = 52.29Kn

Shear force at effective depth from face D VD = RD –

.

.

* dwall – 10.8* dwall = 91.8-

Maximum shear stress τv =

 

   

 

* 0.478 – 10.8* 0.478 = 65.73Kn  

 

 

   

 

.  

.

= 0.14

N/MM2 Permissible Shear Strength of Concrete τc corresponding to p = 0.23 N/MM2 Since τv < τc hence design is safe.

57   

IRC Class 70R Loading LSM design approach with constant steel area 11. Top slab Let us provide area of steel = 1000MM2 Effective depth required d = √ .

d=√

.

M R

= 162.55MM

.

Effective depth provided as per area of steel  =

M .

A

=

.

.

.

= 440.90MM > 162.55MM OK

.

Shear force at effective depth from face of wall T

Vu =

 

.

Vu =

    .

 

 

.

.

 

= 89.46Kn  

Shear Stress τv =

 

     

 

 

 

   

  A

Steel percentage p =

=

 

=

.

= 0.20 N/MM2

 

= 0.23

Permissible Shear Strength of Concrete τc corresponding to p = 0.35 N/MM2 Since τv < τc hence design is safe. 12. Bottom slab Let us provide area of steel = 1200MM2 Effective depth required d = √ .

d=√

.

M R

= 177.39MM

.

Effective depth provided as per area of steel  =

M .

A

=

.

.

.

= 437.61MM > 177.39MM OK

.

Shear force at effective depth from face of wall Vu = Vu =

T .

 

    .

 

.  

Shear Stress τv = Steel percentage p =

 

 

 

.

= 116.29Kn  

   

 

 

 

   

 

A  

=

.

=

.  

.

= 0.27N/MM2

= 0.27

Permissible Shear Strength of Concrete τc corresponding to p = 0.38 N/MM2 Since τv < τc hence design is safe. 58   

Since moments at junctions of side wall are same as that of top slab and bottom slab. Hence same reinforcement is to be continued for side wall. Check for shear for side walls RA = reaction at point A  

=

   

 

   

 

 

 

M

 

   

 

   

 f

 

   

 

 

 

=

   

 

+

 

.

.

.

+

*

* = 58.05Kn

RD = reaction at point D RD

 

=

M

   

 

   

 

 

 

 

   

 

   

 f

 

   

 

 

 

=

.

.

.

+

Pressure at ttop from face A =

   

 

+

*

* = 91.8Kn

Pressure at ttop from face A =

Effective

   

 

height

of

 

. .

*0.25 = 2.5 Kn/M2 *4.25 = 42.5 Kn/M2

side

wall

   

=

clear

height

of

side

wall

+

 

dwall = 4 + 0.5 = 4.5M Effective depth for side wall = effective depth for bottom slab = 450MM Shear force at effective depth from face A VAu = [RA –

.

* dwall – 10.8* dwall = 58.08 -

.

* 0.437 – 10.8*0.437]*1.5 = 79.17Kn

Shear force at effective depth from face D VDu = [RD –

.

.

* dwall – 10.8* dwall = 91.8-

Maximum shear stress τv =

 

   

 

* 0.437 – 10.8* 0.437] = 101.69Kn  

 

 

   

 

.  

.

= 0.23

N/MM2 Permissible Shear Strength of Concrete τc corresponding to p = 0.38 N/MM2 Since τv < τc hence design is safe.

59   

IRC Class A Loading WSM design approach with constant steel area 13. Top slab Let us provide area of steel = 1000MM2 Effective depth required d = √ d=√

.

M

= 196.20MM

.

Effective depth provided as per area of steel  =

M  σ

.

=

A

= 413.40MM > 196.20MM OK

.

Shear force at effective depth from face of wall V=

T

 

   

.

V=

.

 

 

 

 

.

= 64.91Kn

 

 

Shear Stress τv =

   

 

 

 

   

  A

Steel percentage p =

=

 

.

