Mechanics of Solids

Chapter-1
Fundamental principles of mechanics

BITS Pilani, K K Birla Goa Campus

 Fundamental Principles of
Mechanics
Mechanics

Study of Force & Motion

Gross/Overall Motion Localized Motion (Deformation)

(Dynamics) (STATICS)

KINETICS KINEMATICS Rigid Bodies Deformable

bodies

BITS Pilani, K K Birla Goa Campus

Points to be studied
 Basic types of Force
 What is analysis ?
 Step-By-Step procedure to solve problems in mechanics of
solids
 Concept of force
 Causes of force, Classification, interaction of force
 System of forces
 Vector properties of the force
 Moment of the force
Fundamental Principles of
Mechanics
Definitions
 Body: A collection of particles is called a 'body'. It may be a rigid
body or an elastic or deformable body.
 Rigid Body: The particles in a rigid body are so firmly connected
together that their relative positions do not change irrespective of
the forces acting on it. Thus the size and shape of a rigid body are
always maintained constant
 Elastic Body: A body whose size and shape can change under
forces is a deformable body. When the size and shape can be
regained on removal of forces, the body is called an elastic body.

BITS Pilani, K K Birla Goa Campus

Fundamental Principles of
Mechanics
Definitions
Scalar Quantity: A quantity which is fully described by its
magnitude only is a scalar. Arithmetical operations apply to scalars.
Examples are: Time, mass, area and speed.
Vector Quantity: A quantity which is described by its magnitude and
also its direction is a vector. Operations of vector algebra are
applicable to vectors. Examples are: Force, velocity, moment of a
force and displacement .
Force: In physics, a net force acting on a body causes that body to
accelerate; that is, to change its velocity. The concept appeared first
in the second law of motion of classical mechanics.
BITS Pilani, K K Birla Goa Campus
Force:
Force: In physics, a net force acting on a
body causes that body to accelerate; that is,
to change its velocity. The concept
appeared first in the second law of motion
of classical mechanics
There are three basic kinds of forces as
mentioned below
•Tensile force or pull
•Compressive force or push
•Shear force
Compressive Force or Push:

•When equal and opposite forces act at

the ends of a rod or a bar towards the
ends along its axis, they tend to push
the rod or the bar. This kind of force is
called a compressive force or
compression
Tensile Force or Pull:
•When equal and opposite forces are applied at the
ends of a rod or a bar away from the ends, along its
axis, they tend to pull the rod or bar. This kind of a
force is called a tensile force or tension
Shear Force:
When equal and opposite forces act on the
parallel faces of a body, shear occurs on these
planes. The forces tend to make one part of the
material slide over the other part.
Load application

Tensile load
Compressive load
Shear load
Torsion
Bending moments
Along the axis
Offset loading
Combined loading
On
Deformable bodies
Structural elements
Machine elements
Machines
Machine tools
Examples of Mechanical systems
Automotive vehicles: Car, bus, Truck,
Tractor.
Railway vehicles: Locomotive, Wagon,
Passenger coaches
Farm Machinery: Pumps, Thrashers,
harvester-combine planter, seeder
Furniture: Almirah, Table, Chains,
Sofas, Benches
Machine Tools: Lathe, shaper, planer,
Grinder, -- etc
Earth moving machineries
Trusses, bridges, Framework
Turbines, compressors, pumps, Engines
Mechanical systems used in industries
e.g.
1.Textile
2.Automobile
3.Farm Machinery
4.Machine Tools_______etc Aero
planes, Missiles, Satellites, defense
equipments
Newtonian Mechanics
Proportionality of force and
acceleration for a particle
All velocities are small compared with
the speed of light
Deals in engineering the cases of no
acceleration when there is no unbalanced
force.
Permits to determine/ predict the
motion and deformation if the forces are
known and vice versa
Analysis of Mechanical systems
Study of forces
(Tensile, Compressive, Shear, Torque, Moments)
Study of motion
(Straight, curvilinear, displacement,
velocity,acceleration.)
•Gross overall changes in position with time
• Local distortion of shape
e.g. Piston – crank – connecting rod
Mechanism in automobile engine
Study of deformation
(Elongation, compression, twisting)
Application of laws relating the forces to
the deformation
Step-By-Step procedure to solve problems in
mechanics of solids.
Select actual/real system of interest.
Make assumptions regarding desired characteristics
of the system
Develop idealized model of the system
(Structural and Machine elements)
Apply principles of mechanics to the idealized
model to compare these calculated results with the
behaviour of the actual system
If the results (calculated and actual) differ
widely repeat above steps till satisfactory
idealized model is obtained.
 Idealizing assumption about isolated
system

