**NUMERICAL METHODS**

**UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS**

Solution of equation –Fixed point iteration: x=g(x) method – Newton’s method – Solution of linear system by Gaussian elimination and Gauss-Jordon method– Iterative method – Gauss- Seidel method – Inverse of a matrix by Gauss Jordon method – Eigen value of a matrix by power method and by Jacobi method for symmetric matrix.

**UNIT II INTERPOLATION AND APPROXIMATION**

Lagrangian Polynomials – Divided differences – Interpolating with a cubic spline – Newton’s forward and backward difference formulas.

**UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION **

Differentiation using interpolation formulae –Numerical integration by trapezoidal and Simpson’s 1/3 and 3/8 rules – Romberg’s method – Two and Three point Gaussian quadrature formulae–Double integrals using trapezoidal and Simpsons’s rules.

**UNIT IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS**

Single step methods: Taylor series method – Euler method for first order equation – Fourth order Runge – Kutta method for solving first and second order equations – Multistep methods : Milne’s and Adam’s predictor and corrector methods.

**UNIT V BOUNDARY VALUE PROBLEMS IN ORDINARY & PARTIAL DIFFERENTIAL EQUATIONS**

Finite difference solution of second order ordinary differential equation – Finite difference solution of one-dimensional heat equation by explicit and implicit methods – One-dimensional wave equation and two dimensional Laplace and Poisson equations.

**TEXTBOOKS :**

1. Veerarjan, T and Ramachandran, T., “Numerical methods with programming in C”, Second Editiion, Tata McGraw-Hill Publishing.Co.Ltd, 2007.

2. Sankara Rao K, “Numerical Methods for Scientisits and Engineers”, 3rd Edition, Printice Hall of India Private Ltd

**REFERENCE BOOKS:**

1. Chapra, S. C and Canale, R. P., “Numerical Methods for Engineers”, 5th Edition, Tata McGraw-Hill, New Delhi

2. Gerald, C. F. and Wheatley, P.O., “Applied Numerical Analysis”, 6th Edition, Pearson Education, Asia, New Delhi

3. Grewal, B.S. and Grewal,J.S., “ Numerical methods in Engineering and Science”, 6th Edition, Khanna Publishers

**SOIL MECHANICS**

**UNIT I INTRODUCTION**

Nature of Soil – Problems with soil – phase relation – sieve analysis – sedimentation analysis – Atterberg limits – classification for engineering purposes – BIS Classification system – Soil compaction – factors affecting compaction – field compaction methods and monitoring.

**UNIT II SOIL WATER AND WATER FLOW**

Soil water – Various forms – Influence of clay minerals – Capillary rise – Suction – Effective stress concepts in soil – Total, neutral and effective stress distribution in soil – Permeability – Darcy’s Law- Permeability measurement in the laboratory – quick sand condition – Seepage – Laplace Equation – Introduction to flow nets –properties and uses – Application to simple problems.

**UNIT III STRESS DISTRIBUTION, COMPRESSIBILITY AND SETTLEMENT**

Stress distribution in soil media – Boussinesque formula – stress due to line load and Circular and rectangular loaded area – approximate methods – Use of influence charts – Westergaard equation for point load – Components of settlement – Immediate and consolidation settlement – Terzaghi’s one dimensional consolidation theory – governing differential equation – laboratory consolidation test – Field consolidation curve – NC and OC clays – problems on final and time rate of consolidation

**UNIT IV SHEAR STRENGTH**

Shear strength of cohesive and cohesionless soils – Mohr – Coulomb failure theory – Saturated soil – Strength parameters – Measurement of shear strength, direct shear, Triaxial compression, UCC and Vane shear tests –Types of shear tests based on drainage and their applicability – Drained and undrained behaviour of clay and sand – Stress path for conventional triaxial test.

**UNIT V SLOPE STABILITY**

Slope failure mechanisms – Modes – Infinite slopes – Finite slopes – Total and effective stress analysis – Stability analysis for purely cohesive and C- soils – Method of slices – Modified Bishop’s method – Friction circle method – stability number – problems – Slope protection measures.

