INDEXSr. No. Title Author Subject Page No.

1 The Balanced Scorecard: As A Performance Measurement System

Dr. Vinod K. Ramani Accountancy 1-2

2 Corporate Mergers and Acquisitions: Legal, Accounting and Strategic Issues

Mira J. Bhanderi Accountancy 3-4

3 Morphometric analysis of the Sisi river basin, North-East India and some geo-environmental implications

Dr. Uttam Goswami Applied Geology

5-6

4 Careful Evaluation of CARE’s Performance Dr. Bheemanagouda Commerce 7-8

5 Advertisements on Passenger Cars - An Innovative Idea for Outdoor Advertising

Dr. Sangapa Rampure Commerce 9-10

6 Knowledge Management And Knowledge Process Outsourcing

Dr.Santos Singh Bais Commerce 11-13

7 A Study on Micro, Small and Medium Enterprises, Using Sms Marketing as a Tool

Dr.S P. Mathiraj, Mr Anil B. Malali

Commerce 14-16

8 Economic Value Added Dr. Kishor V. Bhesaniya Commerce 17-20

9 CHALLENGES IN COMMERCE DUE TO GLOBALIZATION

Mr. T. Kalimuthu, Dr. R. Ganapathi

Commerce 21-23

10 Estimating Reliability of Component Based Software Using Artificial Neural Network

Mr. Harish Rathod , Mr. Mahesh Parmar, Miss. Rekha Teraiya

Computer Science

24-26

11 Foreign Direct Investment (Fdi), Special Economic Zones (Sezs) And Economic Developments In India: An Empirical Study

M. Marimuthu Economics 27-29

12 Environmental Impact On Agriculture: WTO And Indian Economic Reforms

Dr.Shivasharanappa Dhaba

Economics 30-31

13 Study of regional rural water supply scheme-Kutch Niketa Patel Economics 32-34

14 An Overview of Indian economy of Unemployment in Depression

Dr. Dilip Arjune, Dr. Pawar Ashok S.

Economics 35-37

15 Kendriya Aarthsankalp 2011-12 and 2012-13 ke Tulnatmak Adhayan

Dr. Pawar Ashok S., Dr. Sunita J. Rathod, Shri. Budhwant R.G.

Economics 38-42

16 ADEPTS: Innovative Self-Evaluation Technique for Teachers

Dr. Pawar Ashok S., Dr. Vishal Tayade,Dr. Sunita Rathod

Economics 43-44

17 Bharatiya thet parikiy gunvantkiye dhoran Dr. Pawar Ashok S. Economics 45-48

18 European Euro Sankat and Vyaparchakrache Jagtik Parinam

Dr. Pawar Ashok S., Dr. Sunita J. Rathod, Umare Vilas Devchand

Economics 49-52

19 Higher Education in India: An Appraisal Dr. Sukhwinder Singh jolly

Education 53-56

20 An Investigation on test Anxiety In L2 Learners S. Gandhimathi , Dr. R. Ganesan

Education 57-58

21 Organizational Commitment and Self esteem of Faculty Members of Secondary Level Teacher Training Programme in Mysore

Mr. Moslem Cherabin, Dr. Praveena K. B.

