INTRODUCTION TO STATICS OF LECTURE 1
RIGID BODIES
Topic 1. Introduction and Classification
of Engineering Mechanics
Topic 2. Force Systems
Topic 3. Scalar and Vectors
Topic 4. Resultant of Two Force
STATICS OF RIGID BODIES 2
Engineering Mechanics is the branch of engineering that fuses
the principles of physics and mathematics. The goal of
engineering mechanics is to understand and predict the
behavior of these systems under various loading conditions
(Baskar, 2023).
Engineering Mechanics is divided into two parts:
Statics
Dynamics
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What is Statics and Dynamics?
STATICS
Statics is a branch of engineering mechanics which studies the
effects and distribution of forces of rigid bodies which remains at
rest (Gillesania, 2002). In this area of mechanics, the body in which
forces are acting is assumed to be rigid. The deformation of non-
rigid bodies is treated in Strength of Materials. Statics is essential in
designing and analyzing structures such as bridges, buildings and
dams (Engineering UPdates, 2023).
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What is Statics and Dynamics?
DYNAMICS
Dynamics is a branch of engineering mechanics that deals the
motion of rigid bodies caused by the forces acting upon them
(Gillesania, 2002). Dynamics is essential in designing and analyzing
machines, vehicles and other mechanical systems that involve
moving parts (Engineering UPdates, 2023).
The subject of Dynamics is divided into two branches:
Kinetics
Kinematics
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Engineering Mechanics
Statics Dynamics
Force
Applications Kinematics Kinetics
Systems
Non- Plane Plane
Concurrent Parallel Trusses Centroids Friction Translations Rotation Translation Rotation
Concurrent Motion Motion
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RIGID BODIES:
It is a type of material body can be considered to consist of a very
large number of particles. A rigid body is one which does not deform,
in other words the distance between the individual particles making up
the rigid body remains unchanged under the action of external forces.
For a rigid body to be in equilibrium two conditions need to be
satisfied:
The vector sum of the forces acting on the body must be zero.
The sum of the moments about any point must be zero.
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FORCE:
A force is a vector quantity representing an interaction between
two objects. Forces can be either attractive or repulsive, and they
can be either conservative or non-conservative.
-Internal effect of force
-External effect of force
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FORCE SYSTEM:
A force system is any arrangement where two or more forces act
on a body or on a group of related bodies.
There are two types of Force System
According to Plane
According to Line of Action
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According to Plane
Coplanar Force System: All forces are lying in one plane.
Non-Coplanar Force System: All forces are lying in two or more
planes.
According to Line of Action
Concurrent Force System : The line of action pass through a common
point.
Parallel Force System: The line of action of all forces are not
intersecting in any point.
Non-Concurrent Force System: The line of action of all forces are
intersecting in two or more points.
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FREE-BODY DIAGRAM:
A free body diagram (FBD) is a graphical illustration used to
visualize the applied forces, moments and resulting reactions on a
free body in a given conditions. A series of free bodies and other
diagrams may be necessary to solve complex problems (Rennie &
Law, 2019)
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FREE-BODY DIAGRAM:
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All physical quantities in engineering mechanics are measured
using either scalars and vectors.
Scalar
A scalar is any positive or negative quantity that can be completely
defined only by its magnitude.
Example: length, mass and time.
Vector
A vector is any physical quantity that requires both a magnitude
and a direction for its complete description.
Example: force, position and moment.
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Vector
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Scalar multiplication is a multiplication of a vector by a real
number (scalar).
Suppose we let the letter represent a real number and be the
vector .
Then, the scalar multiple of the vector is
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If a vector is multiplied by a positive scalar, its magnitude is
increased by that amount. Multiplying by a negative scalar will also
change the directional sense of the vector.
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Steps for Multiplying a Vector by a Scalar
Step 1: Identify a given scalar and the horizontal and vertical
components of a given vector.
Step 2: Multiply the scalar with each component. The products
form the components of the new vector.
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When adding two vectors together it is important to account for both their magnitudes and
their directions. To do this we must use the Parallelogram Law of Addition.
To illustrate, the two component vectors A and B shown are added to form a resultant vector
R=A+B
Step 1 : First join the tails of the components at
a point to make them concurrent.
Step 2: From the head of B, draw a line parallel
to A. Draw another line from the head of A that
is parallel to B. These two lines intersect at
point P to form the adjacent sides of a
parallelogram.
Step 3: The diagonal of this parallelogram that
extends to P forms R, which then represents the
resultant vector R=A+B
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There is a special case of Parallelogram Law, whereby vector B is added to vector A in a
“head-to-tail” way, and this is called a Triangle Law
Step 1 : Connect the head of A to the tail
of B.
Step 2: The resultant R extends from the
tail of A to the head of B. In a similar
manner, R can also be obtained by
adding A to B. By comparison, it is seen
that vector addition is cumulative; in
other words, the vectors can be added in
either order
R=A+B=B+A
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The effect of a system of forces on a body is usually expressed in
terms of a resultant. The value of this resultant determines the
motion of the body.
Note:
If a resultant is equals to zero, it means that the body will be in
equilibrium and will note change its original state of motion.
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For example a car driven due east for 4km, then turned sharply
and driven due north for a 3km. What resultant distance has the
car covered?
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Thank You =)
STATICS OF RIGID BODIES
a.almacin.540293@umindanao.edu.ph
