MA1251 NUMERICAL METHODS 3 1 0 100
AIM
With the present development of the computer technology, it is necessary to develop efficient algorithms for solving problems in science, engineering and technology. This course gives a complete procedure for solving different kinds of problems occur in engineering numerically.
OBJECTIVES
At the end of the course, the students would be acquainted with the basic concepts in numerical methods and their uses are summarized as follows:
The roots of nonlinear (algebraic or transcendental) equations, solutions of large system of linear equations and eigen value problem of a matrix can be obtained numerically where analytical methods fail to give solution.
When huge amounts of experimental data are involved, the methods discussed on interpolation will be useful in constructing approximate polynomial to represent the data and to find the intermediate values.
The numerical differentiation and integration find application when the function in the analytical form is too complicated or the huge amounts of data are given such as series of measurements, observations or some other empirical information.
Since many physical laws are couched in terms of rate of change of one/two or more independent variables, most of the engineering problems are characterized in the form of either nonlinear ordinary differential equations or partial differential equations. The methods introduced in the solution of ordinary differential equations and partial differential equations will be useful in attempting any engineering problem.
1. SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS 9
Linear interpolation methods (method of false position) – Newton’s method – Statement of fixed point theorem – Fixed point iteration: x=g(x) method – Solution of linear system by Gaussian elimination and Gauss-Jordon methods - Iterative methods: Gauss Jacobi and Gauss-Seidel methods - Inverse of a matrix by Gauss Jordon method – Eigen value of a matrix by power method.
2. INTERPOLATION AND APPROXIMATION 9
Lagrangian Polynomials – Divided differences – Interpolating with a cubic spline – Newton’s forward and backward difference formulas.
3. NUMERICAL DIFFERENTIATION AND INTEGRATION 9
Derivatives from difference tables – Divided differences and finite differences –Numerical integration by trapezoidal and Simpson’s 1/3 and 3/8 rules – Romberg’s method – Two and Three point Gaussian quadrature formulas – Double integrals using trapezoidal and Simpsons’s rules.
4. INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS 9
Single step methods: Taylor series method – Euler and modified Euler methods – Fourth order Runge – Kutta method for solving first and second order equations – Multistep methods: Milne’s and Adam’s predictor and corrector methods.
5. BOUNDARY VALUE PROBLEMS IN ordinary AND PARTIAL DIFFERENTIAL EQUATIONS 9
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.
L = 45 T = 15 Total = 60
TEXT BOOKS
1. C.F. Gerald and P.O. Wheatley, ‘Applied Numerical Analysis’, Sixth Edition, Pearson Education Asia, New Delhi, 2002.
2. E. Balagurusamy, ‘Numerical Methods’, Tata McGraw Hill Pub.Co.Ltd, New Delhi, 1999.
REFERENCE BOOKS
1. P. Kandasamy, K. Thilagavathy and K. Gunavathy, ‘Numerical Methods’, S.Chand Co. Ltd., New Delhi, 2003.
2. R.L. Burden and T.D. Faires, ‘Numerical Analysis’, Seventh Edition, Thomson Asia Pvt. Ltd., Singapore, 2002.
CE1251 MECHANICS OF SOILS 3 0 0 100
OBJECTIVE
After undergoing this course, the student gains adequate knowledge on engineering properties of soil.
1. INTRODUCTION 10
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.
2. SOIL WATER AND WATER FLOW 8
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.
3. STRESS DISTRIBUTION, COMPRESSIBILITY AND SETTLEMENT 10
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
4. SHEAR STRENGTH 9
Shear strength of cohesive and cohesionless soils - Mohr - Coulomb failure theory – Saturated soil and unsaturated soil (basics only) - 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.
5. SLOPE STABILITY 8
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.
TOTAL : 45
TEXT BOOKS:
Punmia P.C., “Soil Mechanics and Foundations”, Laximi Publications Pvt. Ltd., New Delhi, 1995.
Gopal Ranjan and Rao A.S.R., “Basic and applied soil mechanics”, New Age International Publishers, New Delhi, 2000.
Venkatramaiah, C. “Geotechnical Engineering”, New Age International Publishers, New Delhi, 1995
Khan I.H., “A text book of Geotechnical Engineering”, Prentice Hall of India, New Delhi, 1999.
REFERENCES
Coduto, D.P., “Geotechnical Engineering Principles and Practices”, Prentice Hall of India Private Limited, New Delhi, 2002.
McCarthy D.F., “Essentials of Soil Mechanics and Foundations Basic Geotechniques”, Sixth Edition, Prentice-Hall, New Jersey, 2002.
Das, B.M, “Principles of Geotechnical Engineering”, (fifth edition), Thomas Books/ cole, 2002
Muni Budhu, “Soil Mechanics and Foundations”, John Willey & Sons, Inc, New York, 2000.