=

.  

= 0.16 N/MM2

= 0.24

Permissible Shear Strength of Concrete τc corresponding to p = 0.23 N/MM2 Since τv < τc hence design is safe. 14. Bottom slab Let us provide area of steel = 1200MM2 Effective depth required d = √ d=√

.

M

= 213.25MM

.

Effective depth provided as per area of steel  =

M  σ

.

=

A

= 406.96MM > 213.25MM OK

.

Shear force at effective depth from face of wall V= V=

T

 

   

 

 

 

  .

.

.  

Shear Stress τv = Steel percentage p =

= 78.85Kn  

   

 

 

 

   

 

A  

=

.

=

.  

= 0.19 N/MM2

= 0.29

Permissible Shear Strength of Concrete τc corresponding to p = 0.24 N/MM2 Since τv < τc hence design is safe. 60   

Since moments at junctions of side wall are same as that of top slab and bottom slab. Hence same reinforcement is to be continued for side wall. Check for shear for side walls RA = reaction at point A  

=

   

 

   

 

 

 

M

 

   

 

   

 f

 

   

 

 

 

=

   

 

+

 

.

.

.

+

*

* = 58.05Kn

RD = reaction at point D RD

 

=

M

   

 

   

 

 

 

 

   

 

   

 f

 

   

 

 

 

=

.

.

   

 

+

 

.

+

* = 91.8Kn

Pressure at ttop from face A = Pressure at ttop from face A = Effective

height

   

*

 

of

. .

*0.25 = 2.5 Kn/M2 *4.25 = 42.5 Kn/M2

side

wall

   

=

clear

height

of

side

wall

+

 

dwall = 4 + 0.5 = 4.5M Effective depth for side wall = effective depth for bottom slab = 450MM Shear force at effective depth from face A VA = RA –

.

* dwall – 10.8* dwall = 58.08 -

.

* 0.406 – 10.8*0.406 = 53.16Kn

Shear force at effective depth from face D VD = RD –

.

.

* dwall – 10.8* dwall = 91.8-

Maximum shear stress τv =

 

   

 

* 0.406 – 10.8* 0.406 = 69.65Kn  

 

 

   

 

.  

.

= 0.17

N/MM2 Permissible Shear Strength of Concrete τc corresponding to p = 0.24 N/MM2 Since τv < τc hence design is safe.

61   

IRC Class 70R Loading LSM design approach with constant steel area 15. Top slab Let us provide area of steel = 1000MM2 Effective depth required d = √ .

d=√

.

M R

= 150.47MM

.

Effective depth provided as per area of steel  =

M .

A

=

.

.

.

= 377.86MM > 150.47MM OK

.

Shear force at effective depth from face of wall T

Vu =

 

.

Vu =

    .

 

 

.

.

 

= 99.28Kn  

Shear Stress τv =

 

     

 

A

Steel percentage p =

 

 

   

 

=

 

=

.

= 0.26 N/MM2

 

= 0.26

Permissible Shear Strength of Concrete τc corresponding to p = 0.38 N/MM2 Since τv < τc hence design is safe. 16. Bottom slab Let us provide area of steel = 1200MM2 Effective depth required d = √ .

d=√

.

M R

= 163.55MM

.

Effective depth provided as per area of steel  =

M .

A

=

.

.

.

= 371.96MM > 163.55MM OK

.

Shear force at effective depth from face of wall Vu = Vu =

T

 

   

 

 

 

  .

.

.

.

= 120.51Kn

 

Shear Stress τv = Steel percentage p =

 

   

 

 

 

   

 

A  

=

.

=

.  

.

= 0.32N/MM2

= 0.32

Permissible Shear Strength of Concrete τc corresponding to p = 0.41 N/MM2 Since τv < τc hence design is safe. 62   

Since moments at junctions of side wall are same as that of top slab and bottom slab. Hence same reinforcement is to be continued for side wall. Check for shear for side walls RA = reaction at point A  

=

   

 

   

 

 

 

M

 

   

 

   

 f

 

   

 

 

 

=

   

 

+

 

.