Weight/ gravity of the body

Rigid/flexible/plastic bodies
Friction/frictionless joints
Inextensible but perfectly flexible
string. Cable, belt or rope
Actual support conditions
Effects of the environment
The concept of force:
Force is a vector quantity
Effective means for describing interaction between bodies
Systems physically separated may experience force –
electrostatic, magnetic and gravitational forces.
Weight of the object/Gravitational force
The point of application of each force must be specified in all
the systems (a specific physical part or a group of parts)
We can’t see the force , we can deduce it’s existence by
observing it’s effect
Causes of a force
•Gravity
•Electromagnetism
•Pressure exerted by fluid on structure
•Wind or fluid induced drag or lift forces
•Contact forces
•Friction forces(which also act at contact)
Classification of forces(Based on source)

 External forces

 Constraint forces

 Internal forces
Force Interaction
Effect of force interaction
 They tend to alter the motion of the system involved

 They tend to deform or distort the shape of the system

 FORCE SYSTEMS:
When more than one force act on a body, they
constitute a 'force system', this system may be
classified according to the line of action and the
arrangement of the forces.
1. Coplanar forces, and
2. Non-coplanar forces
Another way to classify them is as
a) Concurrent forces, and
b) Non-concurrent forces.
In fact, each of (1) and (2) may fall into
either (a) or (b).
Coplanar Forces :All the forces of the system lie in
the same plane
Non-Coplanar Forces :All the forces of the system do
not lie in the same plane.
Concurrent Forces :All the forces of the system pass
through a common point, or have a common point of
application.
Non-Concurrent Forces :All the forces of the system
do not pass through a common point; some or all of
the forces may be parallel to each other.
Coplanar-Concurrent Forces :All the forces of the
system lie in the same plane and also are concurrent.
Coplanar-Non-Concurrent Forces :All the forces of
the system lie in the same plane but are not concurrent.
If all the forces are parallel to each other; it is a
coplanar parallel force system.
Non-Coplanar-Concurrent Forces: All the forces of
the system do not lie in a single plane but are
concurrent. This is a concurrent force system in space.
Non-Coplanar-Non-Concurrent Forces All
the forces of the system do not lie in a single
plane and also are not concurrent. If the forces
are parallel to each other, it is a non-coplanar
parallel force system; otherwise, it is a
general force system.
Fundamental Principles and vector
properties of force
•Newton’s Laws of motion
 Components of a force
 Any force ‘F” can be replaced by it’s
components along three mutually
perpendicular axes through the point of
application
F = Fxi +Fyj +Fzk
To find resultant--
•Triangle law of forces/vectors
•Parallelogram law of forces/vectors
•Polygoan law of forces/vectors
Action and Reaction: When two bodies are in contact
with each other, both tend to exert forces on each
other. If the force exerted by the first body on the
second is called 'action', that exerted by the second
body on the first is called 'reaction', and vice-versa.
Action and reaction are equal and opposite according
to Newton's third law of motion.

Equilibrium: When a body is stationary, or at rest, it

is said to be in equilibrium. In this case, either the
body is not acted on by any force or force system, or
the effect of the force system is null.
Principle of Transmissibility
The conditions of the equilibrium or motion of a rigid
body remains, unchanged if a force acting at a given
point of the rigid body is replaced by a force of the same
magnitude and direction , but acting at at a different
point provided that the two forces has the same line of
the action

B B
A F
A
F
Moments force
 The moment of a force is a measure of its tendency to rotate an
object about some point.
 The physical significance of a moment will be discussed later. We
begin by stating the mathematical definition of the moment of a
force about a point.
The moment of force:
 Moment = rF
The moment itself is a vector quantity.
 Its direction is perpendicular to the
plane determined by op and f.
The sense is fixed by the right hand rule
the magnitude of the cross product r  F
= f r sin.
Where r sin is the perpendicular distance
between point o and vector F.
And f is the magnitude of the force
 With several forces, total moment or
torque about a fixed-point o
r1×F1 + r2 ×F2 + ----------rn×Fn = ri ×Fj

Thus,
Moment of a force =Force x perpendicular
distance of the pivot from the force
Unit- Nm
The image part with relationship ID rId2 was not found in the file.
The image part with relationship ID rId2 was not found in the file.