# Engineering Mechanics for BTech First Year

This is an online topic wise solutions & notes on Engineering Mechanics for BTech First Year students.

### UNIT-1 Force Systems Basic concepts:

Definitions
Basic assumptions
Scalar quantities
Vector quantities
Free, Forced and fixed vectors
Force Classification & Representation
Force as a Vector
Composition of forces
Parallelogram Law Resolution
Principle of Transmissibility of forces
Moment of a force
Vector representation
Moment for coplanar force system
Varignon’s Theorem
Couple & Vector representation
Resolution of a force into a force and a couple
Coplanar Concurrent Force system
Coplanar Non Concurrent force systems
Resultant of coplanar force system
Equilibrium of coplanar force system
Free body diagrams
Determination of reactions
Equilibrium of a body under three forces
Lami’s theorem.

### UNIT-2 Basic Structural Analysis:

Plane Truss
Difference between truss and frame
Perfect and imperfect truss
Assumptions and Analysis of Plane Truss
Method of joints
Method of section
Zero force members
Beams
Types of beams
Statically Determinate Beams
Shear force and bending moment in beams
Shear force and bending moment diagrams
Relationships between load, shear and bending moment.

### UNIT-3 Centroid and Moment of Inertia:

Center of Gravity
Center of Mass and Centroid of curves, areas,
volumes, Determination of centroid by integration
Centroid of composite bodies
Definition of Moment of inertia of area
Perpendicular axis theorem
Polar moment of Inertia
Parallel axis theorem
Moment of inertia of simple areas by integration
Moment of Inertia of Composite Areas
Moment of Inertia of masses
Parallel axis theorem for mass moment of inertia
Mass moment of inertia of simple bodies by integration
Mass moment of inertia of composite bodies

### UNIT-4 Kinematics of Rigid Body :

Introduction
Absolute motion
Plane rectilinear motion of rigid body
Plane curvilinear Motion of rigid body
x-y and n-t components
Rotation of rigid bodies
Relative Motion
Plane
Motion of rigid bodies
Instantaneous center of zero velocity.

### Kinetics of Rigid Body:

Introduction
Force
Mass and Acceleration
Newton’s law of motion
D’Alembert’s Principles and Dynamic Equilibrium
Laws of motion applied to planar translation
rotation and plane motion
Work and Energy
Kinetic energy
Principle of work and energy
Conservative forces
Law of conservation of energy
Linear Impulse and Momentum
Conservation of linear momentum.

### UNIT-5 Mechanics of Deformable Solids:

Simple stress and strain:
Normal and shear stresses
Members of varying cross section
Bars in series
Tensile Test diagram for ductile and brittle materials
Elastic constants
Strain energy

Bending of Beams:

Theory of pure bending
Neutral surface and neutral axis
Stresses in beams of different cross sections

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