COURSE FILE: ©subhankar_karmakar |

## COURSE FILE:

**INSTITUTE NAME : VIVEKANAND INSTITUTE OF TECHNOLOGY AND SCIENCE**

**SUBJECT NAME : ENGINEERING MECHANICS**

**SUBJECT CODE : EME-102**

**FACULTY NAME : SUBHANKAR KARMAKAR**

**DEPARTMENT : MECHANICAL ENGINEERING DEPARTMENT**

**YEAR : FIRST YEAR**

## INDEX:

**1 : LESSON PLAN**

2 : TIMETABLE

3 : COURSE PLAN

4 : ASSIGNMENT

5 : LECTURE NOTES

2 : TIMETABLE

3 : COURSE PLAN

4 : ASSIGNMENT

5 : LECTURE NOTES

## LESSON PLAN : EME-102 / 202 : ENGINEERING MECHANICS

UNIT | TOPICS SYNOPSIS | No. of Lectures | DATE |

UNIT I | Two Dimensional Force Systems: Basic concepts, Laws of motion, Principle of Transmissibility of forces, Transfer of a force to parallel position , Resultant of a force system, Simplest Resultant of Two dimensional concurrent and Non-concurrent Force systems, Distributed force system, Free body diagrams, Equilibrium and Equations of Equilibrium, Applications. | 5 | date |

UNIT I | Friction: Introduction, Laws of Coulomb Friction, Equilibrium of Bodies involving Dry-friction, Belt friction, Application. | 3 | date |

UNIT II | Beam: Introduction, Shear force and Bending Moment, Differential Equations for Equilibrium, Shear force and Bending Moment Diagrams for Statically Determinate Beams. | 5 | date |

UNIT II | Trusses: Introduction, Simple Truss and Solution of Simple truss, Method f Joints and Method of Sections. | 3 | date |

UNIT III | Centroid and Moment of Inertia: Centroid of plane, curve, area, volume and composite bodies, Moment of inertia of plane area, Parallel Axes Theorem, Perpendicular axes theorems, Principal Moment Inertia, Mass Moment of Inertia of Circular Ring, Disc, Cylinder, Sphere and Cone about their Axis of Symmetry. | 6 | date |

UNIT IV | Kinematics of Rigid Body: Introduction, Plane Motion of Rigid Body, Velocity and Acceleration under Translation and Rotational Motion, Relative Velocity. | 4 | date |

UNIT IV | Kinetics of Rigid Body: Introduction, Force, Mass and Acceleration, Work and Energy, Impulse and Momentum, D’Alembert’s Principles and Dynamic Equilibrium. | 4 | date |

UNIT V | Simple Stress and Strain: Introduction, Normal and Shear stresses, Stress- Strain Diagrams for ductile and brittle material, Elastic Constants, One Dimensional Loading of members of varying cross-sections, Strain energy. | 3 | date |

UNIT V | Pure Bending of Beams: Introduction, Simple Bending Theory, Stress in beams of different cross sections. | 3 | date |

UNIT V | Torsion: Introduction, Torsion of shafts of circular section, torque and twist, shear stress due to torque. | 3 | date |

**Text books:**

1. Engineering Mechanics by Irving H. Shames, Prentice-Hall

2. Mechanics of Solids by Abdul Mubeen, Pearson Education Asia.

3. Mechanics of Materials by E.P.Popov, Prentice Hall of India Private Limited.

1. Engineering Mechanics by Irving H. Shames, Prentice-Hall

2. Mechanics of Solids by Abdul Mubeen, Pearson Education Asia.

3. Mechanics of Materials by E.P.Popov, Prentice Hall of India Private Limited.

## TIME TABLE:

DAY | 9.30 | 10.20 | 11.10 | 12.00 | LUNCH | 1.40 | 2.30 | 3.20 | 4.10 |

MON | 9.30 | ME-D | 11.10 | ME-F | LUNCH | 1.40 | ME-D | 3.20 | ME-D |

TUE | 9.30 | ME-D | 11.10 | 12.00 | LUNCH | ME-F | 2.30 | ME-D | 4.10 |

WED | ME-F | 10.20 | ME-D | 12.00 | LUNCH | 1.40 | 2.30 | 3.20 | 4.10 |

THU | ME-D | 10.20 | 11.10 | ME-F | LUNCH | 1.40 | 2.30 | 3.20 | 4.10 |

FRI | 9.30 | ME-F | 11.10 | ME-D | LUNCH | 1.40 | 2.30 | 3.20 | 4.10 |

SAT | ME-D | 10.20 | ME-F | 12.00 | LUNCH | ME-F | 2.30 | 3.20 | 4.10 |

## COURSE PLAN:

**SUBJECT NAME: ENGINEERING MECHANICS**

SUBJECT CODE : EME-102

SCOPE :The course aims to provide deeper knowledge, a wider scope and improved understanding of the study of motion and the basic principles of mechanics and strength of materials. It is a concept based subject and it needs the application capabilities of the concepts on the part of the students.