.

.

+

*

* = 58.05Kn

RD = reaction at point D RD

 

=

M

   

 

   

 

 

 

 

   

 

   

 f

 

   

 

 

 

=

.

.

.

+

Pressure at ttop from face A =

   

 

+

*

* = 91.8Kn

Pressure at ttop from face A =

Effective

   

 

height

of

 

. .

*0.25 = 2.5 Kn/M2 *4.25 = 42.5 Kn/M2

side

wall

   

=

clear

height

of

side

wall

+

 

dwall = 4 + 0.5 = 4.5M Effective depth for side wall = effective depth for bottom slab = 450MM Shear force at effective depth from face A VAu = [RA –

.

* dwall – 10.8* dwall = 58.08 -

.

*0.371 – 10.8*0.371]*1.5 =80.367Kn

Shear force at effective depth from face D VDu = [RD –

.

.

* dwall – 10.8* dwall = 91.8 -

Maximum shear stress τv =

 

   

 

*0.371–10.8*0.371] = 107.34Kn  

 

 

   

 

.  

.

= 0.29

N/MM2 Permissible Shear Strength of Concrete τc corresponding to p = 0.41 N/MM2 Since τv < τc hence design is safe.

63   

CHAPTER – 5 RESULT AND DISCUSSION 5.1

Results of Analysis by MS-Excel & STAAD Pro The result of moment analysis by manual calculation, by developed MS-Excel Sheet and STAAD Pro are shown in Table 5.0. Table 5.0 Design Moments by MS-Excel tool and STAAD.Pro Bending Moments (Kn-M) Loading Member

IRC CLASS 70R LOADING By MS-Excel Analysis

IRC CLASS A LOADING

By STAAD. By MS-Excel Pro Analysis Analysis

By STADD. Pro Analysis

Bottom Slab

68.15

72.2

67.64

72.2

Top Slab

51.93

53.00

54.45

55.6

Side Wall

68.15

72.2

67.64

72.2

5.2

Design by MS-Excel tool

5.2.1

Effect on Area of Steel in WSM and LSM Approach A design of a RCC Box Culvert with Span & Height 4M is prepared with the help of developed MS-Excel tool. This design is based on the WSM as well as LSM approaches. From the developed MS-Excel tool the saving in the amount of steel area required with keeping a constant depth of section from WSM to LSM approaches is noted and from these noted data following figures and tables are developed (Table 5.1 and 5.2 & Figure 6.0 and 6.1 ).

64   

Table 5.1 Saving S in Stteel using LS SM approacch over WS SM for Fe4115 Steel Graade  

 

 

 

Fe 41 15 

IRC CLLASS 70R LOA ADING 

IRC CLLASS A LOADIING 

CONCRETE GRADE 

% D DECREAMENTT IN  REINFORCEMEN NT 

% DEECREAMENT IN  REIN NFORCEMENT 

M30 0 

7.54% 

7.54% 

M35 5 

8.75% 

8.75% 

M40 0 

9.84% 

9.84% 

M45 5 

10.84% 

10.84% 

%Sav ving in Area of o Steel 12.00% % 10..76% 10.76% 9.82% 9 9.82%

%Decreament due to LSM

10.00% % 8.00% %

Span=4M M Height=4M M 2 Lane Rooad Steel Gradde Fe415

8.80% 8.80% 7.67% 7.67% % IRC CLASS 70R LOADING%  DECREAMENT IN  REINFORCEMENT

6.00% %

IRC CLASS A LOADING%  DECREAMENT IN  REINFORCEMENT

4.00% % 2.00% % 0.00 0% M30

M35

M40

M M45

Concrete Grade

Figure 6..0 Saving in n Steel usingg LSM apprroach over WSM W for Fee415 Steel Grade G