Education 59-61

22 Comparative Analysis on Various Coded Cooperaative Networks

Pallavi Ingle Electronics and Communication

62-64

23 Effect of Plasma Arc Cutting Speed-voltage On the Unevenness of Hardox-400 Material

A. A. Darji, S. P. Patel, J.V.Desai

Engineering 65-67

24 Design and Simulation of High Speed,Low power Preamplifier Based CMOS Comparator

Gireeja Amin Engineering 68-70

25 Analysis of box culvert considering soil structure interaction

M.G. Kalyanshetti,S.V. Malkhare

Engineering 71-74

26 Soil erosion & Advance Techniques of Soil Conservation Manish Gujarati,Prof. H. M. Gandhi

Engineering 75-77

27 Cotton Crop Performance and Economics under Drip Irrigation at Various Water Application Levels

Jignesh. A. Shah Engineering 78-80

28 Cotton Crop Response to Thermal Regimes under Surface Irrigation at Stress Free Water Application Level

Jignesh A.Shah Engineering 81-82

29 Simulation of Line and Phase Voltages of Inverter Using Switching Function Concept

Prachi M. Palpankar, A.Y.Fadnis

Engineering 83-85

30 Microgrid : A Planning Based on Renewable Sources In Amravati District

Shweta. L. Tiwari, Dr.R.M. Moharil

Engineering 86-89

31 “Phenomenological Modeling of Four Stroke Compression Ignition Engine Processes”

V. M. Makwana Engineering 90-94

32 Designing Aspects of Cryogenic Attachment For Uv/Visible Spectrophotomer

Yagnesh B. Chauhan, Hardik B. Patel, J.M.Patel, Dr. U.S.Joshi

Engineering 95-98

33 Comparison Of Conventional 60/70 grade of Bitumen with CRMB60 for Roads

Zala Kartik S., Mandowara Nirajkumar P., Prof. C.B.Mishra, Dr. F.S.Umrigar

Engineering 99-100

34 Modelling And Analysis of Faults In Wind Based Doubly-Fed Induction Generator

K. Keerthi Deepika,A. Srinivasa Rao

Engineering 101-104

35 Multipoint Hand Gesture Recognition Using Robotic Arm Control

Nishant Madhukar Labhane, Prashant Harsh, Meghan Kulkarni

Engineering 105-107

36 Assessment of Sediment Distribution Hiral Shah, N. N. Borad, R. K. Jain

Engineering 108-111

37 Review and Analysis of Drought Monitoring and Management

Patel Jaydeepkumar J., Prof. G.V.Dihora

Engineering 112-114

38 Flow Forecasting of Tapi River At Mandvi Station By ANN Gajjar Kamleshkumar Hasmukhbhai,Prof. H.M.Gandhi

Engineering 115-118

39 Implementation of Digital Watermarking by Combined Transform Domain Algorithm for Copyright Authentication using Matlab

Raval Keta J., Mrs. Sameena Zafar

Engineering 119-121

40 Use of Rubber Dam In Tapi River Front Development At Surat City

Sagar D Patel, Kiran R.Shah, PROF.R.B.Khasiya

Engineering 122-124

41 Mahatma Gandhi's Ultimate to the Globalization Dr. Ashok Shankarrao Pawar

Engineering 125-129

42 Determination of Reservoir Operating Rules for A Single Reservoir - A case study (March 2012)

J.C.Solanki,B. K.P.Sthar, C. Prof.A.T.Motiai

Engineering 130-132

43 Flow Equation For Elliptical Weir Jigar H. Gamit Engineering 133-135

44 Reducing the Effect of Flood through River Training Work on Shedhi River at Khumarvada Village of Kheda District, Gujarat

Suthar Kandarp kumar P. , Solanki Jitendrasinh C.

Engineering 136-138

45 Case Studies in Community Initiated Rainwater Harvesting Dr Mahalaxmi Krishnan Environment 139-140

46 Impact of Human Activities on Mangroves Ecosystem Arvind A. Dhond Environment 141-143

47 Equator Principles an Innovative Tool for Environmental and Social Sustainability

Ashok R. Bantwa Finance 144-146

48 Investor Activism – The Icahn Effect Ch. Chaitanya Finance 147-149

49 Dividend policy – A fundamental signal Krunal K Bhuva, Dr. Vijay Vyas

Finance 150-151

50 Infrastructure Creation And Utilisation In Railways Mrs. K. Revathi,Dr. R. Ganapathi

General Management

152-154

51 Impact of Environmental Parameters on the Worker’s Work Capacity Involved in Organized Poultry Farm

Tulika Srivastava,Dr. Aditi Vats

Home Science 155-156

52 Impact of Electronic Communication Media on Consumers Sandhya Rani,Dr. Chhaya Shukla

Home Science 157-159

53 A Study On Employee’s Performance Appraisal With Reference To Mitsubishi Heavy Industry Tools Limited.

S.Ragothaman, D.Yuvaraj, S.Sridhar

Human Resource Management

160-162

54 Roles of the Expatriate Kapil Dev Upadhyay, Dr. (Prof.) Vijay Kumar Soni

Human Resource Management

163-164

55 English in Multicultural Society of Asia Bhaveshkumar Rana Literature 165-167

56 Need to Reform General English Syllabus at UG Level in the Affiliate Colleges of the University of Jammu: An Experimental Study