CE1252 STRENGTH OF MATERIALS 3 1 0 100
OBJECTIVE
This subject is useful for a detailed study of forces and their effects along with some suitable protective measures for the safe working condition. This knowledge is very essential for an engineer to enable him in designing all types of structures and machines.
1. ENERGY PRINCIPLES 9
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
2. INDETERMINATE BEAMS 9
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)
3. COLUMNS 9
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.
4. STATE OF STRESS IN THREE DIMENSIONS 9
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
5. ADVANCED TOPICS IN BENDING OF BEAMS 9
Unsymmetrical bending of beams of symmetrical and unsymmetrical sections – curved beams – Winkler Bach formula – stress concentration – fatigue and fracture.
TUTORIALS 15
TOTAL : 60
TEXT BOOKS
Egor P Popov, “Engineering Mechanics of Solids”, Prentice Hall of India, New Delhi, 2003
V.N. Vazirani, M.M.Ratwani, “Analysis of Structures”, Vol-1, Khanna Publishers, New Delhi
REFERENCES
Kazimi S.M.A, “Solid Mechanics”, Tata McGraw-Hill Publishing Co., New Delhi, 2003
William Nash, “Theory and Problems of Strength of Materials”, Schaum’s Outline Series, McGraw Hill International Edition
3. R.S. Khurmi, “Strength of Materials”, S. Chand & Company Ltd, New Delhi, 2003
CE1253 APPLIED HYDRAULIC ENGINEERING 3 1 0 100
OBJECTIVE
Student is introduced to open channel flow characteristics including hydraulic jump and surges. Hydraulic machines viz flow through turbines and pumps including their performance characteristics and design aspects are taught. Student, at the end of the semester will have the abilities to analyse flow characteristics in open channel and design hydraulic machines.
1. OPEN CHANNEL FLOW 8
Open channel flow – Types and regimes of flow – Velocity distribution in open channel – Wide open channel – Specific energy – Critical flow and its computation.
2. UNIFORM FLOW 8
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
3. VARIED FLOW 10
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 – Surge channel transitions.
4. TURBINES 10
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
5. PUMPS 9
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.
TUTORIAL 15
TOTAL : 60
TEXT BOOKS
1. Subramanya K., "Flow in Open channels", Tata McGraw-Hill Publishing Company, 1994.
2. Kumar K.L., "Engineering Fluid Mechanics", Eurasia Publishing House (P) Ltd., New Delhi, (7th Edition), 1995.
3. Jain A.K., "Fluid Mechanics (including Hydraulic Machines)", Khanna Publishers, 8th edition, 1995.
4. Ranga Raju, K.G., “Flow through Open Channels”, Tata McGraw-Hill, 1985
CE1254 SURVEYING II 3 0 0 100
OBJECTIVE
At the end of the course the student will posses knowledge about Tachometric surveying, Control surveying, Survey adjustments, Astronomical surveying and Photogrametry.
1. TACHEOMETRIC SURVEYING 6
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.
2. CONTROL SURVEYING 8
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
3. SURVEY ADJUSTMENTS 8
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.
4. ASTRONOMICAL SURVEYING 11
Celestial sphere - Astronomical terms and definitions - Motion of sun and stars - Apparent altitude and corrections - Celestial co-ordinate systems - Different time systems - Nautical almanac - Star constellations - Practical astronomy - Field observations and calculations for azimuth.
5. OTHER TOPICS 12
Photogrammetry - Introduction - Terrestial and aerial Photographs - Stereoscopy - Parallax - Electromagnetic distance measurement - Carrier waves - Principles - Instruments - Trilateration - 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 - Cartography - Cartographic concepts and techniques - Cadastral surveying - Definition - Uses - Legal values - Scales and accuracies.
TOTAL : 45
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.
REFERENCES
1. Clark D., Plane and Geodetic Surveying, Vols. I and II, C.B.S. Publishers and Distributors, Delhi, Sixth Edition, 1971.
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, New York, Fifth Edition, 1984.
5. Heribert Kahmen and Wolfgang Faig, Surveying, Walter de Gruyter, 1995.
6. Kanetkar T.P., Surveying and Levelling, Vols. I and II, United Book Corporation, Pune, 1994.
CE1255 HIGHWAY ENGINEERING 3 0 0 100
OBJECTIVE
The objective of the course is to educate the students on the various components of Highway Engineering. It exposes the students to highway planning, engineering surveys for highway alignment, Design of Geometric Elements of Highways and Urban roads, Rigid and Flexible pavements design. The students further learn the desirable properties of highway materials and various practices adopted for construction. This course enables the students to develop skill on evaluation of the pavements and to decide appropriate types of maintenance.
1. HIGHWAY PLANNING AND ALIGNMENT 9
Tresaguet and Macadam’s method of Road Construction, Highway Development in India - Jayakar Committee Recommendations and Realisations, Twenty-year Road Development Plans, Concepts of On-going 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.
