CE1011 Engineering Mechanics
Gobithas Tharmarajah
February 2020
Application of Engineering
Application of Engineering
Preliminaries
Mechanics Mechanics is the physical science which deals with the effects of forces on
objects. No other subject plays a greater role in engineering analysis than
mechanics.
Self Learning
Answer Yourself!
What is Engineering Mechanics?
What are fundamental quantities in Engineering
Mechanics?
Difference between scalar and vector
quantities?
Difference between weight and force?
Forces and Moments
Objectives:
“By the end of this session, student will learn the fundamental principles used in
statics analysis, will be able to deal with concurrent forces in an equilibrium
system, will get to know moments and distributed loads”
Where it falls!
What are fundamental quantities of mechanics?
Define, “Space”, “Time”, “Mass” and “Force”.
Space is a........................
Time is an.......................
Mass is a ...............
Force is a ...............
Where it falls!
What are fundamental quantities of mechanics?
Space is the geometric region occupied by bodies whose positions are described by
linear and angular measurements relative to a coordinate system.
Time is the measure of the succession of events and is a basic quantity in dynamics
Mass is a measure of the inertia of a body, which is its resistance to a change of velocity.
Mass can also be thought of as the quantity of matter in a body.
Force is the action of one body on another. A force tends to move a body in the direction
of its action. The action of a force is characterized by its magnitude, by the direction of
its action, and by its point of application.
Scalars and Vectors
Scalar quantities are those with which only a magnitude is associated. Examples of scalar
quantities are time, volume, density, speed, energy and mass
Vector quantities, on the other hand, possess direction as well as magnitude, and must
obey the parallelogram law of addition as described later in this article. Examples of
vector quantities are displacement, velocity, acceleration, force, moment, and
momentum.
Accuracy?
Why accuracy is important in engineering?
Tallest In the World!
343m high
2460m length
“In the final joining of the two halves, the bridge lines up to within one centimeter- accurate to 99.9999%”
Accuracy?
What is the recommended limit of variation to an exact measurement?
It depends!
However in general, ±10% Where,
The numerical values of each calculation and measurement should use
three (3) significant number, such as 1.96 N, 234 m2, 8.91 × 106 Pa.
Forces
Force is the action of one body on another.
It is also defined as that which changes, or tends to change, the velocity
of a body.
It is characterised by its magnitude, direction and point of application.
Thus, it is a vector.
Its basic unit is Newton (N) and kilo Newton (kN).
Forces
What is the difference between mass and force?
Force is not a mass, since mass is a scalar that only has magnitude.
Forces and resultant forces
Weightless rigid beam is attached
to the muscle man and to the car
Moving direction
If the muscle man has enough power to prevent the vehicle from moving,
mark the force applied on the rigid beam.
Mark the reaction force to the force applied by the vehicle.
Consider a section of the beam and mark internal forces.
Forces and resultant forces
What is principle of transmissibility?
The principle of transmissibility states that the point of application of a force can be moved
anywhere along its line of action without changing the external reaction forces on a rigid
body.
Forces and resultant forces
Forces and resultant forces - parallelogram
Forces and resultant forces
Forces and resultant forces – triangle rule
Forces and resultant forces
Forces and components
Sometimes we need replace a single force by two forces to make the
analysis easier.
Forces and components
Sometimes we need replace a single force by two forces to make the analysis
easier.
Problems
Problem 1.1 (Hall et al, 1999)
There is a signal force F = 20 N acting at point O (Figure 7).
Find the components of the force F in the directions of Ox and Oy shown in Figure.
Problems
Problem 1.2 (Hall et al, 1999)
Figure shows four concurrent forces acting at point O.
Find the resultant force. Try to use both numerical method and force polygon method.
Equilibrium and resultant forces
From the 1st and 2nd Newton’s law, we know that if there is external force acting on a
body, the force will result in the acceleration of the body.”
In statics, we consider bodies which are in static condition, means they are not
accelerating in any direction. It means there were no resultant external forces acting
on the body.
Problems
Problem 1.3 (Hall et al, 1999)
Figure displays three concurrent forces acting at point O.
Find the equilibrant force Q to balance the system. Use both numerical method and
force polygon method.
Problems
Problem 1.4 (Hall et al, 1999)
Figure shows two cables AC and BC are supporting the weight 200 kN.
Find the forces in cables AC and BC. Use both numerical method and force polygon method.
Actions and reaction forces
“Once again, the term body is used to specify any object, structure, part of a
structure, or even any arbitrarily chosen group of matters”.
Can you draw the freebody diagram of the block?
A body is resting on a floor
Actions and reaction forces
A body is resting on a floor
Actions and reaction forces
Can you draw the freebody diagram of the block?
Hall et al., 1999
Actions and reaction forces
Friction forces
What is a friction force?
Friction forces
What is a friction force?
“It is caused by surface roughness. The maximum friction force on a sliding surface
can be calculated as shown in equation”
F = μ·N
where?
Problems
Problem 1.5 (Hall et al, 1999)
Figure shows a box of weight W = 80 N on a table. The box is pulled by a rope with a force P at angle θ =
30o. The coefficient of friction between the box and the table is μ = 0.4.
a) Find whether the box will slide under P = 20 N.
b) Find whether the box will slide under P = 40 N.
Problems
Problem 1.6: A ladder 6 meters long and weighing W = 220 N rests against a smooth wall at 30o
Find the reactions at A from the wall (R1) and at B from the floor (R2).
Find the minimum friction coefficient (μ) between the ladder and the floor such that the ladder will
not slip.
Self Learning
Web.....YouTube.........Books!
Reach me.
Email: gobithas.t@sliit.lk
Room: 5th Floor Engineering