65   

Table 5.2 Saving S in Stteel using LSM approaach over WS SM for Fe5000 Steel Graade  

 

 

 

Fe 50 00 

IRC CLA ASS 70R LOAD DING 

IRC CLASSS A LOADING G 

CONCRETE GRADE 

% DEECREAMENT IIN  REIN NFORCEMENTT 

% DECREAMENT IN  REINFFORCEMENT

M30 0 

7.67% 

7.67% 

M35 5 

8.80% 

8.80% 

M40 0 

9.82% 

9.82% 

M45 5 

10.76% 

1 10.76% 

%Saaving in Areaa of Steel 12.00% 4% 10.84 0.84% 10 9.8 84% 9.84%

%D %Decreament t due d to t LSM

10.00%

Span=4M Height=4M 2 Lane Roadd Steel Gradee Fe500

8.75% 8 8.75% 8.00%

7.54% 7.54% IRC CLASS 70 0R LOADING%  DECREAMEN NT IN  REINFORCEM MENT

6.00% 4.00%

IRC CLASS A  LOADING%  NT IN  DECREAMEN REINFORCEM MENT

2.00% 0.00% M30

M35

M M40

45 M4

Concrete Grrade

F Figure 6.1 Saving S in Steeel using LS SM approacch over WSM M for Fe5000 Steel Grad de 66   

5.2.2

Saving in Depth of Section in LSM over WSM with constant Steel Area A design of a RCC Box Culvert with Span & Height 4M is prepared with the help of developed MS-Excel tool. This design is based on the WSM as well as LSM approaches. From the developed MS-Excel tool the variation in the amount of depth of section with keeping a constant steel area required from WSM to LSM approaches is noted and from these noted data following figures and tables are developed (Table 5.3 and 5.4 & Figure 6.2 and 6.3 ).

67   

T Table 5.3 Sav ving in Matterial using LSM approoach over WSM W for Fe4415 Steel Grade  

 

 

 

Fe 415 

IRC CLA ASS 70R LOAD DING 

IRC CLASSS A LOADING G 

Fe415 5 

% DECREAMENT IN DEPTH H OF THE  SECTION 

% DECREAMENT IN DEPTH H OF  THE SECTION 

M30 0 

6.86% 

6 6.85% 

M35 5 

7.91% 

7 7.85% 

M40 0 

8..94% 

8 8.93% 

M45 5 

9.90% 

9 9.71% 

% %Saving in Material 10.00% % 8.94% 8 8.93%

9.00% % %Improvement due to LSM

8.00% % 7.00% %

9.9 90% 9.71%

7.91% 7.85% 6.86% % 6.85%

IRC CLASSS 70R LOADIN NG%  DECREA AMENT IN DEPTTH OF  THE SEC CTION IRC CLASSS A LOADING%  DECREA AMENT IN DEPTTH OF  THE SEC CTION

6.00% % 5.00% % 4.00% % 3.00% 2.00 0% 1.00 0% 0.00 0% M30

Spaan=4m Heiight=4m 2 laane road Steeel Grade Fe4415

M35

M40

M M45

Concretee Grade

Figure 6.2 Saving S in Material M usin ng LSM app proach overr WSM for Fe415 F Steell Grade

68   

T Table 5.4 Sav ving in Matterial using LSM approoach over WSM W for Fe500 Steel Grade G  

 

 