**TEXT BOOKS :**

1. Punmia P.C., “Soil Mechanics and Foundations”, Laximi Publications Pvt. Ltd., New Delhi, 1995.

2. Gopal Ranjan and Rao A.S.R., “Basic and applied soil mechanics”, New Age International Publishers, New Delhi

3. Venkatramaiah, C. “Geotechnical Engineering”, New Age International Publishers, New Delhi, 1995

4. Khan I.H., “A textbook of Geotechnical Engineering”, Prentice Hall of India, New Delhi, 1999.

**REFERENCES:**

1. Coduto, D.P., “Geotechnical Engineering Principles and Practices”, Prentice Hall of India Private Limited,

2. McCarthy D.F., “Essentials of Soil Mechanics and Foundations Basic Geotechniques”, Sixth Edition, Prentice-Hall

3. Das, B.M, “Principles of Geotechnical Engineering”, (fifth edition), Thomas Books/ cole,2002

4. Muni Budhu, “Soil Mechanics and Foundations”, John Willey & Sons, Inc, New York, 2000.

**STRENGTH OF MATERIALS**

**UNIT I ENERGY PRINCIPLES**

Strain energy and strain energy density – strain energy in traction, shear in flexure and torsion – castigliano’s theorems – principle of virtual work – application of energy theorems for computing deflections in beams and trusses – Maxwell’s reciprocal theorems

**UNIT II INDETERMINATE BEAMS**

Propped cantilever and fixed beams-fixed end moments and reactions for concentrated load (central, non central), uniformly distributed load, triangular load (maximum at centre and maximum at end) – theorem of three moments – analysis of continuous beams – shear force and bending moment diagrams for continuous beams – slope & deflections in continuous beams (qualitative study only)

**UNIT III COLUMNS**

Eccentrically loaded short columns – middle third rule – core section – columns of unsymmetrical sections – (angle channel sections) – Euler’s theory of long columns – critical loads for prismatic columns with different end conditions; Rankine-Gordon formula for eccentrically loaded columns – thick cylinders – compound cylinders.

**UNIT IV STATE OF STRESS IN THREE DIMENSIONS**

Spherical and deviatory components of stress tensor – determination of principal stresses and principal planes – volumetric strain – dilatation and distortion – theories of failure – principal stress dilatation – principal strain – shear stress – strain energy and distortion energy theories – application in analysis of stress, load carrying capacity and design of members – residual stresses

**UNIT V ADVANCED TOPICS IN BENDING OF BEAMS**

Unsymmetrical bending of beams of symmetrical and unsymmetrical sections – curved beams – Winkler Bach

formula – stress concentration – fatigue and fracture. TOTAL (L:45+T:15): 60 PERIODS

**TEXT BOOKS :**

1. Egor P Popov, “Engineering Mechanics of Solids”, Prentice Hall of India, New Delhi,2003

2. Rajput R.K. Strength of Materials, S.Chand&company Ltd., New Delhi – 2006

**REFERENCES**

1. Kazimi S.M.A, “Solid Mechanics”, Tata McGraw-Hill Publishing Co., New Delhi, 2003

2. William A .Nash, “Theory and Problems of Strength of Materials”, Schaum’s Outline Series, Tata McGraw Hill Publishing company Ltd, 2007.

3. Srinath, L.S. Advanced mechanics and solids, Tata-McGraw Hill publishing company ltd, 2005.

4. Punmia B.C.Theory of Structures (SMTS) Vol 1&II, Laxmi publishing Pvt Ltd,New Delhi ,2004.

**APPLIED HYDRAULIC ENGINEERING**

**UNIT I OPEN CHANNEL FLOW**

Open channel flow – Types and regimes of flow – Velocity distribution in open channel – Wide open channel – Specific energy – Critical flow and its computation – channel transition.

**UNIT II UNIFORM FLOW**

Uniform flow – Velocity measurement – Manning’s and Chezy’s formula – Determination of roughness coefficients – Determination of normal depth and velocity – Most economical sections – Non-erodible channels

**UNIT III VARIED FLOW**

Dynamic equations of gradually varied flow – Assumptions – Characteristics of flow profiles – Draw down and back water curves – Profile determination – Graphical integration, direct step and standard step method – Flow through transitions – Hydraulic jump – Types – Energy dissipation – Surges.

**UNIT IV PUMPS**

Centrifugal pump – minimum speed to start the pump – multistage Pumps – Jet and submersible pumps – Positive displacement pumps – reciprocating pump – negative slip – flow separation conditions – air vessels -indicator diagram and its variation – savings in work done – rotary pumps.