Dr. Wajahat Hussain Literature 168-169

57 A Study On Employee Retention for Sustaining the Talented Employees in Health Care Industry in a Private Multi-Speciality Organization

Dr C Swarnalatha,TS Prasanna

Management 170-172

58 Present Status Of Women Self Hep Groups In Tamilnadu M.Gurusamy, P.Uma Maheswari, C.Sangeetha

Management 173-175

59 Volatility In Indian Stock Markets Mr. Santanu Kumar Das

Management 176-180

60 Women Entrepreneurs: Role, Development and Contribution in Indian Economy

Siddharth Raval, Yupal Shukla

Management 181-182

61 Talent Management: A Bird Eye View Kalaspathi Vishwakarma

Management 183-184

62 Efficient Positioning For Sustained Leadership Ms.Asha Anotny , Ms.S.Anbu Selvi

Management 185-188

63 “An Imperical Study on Women’s Approach Towards Equity Market”

Ritesh Hasmukhlal Amarsela

Management 189-193

64 A Study on the Role of Securities Exchange Board of India (SEBI) Towards Insider Trading Practices in Indian Capital Market

V. Arockia Jerold Management 194-197

65 Profitability Of Commercial Banks With Special Reference To Indian Overseas Bank

Ms. R. Gokilavani,Dr. R. Ganapathi

Management 198-200

66 Brand Preference For Mineral Water With Reference To Pollachi

Dr. R. Ganapathi,G. Murali Manokari

Management 201-205

67 “ISO 9000 - Impact of Quality Systems on Business Performance”