Fe500 0 

IRC CLA ASS 70R LOAD DING 

IRC CLASSS A LOADING G 

CONCRETE GRADE 

% DECREAMENT IN DEPTH H OF THE  SECTION 

% DECREAMENT IN DEPTH H OF  THE SECTION 

M30 0 

6.82% 

6 6.74% 

M35 5 

7.87% 

7 7.65% 

M40 0 

8.89% 

8 8.55% 

M45 5 

9.70% 

9 9.42% 

%Saving in i Material

10.0 00% 9.0 00%

%Improvement due to LSM

8.0 00% 7.0 00%

7.87% 7.65% %

8.89% 8.55%

9.70% 9.42%

Spaan=4m Height=4m 2 laane road Steeel Grade Fe5500

6.82% %74% 6.7 IRC CLA ASS 70R LOADIN NG%  DECREA AMENT IN DEP PTH OF  THE SEC CTION

6.0 00% 5.0 00% 00% 4.0

IRC CLA ASS A LOADING G%  DECREA AMENT IN DEP PTH OF  THE SEC CTION

3.00% 2.00% 1..00% 0..00% M30 0

M35

M40

M45

Concrrete Grade

Figure 6.3 Sa aving in Maaterial usingg LSM apprroach over WSM W for Fee500 Steel Grade G

69   

5.3

Discussion

5.3.1

There will be three conditions for analysis and designing of Box Culvert (I) Box Empty (II) Box Full with Live Load and (III) Box Full without Live Load.

5.3.2

The water pressure is the only load that produces the moment in the opposite directions on the side walls i.e. counteracting moments.

5.3.3

Box empty condition is the critical load combination because all loads produces the moment in the same directions with no counter balancing from water pressure. This shall make worst condition of analysis and design of box culvert.

5.3.4

Keeping the section constant 6-10% saving in steel can be obtained by shifting from WSM to LSM design approach.

5.3.5 For constant steel area, section of top, wall and bottom can be reduced by 7-12% if design is done by LSM approach instead of WSM approach. 5.3.6

At higher grade of concrete more saving in steel is observed.

5.3.7

Formulas that are used in LSM design are simple to apply and there is separate partial safety factor for both concrete and steel reinforcement.

5.3.8

There are two limits in LSM approach (I) Limit State of Collapse & (II) Limit State of Serviceability. Limit State of Collapse corresponds to the Flexure, Compression, Shear, and Torsion while Limit State of Serviceability corresponds to Deflection, Cracking, Corrosion and Excessive Vibration. These limits are based on the various probabilities and because of this LSM approach is also called as Probabilistic Approach. These make LSM approach is farther better than the WSM approach.

70   

CHAPTER – 6 CONCLUSIONS In the present study on “Analysis & Design of RCC Box Culvert using WSM & LSM” the analysis & design of box culvert under different loading conditions has been carried out. A sample problem of 4M span with Empty Box Condition is analysed by manual and STAAD Pro software. The design for the same is carried out with conventional WSM approach & as per latest guidelines of IRC: 6 – 2014 using LSM approach. A MS – Excel tool is developed for analysis and design of box culvert. The tool is capable of analyzing box culvert for all three possible situations i.e. (I) Case-1 Box Empty (II) Case-2 Box Full (With Live load) & (III) Case-3 Box Full (Without Live Load) and box culvert subjected to 2 types of loading i.e. (I) IRC Class 70R Loading & (II) IRC Class A Loading. With the develop tool design can be carried out using WSM as well as LSM approaches. The results from the develop tool analysis & design are compared with manual & STAAD Pro analysis/calculation. From the study following conclusions may be drawn: 1. The develop MS – Excel tool for analysis & design of box culvert is accurate, fast, easy to use & user friendly application. 2. No software and additional knowledge to run software is required for the analysis and design of box culvert. 3. Empty box culvert condition is found to be most critical loading combination as in this case no counterbalancing moments are available because of non availability of water head. 4. Although IRC Class 70R Loading are higher as compared to IRC Class A Loading but due to higher impact factor in case of IRC Class A Loading sometimes shear check becomes critical. 5. From the parametric study it is observed that for a constant section, a saving of tune of 6-10% may be achieved by using LSM approach, amount of saving is higher for higher grades of concrete. 71   

6. From the parametric study, it is also observed that for a constant Steel Area a saving of the tune of 7-12% may be attained in concrete by using LSM approach over WSM design approach. For higher grades of concrete saving is higher. Scope for Future Study Based on the experience of present study, work can also be extended for the other type of bridges such as (i) Slab Culvert Bridge (ii) T–Beam Bridge and (iii) Plate Girder Bridge. The study may be carried out for the bridge abutment, bridge pier & bridge foundation also.

