BASICS OF ENGINEERING MECHANICS

  

DEFINITION

·         The subject of Engineering Mechanics is that branch of Applied Science, which deals with the Laws and principles of Mechanics, along with their applications to engineering problems.

·         As a matter of fact, knowledge of Engineering Mechanics is very essential for an engineer in planning, designing and construction of his various types of structures and machines.

·         In order to take up his job more skilfully, an engineer must peruse the study of Engineering Mechanics in a most systematic and scientific manner.

DIVISIONS OF ENGINEERING MECHANICS

·       The subject of Engineering Mechanics may be divided into the following two main groups:

·       Statics and Dynamics.

STATICS

·         It is that branch of Engineering Mechanics, which deals with the forces and their effects, while acting upon the bodies at rest.

DYNAMICS

·         It is that branch of Engineering Mechanics, which deals with the forces and their effects, while acting upon the bodies in motion.

·         The subject of Dynamics may be further sub-divided into the following two branches:

·         Kinetics and Kinematics.

KINETICS

·         It is the branch of Dynamics, which deals with the bodies in motion due to the application of forces.

KINEMATICS

·         It is that branch of Dynamics, which deals with the bodies in motion, without any reference to the forces which are responsible for the motion.

FUNDAMENTAL UNITS

·         The measurement of physical quantities is one of the most important operations in engineering. Every quantity is measured in terms of some arbitrary, but internationally accepted units, called fundamental units.

·         All the physical quantities, met with in Engineering Mechanics, are expressed in terms of three fundamental quantities, i.e.

·         Length, Mass and Time.

DERIVED UNITS

·         Sometimes, the units are also expressed in other units (which are derived from fundamental units) known as derived units e.g. units of area, velocity, acceleration, pressure etc.

SYSTEMS OF UNITS

·         There are only four systems of units, which are commonly used and universally recognised. These are known as:

·         C.G.S. units, F.P.S. units, M.K.S. units and S.I. units.

·         In this book, we shall use only the S.I. system of units, as the future courses of studies are conducted in this system of units only.

S.I. UNITS (INTERNATIONAL SYSTEM OF UNITS)

·         The eleventh General Conference* of Weights and Measures has recommended a unified and systematically constituted system of fundamental and derived units for international use. This system of units is now being used in many countries.

·         In India, the Standards of Weights and Measures Act of 1956 (vide which we switched over to M.K.S. units) has been revised to recognise all the S.I. units in industry and commerce.

·         In this system of units, the †fundamental units are metre (m), kilogram (kg) and second (s) respectively. But there is a slight variation in their derived units. The following derived units will be used in this book:

Density (Mass density) kg / m³

Force N (Newton)

Pressure N/mm² or N/m²

Work done (in joules) J = N-m

Power in watts W = J/s

International metre, kilogram and second are discussed here.

 

METRE

·         The international metre may be defined as the shortest distance (at 0°C) between two parallel lines engraved upon the polished surface of the Platinum-Iridium bar, kept at the International Bureau of Weights and Measures at Sevres near Paris.

KILOGRAM

·         The international kilogram may be defined as the mass of the Platinum-Iridium cylinder, which is also kept at the International Bureau of Weights and Measures at Sevres near Paris.

SECOND

·         The fundamental unit of time for all the four systems is second, which is 1/(24 × 60 × 60) = 1/86 400th  of the mean solar day.

·         A solar day may be defined as the interval of time between the instants at which the sun crosses the meridian on two consecutive days. This value varies throughout the year.

      ·         The average of all the solar days, of one year, is called the mean solar day. 

SCALAR QUANTITIES

·         The scalar quantities (or sometimes known as scalars) are those quantities which have magnitude only such as length, mass, time, distance, volume, density, temperature, speed etc.

VECTOR QUANTITIES

·         The vector quantities (or sometimes known as vectors) are those quantities which have both magnitude and direction such as force, displacement, velocity, acceleration, momentum etc. Following are the important features of vector quantities:

REPRESENTATION OF A VECTOR.

·         A vector is represented by a directed line as shown in Fig. It may be noted that the length OA represents the magnitude of the vector O^—→A.

·         The direction of the vector is O^—→A is from O (i.e., starting point) to A (i.e., end point). It is also known as vector P.

·         Unit vector. A vector, whose magnitude is unity, is known as unit vector.

·         Equal vectors. The vectors, which are parallel to each other and have same direction (i.e., same sense) and equal magnitude are known as equal vectors.

·         Like vectors. The vectors, which are parallel to each other and have same sense but unequal magnitude, are known as like vectors.

·         Addition of vectors. Consider two vectors PQ and RS, which are required to be added as shown in Fig.