Manisha Paliwal Management 206-207

68 Perceived Satisfaction of Mobile Prepaid Users and demographic factors

Dr. J. M. Badiyani Management 208-209

69 STUDY ON NPAs IN SBI WITH REFERENCE TO COIMBATORE

Ms. R. Gokilavani,Dr. R. Ganapathi

Management 210-213

70 Consumer Protection – Issues and Impediments In Rural Areas

Mrs. K. Revathi,Dr. R. Ganapathi

Management 214-216

71 Service Quality and Customer Satisfaction in Telecommunication Companies

Mr. Akshay Arora,Ms. Sujitha R

Management 217-219

72 To Study The Organizational Stress It’s Causes, Effects And Remedies of Private Banks At Bhavnagar Region

Mr. Vimal P. Jagad,Mr Mukesh .C Ajmera

Management 220-222

73 Case Study on Utilisation of ATM - With Reference To Erode Town

R. Gokilavani,Dr. R. Ganapathi

Management 223-226

74 Case Study Method – An Ideal Tool of Learning Mr. T. Kalimuthu,Dr. R. Ganapathi

Management 227-229

75 Ethics & Marketing: A Deep Connection Ashish Nathwani Marketing 230-232

76 The Emerging Role of HR in India Axaybharti N Goswami Marketing 233-234

77 Marketing Of Diamond Jewellery In Coimbatore – An Opinion Survey

Dr. R. Ganapathi, G. Murali Manokari

Marketing 235-237

78 A Study On Customer Satisfaction Towards Cable TV Services With Special Reference To Thirumangalam, Madurai District

K. Navarathinam,S. Anbu selvi

Marketing 238-240

79 Changing Consumer Behavior towards IPL Nirav R. Vyas,Dr. Vijay Vyas

Marketing 241-242

80 Q-Level Subnearring Of Q-Intuitionistic L-Fuzzy Subnearrings

M.M.Shanmugapriya, K.Arjunan

Mathematics 243-246

81 Effect of Selected Yogic, Aerobic Exercises and Combined Yogic and Aerobic Practices on Resting Pulse Rate

Dr. Shivarama Reddy. M , Dr. Manjappa. P

Physical Education

247-250

82 Analysis of Long Jump Performance T.Christopher Nallarasu Dr.V.Mahadevan

Physical Education

251-252

83 Panchayats and Women Self Help Groups: (A Study With Special Reference to Gulbarga District of Karnataka)

Dr. Pralhad Chengte Political Science

253-254

84 The Frustration among T.B.Patients-A Psychological study Dr.Kishor N. Mehta Psychology 255-256

85 Voice Activation Detection Algorithm for Estimating the Noise From Human Speech Signal

Kanu Patel,Sameena Zafar

Science 257-269

86 An Analysis of Changing Socio-Cultural Practices Among The Lambadas Of Andhra Pradesh

Dr. M. Sreedevi Xavier Sociology 260-262

87 Sociology of Art: A Theoretical Exploration Dr. Poonam Gandhi-Moirangthem

Sociology 263-265

88 Dalit Nari : Sthan, Paristithi avam Samsya Dr. H.L. Chavda Sociology 266-269

89 Ansuchit jatiyan me lagan sansthan bhal achal - jilla ahmedabad gujarat rajya ke vanshis sandarbhme

Dr. H.L. Chavda Sociology 270-272

90 Techniques of Steganography and Steganalysis Bhavsar Jaimin H, Imran Khan

Technology 273-276

91 Contributions of Tourism – An Analysis Dr. Bheemanagouda Tourism 277-278

Volume : 1 | Issue : 4 | April 2012 ISSN - 2250-1991

PARIPEX - INDIAN JOURNAL OF RESEARCH X 71

Research Paper

* Assistant professor, Civil Engineering Department, Walchand Institute of Technology Solapur

** P.G. student, M.E. (civil) -structures, Walchand Institute of Technology Solapur

Keywords : Box culvert, Stiffness method, Beam on elastic foundation, Modulus of subgrade reaction, Soil structure interaction

Engineering

Analysis of box culvert considering soil structure interaction

* M.G. Kalyanshetti ** S.V. Malkhare

Box culvert is consisting of top, bottom and two vertical side walls built monolithically which forms the square or rectangular single cell. The box structure is highly indeterminate structure which is having continues support as directly rests on soil. Hence to understand its true behaviour, soil structure interaction should taken into account. In practise approximate methods like moment distribution, force or displacement matrix were used. While using these methods certain assumption are made regarding to the boundary condition and it is assumed that bottom slab is infinitely stiff so that it will not undergo any differential settlement. But in reality bottom slab undergoes differential settlement; therefore there will be error in the results obtained by approximate methods. Hence attempt is made to study results obtained by considering soil structure interaction (S.S.I.) and without considering it. The effect of S.S.I. is incorporated by developing stiffness matrix using beam on elastic foundation concept. For this a detailed program is developed in FORTRAN 90/95.A parametric study is carried out for considering S.S.I. and without considering S.S.I. by varying number of cells in box culvert. Also study is carried out for various soil types by considering appropriate soil subgrade reaction to know the effect of type of soil on bending moment. The study reveals that the bottom slab is the element which is severely affected and variation of bending moment in bottom slab is in the range of 50% to 70%, in some other load cases the bending moment also changes the sign.

