A Textbook Of Engineering Mechanics (GBTU)

Engineering mechanics is that branch of science which deals with the behaviour of a
body when the body is at rest or in motion. The engineering mechanics may be divided into
Statics and Dynamics. The branch of science, which deals with the study of a body when the
body is at rest, is known as Statics while the branch of science which deals with the study of a
body when the body is in motion, is known as Dynamics. Dynamics is further divided into
kinematics and kinetics. The study of a body in motion, when the forces which cause the
motion are not considered, is called kinematics and if the forces are also considered for the
body in motion, that branch of science is called kinetics.

Coplanar forces means the forces in a plane. The word collinear stands for the forces
which are having common lines of action whereas the word concurrent stands for the forces
which intersect at a common point. When several forces act on a body, then they are called a
force system or a system of forces. In a system in which all the forces lie in the same plane, it is
known as coplanar force system. Hence this chapter deals with a system of forces which are
acting in the same plane and the forces are either having a common line of action or intersecting
at a common point.

The forces, which are having their line of actions parallel to each other, are known
parallel forces. The two parallel forces will not intersect at a point. The resultant of two coplanar
concurrent forces (i.e., forces intersecting at the same point) can be directly determined by the
method of parallelogram of forces. This method along with other methods for finding resultant
of collinear and concurrent coplanar forces, were discussed in earlier chapters.
The parallel forces are having their lines of action parallel to each other. Hence, for
finding the resultant of two parallel forces, (two parallel forces do not intersect at a point) the
parallelogram cannot be drawn. The resultant of such forces can be determined by applying
the principle of moments. Hence in this chapter first the concepts of moment and principle of
moments will be dealt with. Thereafter the methods of finding resultant of parallel and even
non-parallel forces will be explained.

When some external forces (which may be concurrent or parallel) are acting on a
stationary body, the body may start moving or may start rotating about any point. But if the
body does not start moving and also does not start rotating about any point, then the body* is
said to be in equilibrium. In this chapter, the conditions of equilibrium for coplanar concurrent
forces (i.e., forces meeting at a point) and for coplanar parallel forces will be described. Also
the concept of free body diagram, different types of support reactions and determination of
reactions will be explained.

When a number of forces are acting on a body, and the body is supported on another
body, then the second body exerts a force known as reactions on the first body at the points of
contact so that the first body is in equilibrium. The second body is known as support and the
force, exerted by the second body on the first body, is known as support reactions.

When a solid body slides over a stationary solid body, a force is exerted at the surface of
contact by the stationary body on the moving body. This force is called the force of friction and
is always acting in the direction opposite to the direction of motion. The property of the bodies
by virtue of which a force is exerted by a stationary body on the moving body to resist the
motion of the moving body is called friction. Friction acts parallel to the surface of contact and
depends upon the nature of surface of contact.

A structure made up of several bars (or members) riveted or welded together is known
as truss. The isometric view of a structure made of trusses is shown in Fig. 7.1 (a) and front
view is shown in Fig. 7.1 (b). If the members of the structure are hinged or pin-joined, then the
structure is known as a Frame. Hence the difference between truss and frame is that incase of
truss members are riveted or welded whereas incase of frame the members are hinged or pinjoined.
If the frame is composed of such members which are just sufficient to keep the frame in
equilibrium, when the frame is supporting an external load, then the frame is known as perfect frame. Though in actual practice the members are welded or riveted together at their joints,
yet for calculation purposes the joints are assumed to be hinged or pin-joined. In this chapter,
we shall discuss how to determine the axial forces in the members of a perfect frame, when it
is subjected to some external load.

The following are the important types of beams :
1. Cantilever beam, 2. Simply supported beam,
3. Overhanging beam, 4. Fixed beams, and
5. Continuous beam.
8.1.1. Cantilever Beam. A beam which is fixed at one end and free at the other end, is
known as cantilever beam. Such beam is shown in Fig. 8.1. At the fixed end, there will be
fixing moment. Also at the fixed end, there can be horizontal and vertical reactions, depending
upon the type of load acting on the beam.

Centre of gravity of a body is the point through which the whole weight of the body acts.
A body is having only one centre of gravity for all positions of the body. It is represented by
C.G. or simply G.

Kinematics is that branch of Engineering Mechanics which deals with motion of particles
and bodies without consideration of forces required to produce them. Hence, the term kinematic
stands for the displacement, velocity and acceleration of a particle or of a body. Particle is a
body whose size can be neglected whereas the rigid body is a body in which the distance
between any two points remains fixed for all the time.

Kinetics is that branch of Engineering Mechanics which deals with the force system
which produces acceleration and resulting motion of bodies. In the previous chapter i.e., chapter
of Kinematics of Rigid Bodies, we have dealt with the motion of the bodies (i.e., displacement,
velocity and acceleration of Rigid bodies) without consideration of the forces which produce
these motion.

When an external force acts on a body, the body tends to undergo some deformation.
Due to cohesion between the molecules, the body resists deformation. This resistance by which
material of the body opposes the deformation is known as strength of material. Within a
certain limit (i.e., in the elastic stage) the resistance offered by the material is proportional to
the deformation brought out on the material by the external force. Also within this limit the
resistance is equal to the external force (or applied load). But beyond the elastic stage, the
resistance offered by the material is less than the applied load. In such a case, the deformation
continues, until failure takes place.

When a body is subjected to an axial tensile load, there is an increase in the length of
the body. But at the same time there is a decrease in other dimensions of the body at right
angles to the line of action of the applied load. Thus the body is having axial deformation and
also deformation at right angles to the line of action of the applied load (i.e., lateral deformation).
This chapter deals with these deformations, Poisson’s ratio, volumetric strains, bulk modulus,
relation between Young’s modulus and modulus of rigidity and relation between Young’s
modulus and bulk modulus.

Whenever a body is strained, the energy is absorbed in the body. The energy, which is
absorbed in the body due to straining effect is known as strain energy. The straining effect
may be due to gradually applied load or suddenly applied load or load with impact. Hence the
strain energy will be stored in the body when the load is applied gradually or suddenly or with
an impact. The strain energy stored in the body is equal to the work done by the applied load
in stretching the body.

When some external load acts on a beam, the shear force and bending moments are set
up at all sections of the beam. Due to the shear force and bending moment, the beam undergoes
certain deformation. The material of the beam will offer resistance or stresses against
these deformations. These stresses with certain assumptions can be calculated. The stresses
introduced by bending moment are known as bending stresses. In this chapter, the theory of
pure bending, expression for bending stresses, bending stress in symmetrical sections will be
discussed.

A shaft is said to be in torsion, when equal and opposite torques are applied at the two
ends of the shaft. The torque is equal to the product of the force applied (tangentially to the
ends of a shaft) and radius of the shaft. Due to the application of the torques at the two ends,
the shaft is subjected to a twisting moment. This causes the shear stresses and shear strains
in the material of the shaft. Twisting moment is due to twist.

Objective Type Questions