**UNIT V TURBINES**

Turbines – draft tube and cavitations – Application of momentum principle – Impact of jets on plane and curved plates – turbines – classification – radial flow turbines – axial flow turbines – Impulse and Reaction

**TEXT BOOKS :**

1. Subramanya K., “Flow in Open channels”, Tata McGraw-Hill PublishingCompany, 1994.

2. Modi, P.N, and Seth S.M. Hydraulic and Fluid Mechanics Standard Book House, 2000.

3. Bansal R.K, Fluid mechanics & Hydraulic machines, Laxmi Publishing Pvt Ltd, New Delhi –

**REFERENCES :**

1. Jain A.K., “Fluid Mechanics (including Hydraulic Machines)”, Khanna Publishers,8th edition, 1995.

2. Ranga Raju, K.G., “Flow through Open Channels”, Tata McGraw-Hill, 1985

**SURVEYING II**

**UNIT I TACHEOMETRIC SURVEYING**

Tacheometric systems – Tangential, stadia and subtense methods – Stadia systems – Horizontal and inclined sights – Vertical and normal staffing – Fixed and movable hairs – Stadia constants – Anallactic lens – Subtense bar.

**UNIT II CONTROL SURVEYING**

Working from whole to part – Horizontal and vertical control methods – Triangulation – Signals – Base line – Instruments and accessores – Corrections – Satellite station – Reduction to centre – Trignometric levelling – Single and reciprocal observations – Modern trends – Bench marking

**UNIT III SURVEY ADJUSTMENTS**

Errors – Sources, precautions and corrections – Classification of errors – True and most probable values – weighted observations – Method of equal shifts – Principle of least squares – Normal equation – Correlates – Level nets – Adjustment of simple triangulation networks.

**UNIT IV ASTRONOMICAL SURVEYING**

Celestial sphere – Astronomical terms and definitions – Motion of sun and stars – Apparent altitude and corrections – Celestial co-ordinate systems – Different time systems – use of Nautical almanac – Star constellations – calculations for azimuth of a line.

**UNIT V HYDROGRAPHIC AND ADVANCE SURVEYING**

Hydrographic Surveying – Tides – MSL – Sounding methods – Location of soundings and methods – Three point problem – Strength of fix – Sextants and station pointer – River surveys – Measurement of current and discharge – Photogrammetry – Introduction – Basic concepts of Terrestrial and aerial Photographs – Stereoscopy – Definition of Parallax. Electromagnetic distance measurement – Basic principle Instruments – Trilateration. Basic concepts of Cartography and Cadastral surveying.

**TEXT BOOKS:**

1. Bannister A. and Raymond S., Surveying, ELBS, Sixth Edition, 1992.

2. Punmia B.C., Surveying, Vols. I, II and III, Laxmi Publications, 1989.

3. Kanetkar T.P., Surveying and Levelling, Vols. I and II, United Book Corporation, Pune,1994.

**REFERENCES:**

1. Clark D., Plane and Geodetic Surveying, Vols. I and II, C.B.S. Publishers and Distributors, Delhi, Sixth Edition

2. James M.Anderson and Edward M.Mikhail, Introduction to Surveying, McGraw-Hill Book Company, 1985.

3. Wolf P.R., Elements of Photogrammetry, McGraw-Hill Book Company, Second Edition,1986.

4. Robinson A.H., Sale R.D. Morrison J.L. and Muehrche P.C., Elements of Cartography, John Wiley and Sons

5. Heribert Kahmen and Wolfgang Faig, Surveying, Walter de Gruyter, 1995.

**HIGHWAY ENGINEERING**

**UNIT I HIGHWAY PLANNING AND ALIGNMENT**

History of Road Construction, Highway Development in India – Jayakar Committee Recommendations and Realisations, Twenty-year Road Development Plans, Concepts of Ongoing Highway Development Programmes at National Level, Institutions for Highway Development at National level – Indian Roads Congress, Highway Research Board, National Highway Authority of India, Ministry of Road Transport and Highways (MORTH) and Central Road Research Institute. Requirements of Ideal Alignment, Factors Controlling Highway Alignment Engineering Surveys for Alignment – Conventional Methods and Modern Methods (Remote Sensing, GIS and GPS techniques) Classification and Cross Section of Urban and Rural Roads (IRC), Highway Cross Sectional Elements – Right of Way, Carriage Way, Camber, Kerbs, Shoulders and Footpaths [IRC Standards], Cross sections of different Class of Roads – Principles of Highway Financing

**UNIT II GEOMETRIC DESIGN OF HIGHWAYS **

Design of Horizontal Alignment – Horizontal Curves Super elevation, Widening of Pavements on Horizontal Curves and Transition Curves Design of Vertical Alignments – Rolling, Limiting, Exceptional and Minimum Gradients, Summit and Valley Curves-Sight Distances – Factors affecting Sight Distances, PIEV theory, Stopping Sight Distance (SSD), Overtaking Sight Distance (OSD), Sight Distance at Intersections, Intermediate Sight Distance and Illumination Sight Distance [Derivations and Problems in SSD and OSD] -Geometric Design of Hill Roads.