ABSTRACT

1. IntroductionAnalysis of box culvert is done by stiffness matrix method. Two models with respect to support conditions have been considered. In the first model box culvert is assumed as ex-ternally determinate assuming discrete boundary conditions. In the second model the bottom chord of the box culvert is assumed as resting on elastic foundation. Here the soil struc-ture interaction is taken into account for bottom chord. Single cell box structure is assumed as rigid frame structure consist-ing of top slab, bottom slab and two vertical side walls which forms a closed rigid box frame. A basic assumption in analysis of the box culvert is the displacement and forces are uniform in the longitudinal direction of the culvert. This assumption holds true for certain type of loadings than others. For exam-ple soil loading applied to the surface or pavement maybe considered as uniform in the longitudinal direction. Solution therefore is independent of one of the three orthogonal axes and can be formulated in remaining two axes. Thus problem can be treated as two dimensional. The analysis is performed considering a unit wide strip along the longitudinal axes. This strip is said to be in plain strain condition signifies the fact that the out of plane deformations are zero. The loads applied through small areas of contact between wheels and pave-ment. Such loads for practical are considered as point loads. While analyzing the box structure in first model some basic assumptions are made to simplify the problem. It is assumed that structure is externally determinate. Also the pressure dis-tribution at the bottom is assumed linear. In case of second mode which is highly indeterminate, it is assumed that bottom chord members are continuously supported. They undergo differential settlements and offer a resistance proportional to the transverse deflection. In both the modes axial and shear deformations are neglected. Based on above assumptions analysis is carried out for both models by displacements ma-trix method considering appropriate stiffness of the bottom chord members.

2. Stiffness methodThe force displacement relationship for a prismatic member is shown in figures 1and 2

Fig. 1 Forces and moments generated ends due to unit rotation.

Fig. 2 Forces and moments generated at the ends due to unit displacement.

Volume : 1 | Issue : 4 | April 2012 ISSN - 2250-1991

72 X PARIPEX - INDIAN JOURNAL OF RESEARCH

Fig. 3

Single cell box culvert showing degrees of freedom.

2.1 Formation of a stiffness matrix for single cellConsider a box structure as shown in the fig.3 In this case we have three unknown support reaction. i.e. two at hinge sup-port at left and one at roller support at, right. Since three equi-librium equations are available this single cell box structure is externally statically determinate. The internal static indetermi-nacy is three. This structure is kinematically indeterminate to fifth degree if axial deformations are neglected. Each joint of rigid jointed plane frame has three independent displacement components viz. two linear displacements and one rotational component. Therefore, Degree of kinematic indeterminacy of the rigid jointed plane frame is given by the equation given below.

Where,

D (IK) =. degree of kinematic indeterminacy.

j = number of joints

NR = number of reaction components.

Nm = number of constrains imposed by support condition and other factors such as inextensibility of members.

Applying the equation (1) degree of kinematic indeterminacy for the single cell box structure as shown in fig. 3 can be cal-culated as below.

D (IK) = (3x4)-(3+4) = 5

Therefore single cell box structure is kinematically indetermi-nate to fifth degree. In order to generate elements of stiffness matrix a unit displacement is imparted at each degree of free-dom successively. The first four displacements are angular and fifth is linear. The equation 2 shows the stiffness matrix generated for single cell box culvert.

3. Beam on elastic foundation method.Many times structural member rests on spongy material, here after called as an elastic foundation, which offers a resistance proportional to the transverse deflection. Thus there are un-known transverse forces, equal to the product of the “stiff-

ness modulus” of the supporting material and yet unknown transverse deflection, acting on structural members on elastic foundation. In case of box structure in which bottom members are subjected to resistance proportional to the transverse de-flection, the stiffness method of analysis can still be used, pro-vided that expressions for the member stiffness matrix and for the fixed-end reactions and moments due to common types of transverse load can be found as functions of the stiffness modulus. In the following articles, these expressions will be derived.

3.1 The basic Differential Equation for beam on Elastic Foundation.Consider a structural member AB and its elastic curves A’ B’ as shown in fig. 5. It is subjected to a varying down ward load of w per unit length and to an upward reactive force of KY per unit length, where k is the stiffness modulus of the elastic foundation, measured in force per unit displacement.

Fig. 5

Structural member on elastic foundation.

