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.

**Friction:**

Introduction

Wet friction

Dry friction

Theory of Dry friction

Angle of friction

Angle of Repose

Cone of friction

Coulomb’s laws of friction.

**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

One Dimensional Loading

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