Lectures notes
On
Engineering Mechanics
Course Code- BME-101
Prepared by
Prof. Mihir Kumar Sutar
Asst. professor,
Department of Mechanical Engg.
,
, Lesson Plan
Subject: Engineering Mechanics (BME- 101),
Date Lecture Topics to be covered
08.01.2015 Lecture 1 Concurrent forces on a plane: Introduction to engineering
mechanics,
09.01.2015 Lecture 2 Composition of forces, parallelogram law, numerical
problems.
10.01.2015 Lecture 3 Resolution of forces, equilibrium of collinear forces, super
position and transmissibility, free body diagram,
12.01.2015 Lecture 4 Equilibrium of concurrent forces: Lami’s theorem, method of
projection, equilibrium of three forces in a plane,
15.01.2015 Lecture 5 Method of moments, numerical problems on equilibrium of
concurrent forces
16.01.2015 Lecture 6 Friction: Definition of friction, static friction, dynamics
friction, coefficient of friction, angle of friction, angle of
repose. Wedge friction, simple friction problems based on
sliding of block on horizontal and inclined plane and wedge
friction
17.01.2015 Lecture 7 Ladder and rope friction, simple problems on ladder and rope
friction.
19.01.2015 Lecture 8 General case of parallel forces, center of parallel forces,
numerical problems.
22.01.2015 Lecture 9 Center of gravity, centroid of plane figure and curves,
numerical examples.
29.01.2015 Lecture 10 Centroid of composite figures figure and curves, numerical
problems.
30.01.2015 Lecture 11 Numerical examples on centroid of plane figure and curves
31.01.2015 Lecture 12 Composition and equilibrium of forces in a plane:
Introduction to plane trusses, perfect, redundant truss,
,02.02.2015 Lecture 13 Solving problem of truss using method of joint.
05.02.2015 Lecture 14 Numerical examples on solving truss problems using method
of joint.
06.02.2015 Lecture 15 Method of section, numerical examples.
07.02.2015 Lecture 16 Numerical examples on method of joint and method of
section
09.02.2015 Lecture 17 Principle of virtual work: Basic concept, virtual displacement,
numerical problems
12.02.2015 Lecture 18 Numerical problems on virtual work.
13.02.2015 Lecture 19 Numerical problems on virtual work.
14.02.2015 Lecture 20 Moment of Inertia of plane figure with respect to an axis in its
plane, numerical examples.
16.02.2015 Lecture 21 Moment of Inertia of plane figure with respect to an axis and
perpendicular to the plane, parallel axis theorem, numerical
examples.
19.02.2015 Lecture 22 Numerical examples on MI of plane figures.
20.02.2015 Lecture 23 Rectilinear Translation: Kinematics of rectilinear translation,
displacement, velocity, acceleration, numerical problems on
rectilinear translation
21.02.2015 Lecture 24 Principle of Dynamics: Newton’s Laws, General equation of
motion of a particle, differential equation of rectilinear
motion, numerical problems.
23.02.2015 Lecture 25 Numerical problems on principle of dynamics
26.02.2015 Lecture 26 D’Alembert’s Principle: Basic theory and numerical
problems.
27.02.2015 Lecture 27 Numerical problems on D’Alembert’s Principle.
28.02.2015 Lecture 28 Momentum and Impulse: Basic theory and numerical
, problems
02.03.2015 Lecture 29 Numerical problems on momentum and impulse.
07.03.2015 Lecture 30 Work and Energy: Basic theory and numerical problems
09.03.2015 Lecture 31 Ideal systems: Conservation of energy: Basic theory and
numerical problems
12.03.2015 Lecture 32 Impact: Plastic impact, elastic impact, semi-elastic impact,
coefficient of restitution numerical problems on impact on
various conditions.
13.03.2015 Lecture 33 Numerical problems on impact.
14.03.2015 Lecture 34 Curvilinear Translation: Kinematics of curvilinear translation,
displacement, velocity and acceleration, numerical problems
on curvilinear translation
16.03.2015 Lecture 35 Differential equation of curvilinear motion: Basic theory and
numerical problems
19.03.2015 Lecture 36 Motion of a Projectile:
20.03.2015 Lecture 37 Numerical problems on projectile for different cases.
21.03.2015 Lecture 38 D Alembert’s Principles in Curvilinear Motion: Basic theory
and numerical problems.
23.03.2015 Lecture 39 Rotation of rigid body: Kinematics of rotation and numerical
problems.
26.03.2015 Lecture 40 Numerical problems on rotation of rigid bodies.
,Mechanics
It is defined as that branch of science, which describes and predicts the conditions of
rest or motion of bodies under the action of forces. Engineering mechanics applies the
principle of mechanics to design, taking into account the effects of forces.