72   

References [1]

B.N. Sinha and R.P. Sharma ‘RCC Box Culvert – Methodology and Designs including Computer Method’ Paper no. 555 Journal of Indian Road Congress, 2009

[2]

Ravindra Bhimarao Kulkarni and Rohan Shrikant Jirage ‘Comparative Study of Steel Angles as Tension Members Designed by Working Stress Method and Limit State Method’ International Journal of Scientific & Engineering Research, Volume 2, Issue 11, 2011

[3]

Ping Zhu, Run Liu, Wenbin Liu and Xinil Wu ‘Study on Optimal Design of a Box Culvert under Road’ Civil Engineering and Urban Planning 2012 (CEUP 2012)

[4]

B.H. Solanki and M.D. Vakil ‘Comparative Study for Flexure Design using IRC 112:2011 & IRC 21:2000’ International Journal of Scientific & Engineering Research, Volume 4, Issue 6, 2013

[5]

Sujata Shreedhar and R. Shreedhar ‘Design Coefficients for Single and Two cells Box Culverts’ International Journal of Civil and Structural Engineering, Volume 3, Issue 3, 2013

[6]

RajaVarma ‘Study the Working Stress Method and Limit State Method and in RCC Chimney Design’ International Journal of Technical Research and Applications, Volume 2, Issue 1, 2014

[7]

Neeta K. Meshram and P.S.Pajgade ‘Comparative Study of Water Tank Using Limit State Method and Working Stress Method’ International Journal of Research in Advent Technology, Volume 2, Issue 8, 2014

[8]

Neha Kolate, Molly Mathew and Snehal Mali ‘Analysis and Design of RCC Box Culvert’ International Journal of Scientific & Engineering Research, Volume 5, Issue 12, 2014

[9]

Paul Tom P. ‘Analysis and Design of RCC Bridges and Box Culvert’ Research Report, https://www.researchgate.net/publication/275272796, 2015

[10]

Shivanand Tenagi and R. Shreedhar ‘Comparative Study of Slab Culvert Design using IRC 112:2011 and IRC21:2000’ International Journal for Scientific Research & Development, Volume 3, Issue 05, 2015

73   

[11]

Y. Vinod Kumar and Chava Srinivas ‘Analysis and Design of Box Culvert by using Computational Methods’ International Journal of Engineering & Science Research IJESR, Volume 5, Issue 7, 2015

[12]

Sudip Jha, Cherukupally Rajesh and P.Srilakshmi ‘Comparative Study of RCC Slab Bridge by Working Stress (IRC: 21-2000) and Limit State (IRC: 112-2011)’ International Journal & Magazine of Engineering, Technology, Management and Research, Volume 2, Issue 8, 2015

[13]

IRC: 6 - 2000 Standard Specifications and Code for practice for Road Bridges Section-II Loads and Stresses (Fourth revision)

[14]

IRC: 21 - 2000 Standard Specifications and Code of practice for Road Bridges Section-III Cement Concrete (Plain and Reinforced)

[15]

IRC: 6 - 2014 Standard Specifications and Code of practice for Road Bridges Section-II Loads and Stresses (Revised edition)

[16]

IRC: 112 – 2011 Code of practice for Concrete Road Bridges

[17]

IS: 456 - 2000 Plain and Reinforced Concrete- Code of practice (Fourth revision)

[18]

D J Victor ‘Essentials of Bridge Engineering’ Oxford & IBH. 1980

[19]

M. A. Jayaram ‘Design of Bridge Structures’ Prentice-Hall of India Pvt. Limited, 2004

[20]

N Krishna Raju, ‘Design of Bridges, Oxford and LBH publishing co. Pvt. Ltd., New Delhi, Fourth edition.

74