Introduction To Engineering Mechanics

Definition

The branch of applied mathematics or Engineering science dealing with motion and forces producing motion is called mechanics. It basically deals with various laws of nature and by using them we can find solutions to our Engineering problems.

It can be further divided in two main branches:

1. Statics: It deals with the study of bodies at rest.
2. Dynamics: It deals with the study of bodies in motion.

Fundamental Concepts

1. Space: To fix the position of a point
2. Time: To relate the sequence of events
3. Mass: To distinguish behaviour of the two bodies under the action of an identical force. 
4. Force: It is an essential agency which changes or tend to change the state of rest or uniform motion of body.

Fundamental Principles

1. Newton's Three Laws of motion
2. Newton's Law of Gravitation
3. The parallelogram Law for Addition of forces
4. The principle of transmissibility of forces.

Fundamental units

In mechanics there are three basic units to express any unit which is internationally accepted.

1. Length
2. Mass
3. Time
   

Derived units

Those units derived from the fundamental units are called derived units.

Eg. Unit of velocity, area, volume, pressure etc

System of Units

1. C.G.S. - centimeter-gram-second system
2. F.P.S. - foot-pound-second system
3. M.K.S. - metre-kilogram-second system
4. S.I. - International system of units
   

Quantities

It may be either scalar or vector

1. Scalar quantity: Those quantities which have magnitude only such as length, mass, time, distance, volume, density, temperature etc.
2. Vector quantity: those quantities which have both magnitude and direction such as force, displacement, velocity, acceleration, momentum etc.

Methods of problem solution

On the basis of definitions of concurrent, co-planer, non concurrent, non co-planer forces, there are mainly two methods for problem solutions:

Analytical methods

Law of parallelogram, Lami's theorem, Resolution and addition of forces, Conditions of equilibrium, free body diagrams, Joint method in truss, section method in truss etc.

Graphics Statics

In general this deals with drawing space diagram and vector diagram

e.g. law of triangle, Funnicular Polygon etc.