**UNIT III FLEXIBLE AND RIGID PAVEMENTS**

Rigid and Flexible Pavements- Components and their Functions -Design Principles of Flexible and Rigid Pavements, Factors affecting the Design of Pavements – ESWL, Climate, Sub-grade Soil and Traffic – Design Practice for Flexible Pavements [IRC Method and Recommendations- Problems] – Design Practice for Rigid Pavements – IRC Recommendations – concepts only.

**UNIT IV HIGHWAY MATERIALS AND CONSTRUCTION PRACTICE**

Desirable Properties and Testing of Highway Materials: Soil – California Bearing Ratio Test, Field Density Test – Aggregate – Crushing, Abrasion, Impact Tests, Water absorption, Flakiness and Elongation indices and Stone polishing value test – Bitumen – Penetration, Ductility, Viscosity, Binder content and Softening point Tests. – Construction Practice – Water Bound Macadam Road, Bituminous Road and Cement Concrete Road [as per IRC and MORTH specifications] – Highway Drainage [IRC Recommendations]

**UNIT V HIGHWAY MAINTENANCE **

Types of defects in Flexible pavements – Surface defects, Cracks, Deformation, Disintegration – Symptoms, Causes and Treatments. – Types of Pavement, Failures in Rigid Pavements – Scaling, Shrinkage, Warping, Structural Cracks Spalling of Joints and Mud Pumping – and Special Repairs. – Pavement Evaluation – Pavement Surface Conditions and Structural Evaluation, Evaluation of pavement Failure and strengthening – Overlay design by Benkelman Beam Method

**TEXT BOOKS:**

1. Khanna K and Justo C E G, Highway Engineering, Khanna Publishers, Roorkee, 2001.

2. Kadiyali L R, Principles and Practice of Highway Engineering, Khanna Technical Publications, Delhi, 2000.

**REFERENCES:**

1. Transportation Engineering & Planning, C.S. Papacostas, P.D. Prevedouros, Prentice Hall of India Pvt ltd, 2006.

2. IRC Standards (IRC 37 – 2001 & IRC 58 -1998)

3. Bureau of Indian Standards (BIS) Publications on Highway Materials

4. Specifications for Road and Bridges, MORTH (India)

**STRENGTH OF MATERIALS LABORATORY**

LIST OF EXPERIMENTS :

1. Test involving axial compression to obtain the stress – strain curve

2. Test involving axial tension to obtain the stress – strain curve and the strength

3. Test involving torsion to obtain the torque vs. angle of twist and hence the stiffness

4. Test involving flexure to obtain the load deflection curve and hence the stiffness

5. Tests on springs

6. Hardness tests

7. Shear test

8. Test for impact resistance

9. Tests on Cement

**HYDRAULIC ENGINEERING LAB**

LIST OF EXPERIMENTS :

1. Determination of co-efficient of discharge for orifice

2. Determination of co-efficient of discharge for notches

3. Determination of co-efficient of discharge for venturimeter

4. Determination of co-efficient of discharge for orifice meter

5. Study of impact of jet on flat plate (normal / inclined)

6. Study of friction losses in pipes

7. Study of minor losses in pipes

8. Study on performance characteristics of Pelton turbine.

9. Study on performance characteristics of Francis turbine

10. Study on performance characteristics of Kaplan turbine

11. Study on performance characteristics of Centrifugal pumps (Constant speed / variable speed)

12. Study on performance characteristics of reciprocating pump.

**SURVEY PRACTICAL II**

LIST OF EXPERIMENTS :

1. Study of theodolite

2. Measurement of horizontal angles by reiteration and repetition and vertical angles

3. Theodolite survey traverse

4. Heights and distances – Triangulation – Single plane method.

5. Tacheometry – Tangential system – Stadia system – Subtense system.

6. Setting out works – Foundation marking – Simple curve (right/left-handed) – Transition curve.

7. Field observation for and Calculation of azimuth

8. Fieldwork using Total Station.