SUBJECT CODE : EME-102

SCOPE :

### SESSIONAL EVALUATION SCHEME:

PARTICULAR | WEIGHTAGE | MARKS |

TWO SESSIONALS | 60% | 30 |

ATTENDANCE | 20% | 10 |

TEACHER'S ASSESSMENT(TA)* | WEIGHTAGE | MARKS |

*TA will be based on the Assignments given, Unit test Performances and Attendance in the class for a particular student.

### Lecture Schedule of Unit – 1

Total Number of Lectures: 8

• Lecture Details & Synopsis :

• Lecture- 1: Introduction, mass, particle, rigid body, position vector, change of position, velocity, momentum, change of momentum, force acceleration, Newton’s law of motion, conservation of momentum, conservation of energy.

• Lecture- 2: Definition of force, characteristics of force, Force as a vector, Force addition, triangle’s & parallelogram laws of force addition, magnitudes & direction of resultant force, negative force, resolution of force, oblique and orthogonal resolutions, component of a vector along a line, classification of a force system, force system in one dimension, like & unlike forces, two dimensional force system, co-planar force system, non coplanar force system, concurrent force system, coplanar concurrent force system, coplanar parallel force system

• Lecture- 3: The concepts of rigid body, principle of transmissibility of forces, resultant of coplanar concurrent force system, equilibrium of forces, conditions of static equilibrium for concurrent force system, actions & reactions in case of equilibrium in (i) spherical balls in a channel, (ii) blocks of mass in an inclined plane, (iii) reactions in strings, wires & ropes. Types of force (i) tension (ii) compression. Concepts of free body diagrams. Lami’s theorem.

• Lecture- 4: Applications of the conditions of static equilibrium in case of concurrent forces in the analysis of a concurrent force system & numericals based on this. Numericals based on the resultant of a force system. Numericals based on Lami’s theorem.

•Lecture- 5: Normal reactions, concepts of friction, angle of friction, coefficient of friction, angle of repose, laws of coulomb friction, limiting friction, coefficient of static friction & kinematics friction, Equilibrium of bodies involving dry friction. Use of Friction, Friction as a necessary EVIL.

• Lecture- 6: Numericals based on static friction, ladder friction, friction in inclined plane, numericals on ladder friction & friction in inclined plane. Objective type questions in friction.

• Lecture- 7: Theory of Belt Friction, Slack & tight side of a belt, Concepts of Included angle, power delivered by belt drive, Numericals on Belt friction & objective type Questions.

• Lecture- 8: Doubt clearing Sessions on Unit- 1, (Static Equilibrium Analysis, Resultant Forces, Resolution of Forces, Lami’s Theorem, Concepts of Dry & belt Friction.)

•Reference books:

•(i)Engineering Mechanics by Timoshenko & Young

(ii)Engineering Mechanics by R. K. Rajput

(iii) Engineering Mechanics by Irving H. Shames

### Lecture Schedule of Unit – 2

Total Number of Lectures: 8

• Lecture Details & Synopsis:

• Lecture- 9: Concepts of Beam, Classification of Beams, simply supported beam, cantilever beam, over hanging beam, continuous beam,Types of Support Reactions, Pin/hinged joints, Roller joints, fixed joints, determination of support reactions in beam, types of loading in beams, concentrated load, distributed load on the beam, uniformly distributed load (UDL), uniformly varying load (UVL), pure moment loading.

• Lecture- 10: Concepts of Shear Force, sign convention for shear force, determination of shear force at each point of the beam over the complete length of the beam, shear force diagrams (SFD), differential equations for equilibrium, concepts of bending moments, sign conventions for bending moments, determination of bending moments at each point of the beam over the complete length of the beam, bending moment diagrams (BMD), maximum bending moment, point of contra-flexure and its importance.

• Lecture- 11: SFD & BMD in case of (i) simply supported beam, (ii) cantilever beam, (iii) over-hanging beam with (a) concentrated loading, (b) uniformly distributed loading, (c) uniformly varying loading.

• Lecture- 12: Numericals on SFD & BMD for all types of beam.

• Lecture- 13: Numericals on SFD & BMD for all types of beam and to find point of contra-flexure.

• Lecture- 14: Concepts of Truss, Linkages, and Joints, Classification of Trusses, Perfect Truss, Deficient Truss, Redundant Truss, Simple Truss, Analysis of a Truss by (i) Method of Joints (ii) Method of Sections.

• Lecture- 15: Numericals on Truss analysis by method of joints & method of Sections.

• Lecture- 16: Numericals on Truss analysis by method of sections.

### Lecture Schedule of Unit – 3

Total Number of Lectures: 6

• Lecture Details & Synopsis:

• Lecture- 17: Concepts of geometrical Centroid, Center of Mass & Center of Gravity, Centroid of Plane, Curve, Area, & Volume, determination of centroid of composite bodies.

• Lecture- 18: Numericals on determination of Centroid of composite bodies.

• Lecture- 19: Concepts of Rotation & Moment of Inertia, concepts of area moment of inertia & mass moment of inertia, Determination of moment of Inertia with the help of calculus, Parallel axis theorem & Perpendicular axis theorem of Moment of Inertia.