Statics
Statics deal with the condition of equilibrium of bodies acted upon by forces.
Rigid body
A rigid body is defined as a definite quantity of matter, the parts of which are fixed in
position relative to each other. Physical bodies are never absolutely but deform slightly
under the action of loads. If the deformation is negligible as compared to its size, the
body is termed as rigid.
Force
Force may be defined as any action that tends to change the state of rest or motion of a
body to which it is applied.
The three quantities required to completely define force are called its specification or
characteristics. So the characteristics of a force are:
1. Magnitude
2. Point of application
3. Direction of application
1
,Concentrated force/point load
Distributed force
Line of action of force
The direction of a force is the direction, along a straight line through its point of
application in which the force tends to move a body when it is applied. This line is
called line of action of force.
Representation of force
Graphically a force may be represented by the segment of a straight line.
Composition of two forces
The reduction of a given system of forces to the simplest system that will be its
equivalent is called the problem of composition of forces.
Parallelogram law
If two forces represented by vectors AB and AC acting under an angle α are applied to
a body at point A. Their action is equivalent to the action of one force, represented by
vector AD, obtained as the diagonal of the parallelogram constructed on the vectors
AB and AC directed as shown in the figure.
2
,Force AD is called the resultant of AB and AC and the forces are called its
components.
R P 2
Q 2 2 PQ Cos
Now applying triangle law
P Q R
Sin Sin Sin( )
Special cases
Case-I: If α = 0˚
R P 2
Q 2 2 PQ Cos 0 ( P Q ) 2 P Q
P Q R
R = P+Q
Case- II: If α = 180˚
R P 2
Q 2 2 PQ Cos180 ( P 2 Q 2 2 PQ ) ( P Q ) 2 P Q
Q P R
3
,Case-III: If α = 90˚
R P 2
Q 2 2 PQ Cos90 P 2 Q 2 Q
R
α = tan-1 (Q/P)
α
P
Resolution of a force
The replacement of a single force by a several components which will be equivalent in
action to the given force is called resolution of a force.
Action and reaction
Often bodies in equilibrium are constrained to investigate the conditions.
w
4
, Free body diagram
Free body diagram is necessary to investigate the condition of equilibrium of a body or
system. While drawing the free body diagram all the supports of the body are removed
and replaced with the reaction forces acting on it.
1. Draw the free body diagrams of the following figures.
R
2. Draw the free body diagram of the body, the string CD and the ring.
5
On
Engineering Mechanics
Course Code- BME-101
Prepared by
Prof. Mihir Kumar Sutar
Asst. professor,
Department of Mechanical Engg.
,
, Lesson Plan
Subject: Engineering Mechanics (BME- 101),
Date Lecture Topics to be covered
08.01.2015 Lecture 1 Concurrent forces on a plane: Introduction to engineering
mechanics,
09.01.2015 Lecture 2 Composition of forces, parallelogram law, numerical
problems.
10.01.2015 Lecture 3 Resolution of forces, equilibrium of collinear forces, super
position and transmissibility, free body diagram,
12.01.2015 Lecture 4 Equilibrium of concurrent forces: Lami’s theorem, method of
projection, equilibrium of three forces in a plane,
15.01.2015 Lecture 5 Method of moments, numerical problems on equilibrium of
concurrent forces
16.01.2015 Lecture 6 Friction: Definition of friction, static friction, dynamics
friction, coefficient of friction, angle of friction, angle of
repose. Wedge friction, simple friction problems based on
sliding of block on horizontal and inclined plane and wedge
friction
17.01.2015 Lecture 7 Ladder and rope friction, simple problems on ladder and rope
friction.
19.01.2015 Lecture 8 General case of parallel forces, center of parallel forces,
numerical problems.
22.01.2015 Lecture 9 Center of gravity, centroid of plane figure and curves,
numerical examples.
29.01.2015 Lecture 10 Centroid of composite figures figure and curves, numerical
problems.
30.01.2015 Lecture 11 Numerical examples on centroid of plane figure and curves
31.01.2015 Lecture 12 Composition and equilibrium of forces in a plane:
Introduction to plane trusses, perfect, redundant truss,
,02.02.2015 Lecture 13 Solving problem of truss using method of joint.
05.02.2015 Lecture 14 Numerical examples on solving truss problems using method
of joint.
06.02.2015 Lecture 15 Method of section, numerical examples.
07.02.2015 Lecture 16 Numerical examples on method of joint and method of
section
09.02.2015 Lecture 17 Principle of virtual work: Basic concept, virtual displacement,
numerical problems
12.02.2015 Lecture 18 Numerical problems on virtual work.
13.02.2015 Lecture 19 Numerical problems on virtual work.
14.02.2015 Lecture 20 Moment of Inertia of plane figure with respect to an axis in its
plane, numerical examples.