From the equilibrium equations of resolution and rotation of an infinitesimal segment of the structural member,

(5)

(6)

Where in positive directions of shear V and bending moment M are as shown in above figure. The change in slope in be-tween any two consecutive points at infinitesimal distance dx apart is equal to

(7)

The negative sign is due to fact that the slope is decreasing in positive or concave bending. Combining equation a, b, c gives the basic differential equation of elastic curve

(8)

The shear and bending moment become

(9)

(10)

3.2 General solution of the differential equation Where there is no transverse loading on the member, the ba-sic differential equation (8) becomes

(11)

Of which the general solution can be given as

xL

sinhxL

sinDxL

coshxL

CsinxL

sinhxL

BcosxL

coshxL

AcosY φφ+

φφ+

φφ+

φφ=

(12)

3.3 Boundary condition of an unloaded memberThe general solution of the differential equation of an un-loaded member resting on as elastic foundation includes four arbitrary constants; four boundary conditions are required for evaluation of these constants. Two common approaches are

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PARIPEX - INDIAN JOURNAL OF RESEARCH X 73

1. Specifying the bending moments Mi, Mj, and the shears Vi,Vj at the points i, j

2. Specifying the slopes θi, θj and the transverse deflection ∆i, ∆j.

Fig. 6

Direction of forces and boundary conditions of structural member.

Using the first approach will yield a [4x4] flexibility matrix of member on elastic foundation, and the use of second ap-proach will give the [4x4] stiffness matrix.

Hence stiffness matrix [S] of a member on elastic foundation is obtained as

θi θj ∆i ∆j

Mi T1 T 2 T 5 - T 6Mj T2 T1 T6 -T5Vi T5 T6 T3 T4Vj -T6 -T5 T4 T3

Where,

The degenerate values of T1 to T6 at ф=0 are stiffness coef-ficients of an ordinary prismatic member as shown in fig.5 and fig.6.

4. Parametric studyThe parametric study contains variation of bending moment for with and without S.S.I. which is done For 3 types of box culvert namely single cell(4m X 4m), double cell(4m X 4m two cells) and triple cell (4m X 4m three cells) and for three load cases as shown in figure7 . Also study is carried out for various soil types by considering appropriate soil subgrade reaction to know the effect of type of soil on bending moment. For this a detailed program is developed in FORTRAN 90/95.

Case1: - Considering live load and dead load on top slab, lateral load due to live load and earth pressure.

Case2: - Considering live load and dead load on top slab, lat-eral load due to live load and earth pressure and water pres-sure from inside.

Case3: - Considering live load and dead load on top slab, lateral load due to earth pressure, water pressure from inside and lateral load due to live load.

Case 1 Case 2 Case 3 Fig. 7

Load cases for box culvertModel values obtained by analysis of load case 1 are pre-sented in this work. The loading magnitudes for case study are taken from the fig. 8 which obtained by solving a typical example of single cell box culvert (4m X 4m) carrying IRC class AA tracked loading.

Fig. 8

Total loading diagram for box culvertThe results obtained for considering S.S.I. and without con-sidering S.S.I. by varying number of cells in box culvert are shown in fig. 9 and fig. 10. While considering S.S.I. subgrade reaction of soil is assumed as 4800kN/m3 (loose sand).

Fig.9

Comparison of bending moments developed for case1 in bot-tom slab for all three types of culverts.

Fig. 10

Comparison of bending moments developed for case1 in top slab for all three types of culverts

The modulus of subgrade reaction is a conceptual relation-ship between soil pressure and deflection that is widely used in the structural analysis of foundation members like con-tinues footings, mat or raft foundations etc. The modulus of subgrade reaction is the ratio of stress to deformation. The table no. 1 shows the values of subgrade reaction for various types of soils according to Bowels (1988). Here results are presented in fig. 11 to 13 are for variation of bending moment for various soil subgrade reactions.