2. GEOMETRIC DESIGN OF HIGHWAYS 9
Design of Horizontal Alignments – Superelevation, Widening of Pavements on Horizontal Curves and Transition Curves [Derivation of Formulae and Problems]
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 [IRC Standards Only]
3. DESIGN OF RIGID AND FLEXIBLE PAVEMENTS 9
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 [CBR method, IRC Method and Recommendations- Problems]
Design Practice for Rigid Pavements – [IRC Recommendations-Problems] – Joints
4. HIGHWAY MATERIALS AND CONSTRUCTION PRACTICE 9
Desirable Properties and Testing of Highway Materials: - (Tests have to be demonstrated in Highway Engineering Laboratory)
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]
5. HIGHWAY MAINTENANCE 9
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 [Procedure only], Principles of Highway Financing
TOTAL : 45
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. IRC Standards (IRC 37 - 2001 & IRC 58 -1998)
2. Bureau of Indian Standards (BIS) Publications on Highway Materials
3. Specifications for Road and Bridges, MORTH (India)
CE1256 STRENGTH OF MATERIALS LABORATORY 0 0 3 100
OBJECTIVE
The experimental work involved in this laboratory should make the student understand the fundamental modes of loading of the structures and also make measurements of loads, displacements and strains. Relating these quantities, the student should be able to obtain the strength of the material and stiffness properties of structural elements.
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
Tests on springs
Hardness tests
Shear test
Test for impact resistance
The student should learn the use of deflectometer, extensometer, compressometer and strain gauges.
LIST OF EQUIPMENTS
(For a batch of 30 students)
| Sl. No. | Description of Equipments | Quantity |
| 1. | UTM of minimum 400 KN capacity | 1 |
| 2. | Torsion testing machine for steel rods | 1 |
| 3. | Izod impact testing machine | 1 |
| 4. | Hardness testing machine Rockwell Vicker’s (any 2) Brinnel | 1 each |
| 5. | Beam deflection test apparatus | 1 |
| 6. | Extensometer | 1 |
| 7. | Compressometer | 1 |
| 8. | Dial gauges | Few |
CE1257 HYDRAULIC ENGINEERING LAB 0 0 3 100
OBJECTIVE
Student should be able to verify the principles studied in theory by conducting the experiments.
LIST OF EXPERIMENTS
Determination of co-efficient of discharge for orifice
Determination of co-efficient of discharge for notches
Determination of co-efficient of discharge for venturimeter
Determination of co-efficient of discharge for orifice meter
Study of impact of jet on flat plate (normal / inclined)
Study of friction losses in pipes
Study of minor losses in pipes
Study on performance characteristics of Pelton turbine.
Study on performance characteristics of Francis turbine
Study on performance characteristics of Kaplan turbine
Study on performance characteristics of Centrifugal pumps (Constant speed / variable speed)
Study on performance characteristics of reciprocating pump.
LIST OF EQUIPMENTS
1. Bernoulli’s theorem – Verification Apparatus - 1 No.
2. Calculation of Metacentric height
water tank - 1 No.
Ship model with accessories - 1 No.
3. Measurement of velocity
Pirot tube assembly - 1 No.
4. Flow measurement
open channel flow
(i) Channel with provision for fixing notches
(rectangular, triangular & trapezoidal forms) - 1 Unit
(ii) Flume assembly with provisions for conducting
experiments on Hydraulic jumps, generation of
surges etc. - 1 Unit
5. Flow measurement in pipes
Venturimeter, U tube manometer fixtures like
Valves, collecting tank - 1 Unit
Orifice meter, with all necessary fittings in
pipe lines of different diameters - 1 Unit
Calibration of flow through orifice tank with
Provisions for fixing orifices of different shapes,
collecting tank - 1 Unit
Calibration of flow through mouth piece
Tank with provisions for fixing mouth pieces
Viz external mouth pieces & internal mouth piece
Borda’s mouth piece - 1 Unit
6. Losses in Pipes
Major loss – Friction loss
Pipe lengths (min. 3m) of different diameters with
Valves and pressure rapping & collecting tank - 1 Unit
Minor Losses
Pipe line assembly with provisions for having
Sudden contractions in diameter, expansions
Bends, elbow fitting, etc. - 1 Unit
7. Pumps
Centrifugal pump assembly with accessories
(single stage) - 1 Unit
Centrifugal pump assembly with accessories
(multi stage) - 1 Unit
(iii) Reciprocating pump assembly with accessories - 1 Unit
(iv) Deep well pump assembly set with accessories - 1 Unit
8. Turbine
(i) Impulse turbine assembly with fittings
& accessories - 1 Unit
Francis turbine assembly with fittings
& accessories - 1 Unit
Kaplan turbine assembly with fittings
& accessories - 1 Unit
CE1258 SURVEY PRACTICAL II 0 0 4 100
OBJECTIVE
At the end of the course the student will posses knowledge about Survey field techniques.
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. Demonstration of EDM.
TOTAL : 60