16.02.2015 Lecture 21 Moment of Inertia of plane figure with respect to an axis and
perpendicular to the plane, parallel axis theorem, numerical
examples.
19.02.2015 Lecture 22 Numerical examples on MI of plane figures.
20.02.2015 Lecture 23 Rectilinear Translation: Kinematics of rectilinear translation,
displacement, velocity, acceleration, numerical problems on
rectilinear translation
21.02.2015 Lecture 24 Principle of Dynamics: Newton’s Laws, General equation of
motion of a particle, differential equation of rectilinear
motion, numerical problems.
23.02.2015 Lecture 25 Numerical problems on principle of dynamics
26.02.2015 Lecture 26 D’Alembert’s Principle: Basic theory and numerical
problems.
27.02.2015 Lecture 27 Numerical problems on D’Alembert’s Principle.
28.02.2015 Lecture 28 Momentum and Impulse: Basic theory and numerical
, problems
02.03.2015 Lecture 29 Numerical problems on momentum and impulse.
07.03.2015 Lecture 30 Work and Energy: Basic theory and numerical problems
09.03.2015 Lecture 31 Ideal systems: Conservation of energy: Basic theory and
numerical problems
12.03.2015 Lecture 32 Impact: Plastic impact, elastic impact, semi-elastic impact,
coefficient of restitution numerical problems on impact on
various conditions.
13.03.2015 Lecture 33 Numerical problems on impact.
14.03.2015 Lecture 34 Curvilinear Translation: Kinematics of curvilinear translation,
displacement, velocity and acceleration, numerical problems
on curvilinear translation
16.03.2015 Lecture 35 Differential equation of curvilinear motion: Basic theory and
numerical problems
19.03.2015 Lecture 36 Motion of a Projectile:
20.03.2015 Lecture 37 Numerical problems on projectile for different cases.
21.03.2015 Lecture 38 D Alembert’s Principles in Curvilinear Motion: Basic theory
and numerical problems.
23.03.2015 Lecture 39 Rotation of rigid body: Kinematics of rotation and numerical
problems.
26.03.2015 Lecture 40 Numerical problems on rotation of rigid bodies.
,Mechanics
It is defined as that branch of science, which describes and predicts the conditions of
rest or motion of bodies under the action of forces. Engineering mechanics applies the
principle of mechanics to design, taking into account the effects of forces.
Statics
Statics deal with the condition of equilibrium of bodies acted upon by forces.
Rigid body
A rigid body is defined as a definite quantity of matter, the parts of which are fixed in
position relative to each other. Physical bodies are never absolutely but deform slightly
under the action of loads. If the deformation is negligible as compared to its size, the
body is termed as rigid.
Force
Force may be defined as any action that tends to change the state of rest or motion of a
body to which it is applied.
The three quantities required to completely define force are called its specification or
characteristics. So the characteristics of a force are:
1. Magnitude
2. Point of application
3. Direction of application
1
,Concentrated force/point load
Distributed force
Line of action of force
The direction of a force is the direction, along a straight line through its point of
application in which the force tends to move a body when it is applied. This line is
called line of action of force.
Representation of force
Graphically a force may be represented by the segment of a straight line.
Composition of two forces
The reduction of a given system of forces to the simplest system that will be its
equivalent is called the problem of composition of forces.
Parallelogram law
If two forces represented by vectors AB and AC acting under an angle α are applied to
a body at point A. Their action is equivalent to the action of one force, represented by
vector AD, obtained as the diagonal of the parallelogram constructed on the vectors
AB and AC directed as shown in the figure.
2
,Force AD is called the resultant of AB and AC and the forces are called its
components.
R P 2
Q 2 2 PQ Cos
Now applying triangle law
P Q R
Sin Sin Sin( )
Special cases
Case-I: If α = 0˚
R P 2
Q 2 2 PQ Cos 0 ( P Q ) 2 P Q
P Q R
R = P+Q
Case- II: If α = 180˚
R P 2
Q 2 2 PQ Cos180 ( P 2 Q 2 2 PQ ) ( P Q ) 2 P Q
Q P R
3
,Case-III: If α = 90˚
R P 2
Q 2 2 PQ Cos90 P 2 Q 2 Q
R
α = tan-1 (Q/P)
α
P
Resolution of a force
The replacement of a single force by a several components which will be equivalent in
action to the given force is called resolution of a force.
Action and reaction
Often bodies in equilibrium are constrained to investigate the conditions.
w
4
, Free body diagram
Free body diagram is necessary to investigate the condition of equilibrium of a body or
system. While drawing the free body diagram all the supports of the body are removed
and replaced with the reaction forces acting on it.
1. Draw the free body diagrams of the following figures.
R
2. Draw the free body diagram of the body, the string CD and the ring.
5