• Lecture- 20: Concepts of Principal Moment of Inertia, determination of Mass Moment of Inertia of (i) Circular Ring, (ii) Disc, (iii) Cylinder, (iv) Sphere & (v) Cone about their axis of symmetry

• Lecture- 21: Numericals on determination of Moment of Inertia of different objects.

• Lecture- 22: Numericals on determination of M.O.I of different objects.

### Lecture Schedule of Unit – 4

Total Number of Lectures: 8

• Lecture Details & Synopsis:

• Lecture- 23: Introduction of rigid body, Motion of Rigid Body, Velocity & Acceleration under Translational Motion, Equation of motion due to gravity, concepts of Relative Velocity, Problems on Projectile Motion.

• Lecture- 24: Concepts of Rotational Motion, Angular Displacement, Angular Velocity, Laws of Motion for Rotation, Concepts of Moment, Torque & Couple, Angular Acceleration, Relations between angular velocity & linear velocity, Relation between angular acceleration & linear acceleration, concepts of centripetal acceleration, concepts of Pseudo Force ie. Centrifugal acceleration.

• Lecture- 25: Motion on Level road, Banking of road & Super elevation of rails, Analysis of Slider-crank mechanism (Four bar mechanism) & numericals on rotational motion.

• Lecture- 26: Numericals on Rotational motion & its application.

• Lecture- 27: Concepts of Force, Newton’s Laws of Motion, Definition of Mass, Gravitational Mass & Inertial Mass, Concepts of Work & Energy, Conservation of Mass Principle, Principle of Conservation of Momentum.

• Lecture- 28: Principle of Conservation of Energy, Work- Energy Theorem, Concepts of Conservative Force & Potential Energy. Collision of two bodies, Elastic & Inelastic Collision, Impulse & Impulsive Force, Impulse & change of Momentum. Power.

• Lecture- 29: Concepts of Dynamic Equilibrium, Inertial Mass & D’ Alembert’s Principle of Dynamic Equilibrium, Motion on an Inclined Plane, Analysis of Lift Motion, Analysis of Motion of Connected Bodies (i) System of Pulleys (ii) Two Bodies connected by a string.

• Lecture- 30: Numericals on Dynamic Equilibrium & System of Pulleys.

### Lecture Schedule of Unit – 5

Total Number of Lectures: 10

• Lecture Details & Synopsis:

• Lecture- 31: Deformation of Rigid Bodies under the action of External Force, Resistance against deformation & induction of internal resistive force, Unit deformation & strain, internal force & stress, linear deformation and normal stress, Hooke’s Law & Modulus of Elasticity ( E, Young’s modulus), angular deformation, Shear Strain, & shear Stress, Modulus of Rigidity ( G ), Complimentary Shear Stress.

• Lecture-32: Simple Stress-Strain Diagrams for (i) Ductile Materials, (ii) Brittle Materials, One Dimensional Loading of members of Varying Cross Sections (i) Circular Bar of Uniform Taper, (ii) Bar of Uniform Strength (iii) Bar of (a) Uniform & (b) Taper Cross section due to Self Weight, (iv) Composite Bar, Impact loading (i) Gradually Applied load, (ii) Suddenly Applied Load.

• Lecture- 33: Concepts of Strain Energy & Resilience, Concepts of (i) Longitudinal & (ii) Lateral Strain, Poisson’s Ratio, Hydro-static Compression & Volumetric Strain, Bulk Modulus (K), relation between (i) E, G, & K, (ii) E, K, m (iii) E, G, m. simple numericals on stress & strain.

• Lecture- 34: Numericals on Simple Stress & Simple Strain, Shear Strain & Shear Stress, numericals on composite bars.

• Lecture- 35: Concepts of Pure Bending, Assumptions in simple theory of bending, Concepts of Bending Stress, Neutral Layer & Neutral Axis, Bending Stress Diagrams, Difference between Simple Stress & Bending Stress, Derivation of Bending Equation, Section Modulus (Z), Relation between max. Tensile & max. Compressive Stress,

• Lecture- 36: Stress in Beams of different cross sections, Numericals on Bending Stresses.

• Lecture- 37: Doubt clearance class on (i) stress, strain (ii) pure bending

• Lecture- 38: Introduction of Shaft & Torsion, concept of pure torsion, Polar Moment of Inertia ( J ), Section Modulus (Z), Polar Modulus ( Zp), Assumption for Deriving the Torsional Formulas, Torsional Equation,

• Lecture- 39: Torsional Rigidity or Torsional Stiffness ( K ), Comparison of strength of (i) Solid & (ii) Hollow Circular Shaft (Tmax), Power Transmission by a Shaft, Importance of Angle of Twist, numerical based on Torsion in Shaft.

• Lecture- 40: Doubt clearing classes on Torsion.

**• Reference Books:**

• Engineering Mechanics by R. S. Khurmi

• Engineering Mechanics by Bhavikatti

• Engineering Mechanics by D. S. Kumar.

• Engineering Mechanics by Timoshenko & Young.

• Engineering Mechanics by R. S. Khurmi

• Engineering Mechanics by Bhavikatti

• Engineering Mechanics by D. S. Kumar.

• Engineering Mechanics by Timoshenko & Young.

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