Table no. 1 Values of modulus of subgrade reaction [Bowles (1988)]

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74 X PARIPEX - INDIAN JOURNAL OF RESEARCH

REFERENCES

1. Dr. Trivedi, H.V., and Shah, V.S., ,(June 1993), analysis of box structure by matrix force method, the bridge and structural engineer quarterly journal of Indian national group of International Association of Bridge and Structural Engineering. Vol.23, No. 2. 2. Heteyni M., 1958: Beams on elastic foundation, university of Michigan press, Ann Arbor 3.Seetharamalu, K., Balwant, Rao, B., Sakar, K., B, Velayutham, V., Soil-structure interaction in box cell bridges, Lecture Notes in Civil Engg., I.I.T., Delhi, pp 319-326.Books: 1. Bowels Joseph E., foundation analysis and design, third Ed., Macgraw - Hill Book Co., (1982). 2. Weaver William, Gere James M., Matrix analysis of framed structures, Second Ed., CBS Publishers and Distributers. 3. Wang, C., K., Indeterminate Structural Analysis, MacGraw Hill Publishing Co. (1983). 4. Pandit, G., S., And Gupta, S., P., Structural analysis of matrix approach, Tata MacGraw Hill Publishing Co. Ltd., (1986). 5. D. Johnson Victor, Essentials of bridge engineering, oxford and IBH publishing Pvt. Limited New Delhi. 6. Jagdish, T.R., & Jairam, M.A., Design of bridge structures, prentice hall of India Private Limited, New Delhi

Type of soil Modulus of subgrade reaction (k) in kN/m3

Loose sand 4800- 16000Medium dense sand 9600- 80000clayey medium dense sand 32000- 80000Dense sand 64000-128000

Fig. 11

Variation of bending moment in top and bottom for various subgrade reactions slab for case 1 in single cell box culvert

Fig. 12

Variation of bending moment in top and bottom slab for vari-ous subgrade reactions for case 1 in double cell box culvert.

Fig. 13

Variation of bending moment in top and bottom slab for vari-ous subgrade reactions for case 1 in triple cell box culvert.

5. Observations and Conclusion 5.1 ObservationsIn previous chapter the box structure is analyzed for various conditions by changing number of cells, for different load cas-es and for various types of soil subgrade reaction. From that we can observe that in

1. Single cell box culvert.• When values of modulus of soil subgrade reaction are

changed from loose soil to dense soil bending moment varies substantially (45%) in bottom slab and marginal (6%) in top slab.

• In all three cases bending moment generation is higher in case of supports having lower values of soil subgrade (i.e. loose soils) when compared with nonyielding sup-ports.

2. Double cell box culvert.• When values of modulus of soil subgrade reaction are

changed from loose soil to dense soil bending moment varies substantially (55%) in bottom slab and marginal (3%) in top slab.

• In case of structure with S.S.I. maximum moments are developed at central nodes of the bottom slab, where as in case of structure without S.S.I. maximum moments are developed at edge nodes of bottom slab.

3. Triple cell box culvert• When values of modulus of soil subgrade reaction are

changed from loose soil to dense soil bending moment varies substantially (50%) in bottom slab and marginal (3%) in top slab.

• In case of structure with S.S.I. maximum moments are developed at just right of the second node or just left of the third node in bottom slab (i.e. in middle span), where as In case of structure without S.S.I. where discrete non-yielding supports are considered maximum moments are developed at edges of the bottom slab.

4.2 Conclusion From the above observations it can be stated that for bottom slab the positive bending moment (tension at bottom) starts reducing as modulus of subgrade reaction is varied from lower values of soil subgrade (loose sand) to higher values of soil subgrade (dense sand) and for further higher values of subgrade reactions i.e. for rock the values of bending mo-ment may be equal or nearer to the values obtained for the nonyielding supports.

Considering S.S.I. variation of bending moment is marginal in top slab and substantial in bottom slab. In the vertical mem-bers also variation of bending moment is marginal. Thus most critical element of box culvert is bottom slab and moment in this slab is to be calculated by appropriate S.S.I. effect.

Volume : 1 | Issue : 4 | April 2012 ISSN - 2250-1991

PARIPEX - INDIAN JOURNAL OF RESEARCH X 279