Engineering Mechanics
UNIT I
Principle of statics
• Statics is a branch of mechanics that deals with the study of
objects at rest or in equilibrium under the action of external
forces. The principles of statics are crucial in understanding and
analyzing the behavior of structures, machines, and other objects
that are not in motion.
• The fundamental principles of statics include:
Principle of statics
1. First Law of Newton - An object at rest will remain at rest, and
an object in motion will remain in motion with a constant
velocity unless acted upon by a net external force. In statics,
this principle is applied to objects that are at rest.
2. Second Law of Newton - The sum of the forces acting on an
object is equal to the mass of the object multiplied by its
acceleration (F = m*a). In statics, since objects are not
accelerating, the sum of the forces acting on an object is zero.
3. Third Law of Newton - For every action, there is an equal and
opposite reaction.
Newton’s Laws
Principle of statics
4. Principle of Transmissibility - The effects of a force acting on a
rigid body are the same, regardless of where the force is applied
along its line of action. In other words, a force can be moved along
its line of action without changing its effect on the body.
5. Principle of Equilibrium - For an object to be in static
equilibrium, both the net force acting on it and the net torque
(rotational force) acting on it must be zero. This principle is
expressed by the equations ΣF = 0 (sum of forces is zero) and Στ = 0
(sum of torques is zero).
Force System
• Coplanar forces: The forces, whose lines of action lie on the same plane, are known as
coplanar forces.
• Collinear forces: The forces, whose lines of action lie on the same line, are known as
collinear forces.
• Concurrent forces: The forces, which meet at one point, are known as concurrent forces.
The concurrent forces may or may not be collinear
• Coplanar concurrent forces: The forces, which meet at one point and their line of action
also lay on the same plane, are known as coplanar concurrent forces.
• Coplanar non-concurrent forces: The forces, which do not meet at one point, but their
lines of action lie on the same, are known as coplanar non-concurrent forces.
• Non-Coplanar concurrent forces: The forces, which meet at one point, but their lines of
action do not lie on the same plane, are known as non-coplanar concurrent forces.
Force System
• Non-Coplanar non-concurrent forces: The forces, which do not meet at one point and
their lines of action do not lie on the same plane, are called non-coplanar non-concurrent
force
Resolution of Forces
• Resolution of forces involves breaking down a single force into its
components along specific axes or directions. This is often done to
simplify the analysis of forces, especially when dealing with forces
acting at angles.
Composition of Forces
• Composition of forces involves combining two or more forces into
a single equivalent force. This is particularly useful when dealing
with forces acting at different points or directions.
Resultant of concurrent forces
• The resultant of concurrent forces refers to the single force that
can replace a system of concurrent forces without altering the
external effects on a body. In other words, it is the single force
that has the same effect as the combination of multiple
concurrent forces. The concept of concurrent forces implies that
all the forces have the same point of application.
Parallelogram Law
• “If two forces, acting at a point be represented in magnitude and
direction by the two adjacent sides of a parallelogram, then their
resultant is represented in magnitude and direction by the
diagonal of the parallelogram passing through that point.”
Parallelogram Law
Moment of Force
• A moment of force is a measure of the tendency of that force to
rotate a body about a selected point or axis, called the moment
center. This tendency increases with the magnitude of the force,
and also with the distance between the line-of-action of the force
and the moment center.
• Moments are vector quantities, so they have magnitude and
direction
• M = F*d
Couple
A couple consists of two parallel forces, equal in magnitude,
opposite in direction, and non-coincident. Couples are special
because the pair of forces always cancel each other, which means
that a couple produces a rotational effect but never translation. For
this reason, couples are sometimes referred to as “pure moments.”
The strength of the rotational effect is called the moment of the
couple or the couple-moment.
Couple
A couple consists of two parallel forces, equal in magnitude,
opposite in direction, and non-coincident. Couples are special
because the pair of forces always cancel each other, which means
that a couple produces a rotational effect but never translation. For
this reason, couples are sometimes referred to as “pure moments.”
The strength of the rotational effect is called the moment of the
couple or the couple-moment.
Varignon’s Theorem
• It states that sum of the moments of several concurrent forces
about a point is equal to the moment of the resultant of those
forces about a point.
Varignon’s Theorem
Numerical 1
Numerical 2
Numerical 3
