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Engineering Mechanics
May be defined as the science which considers the effects of forces on rigid bodies.
Has 2 branches: Statics and Dynamics.
Statics
We consider the effects and distribution of forces on rigid bodies which are at rest.
Statics also has sub-branches: Force systems and Applications.
Dynamics on the other hand focuses on the motion of rigid bodies caused by forces acting upon them.
Rigid Body
Defined as the amount of matter the parts of which are fixed in position relative to each other.
Force
An influence that tends to change the state of motion of a body. It has external and internal effects. External effects are the cause of its motion. Internal effects produces stress and deformation.
MAGNITUDE
POSITION OF ITS LINE OF ACTION
DIRECTION (SENSE)IN WHICH THE FORCE ACTS
Characteristics of Force
PRINCIPLE OF TRANSMISSIBILITY
It states that the external effect of a force on a body is the same for all point of its application along its line of action. It is independent on the point of application.
Force System
Is any arrangement where two or more forces act on a body or on a group of related bodies. They are identified to either line of action or its points of application.
Free Body Diagram
One of the most important concepts in mechanics, is a representation of an object with all the forces that act on it.
Axioms of Mechanics
The parallelogram law: The resultant of two forces is the diagonal of the parallelogram formed on the vectors of these forces.
Axioms of Mechanics
Two forces are in equilibrium only when equal in magnitude, opposite in direction, and collinear in action.
A set of forces in equilibrium may be added to any system of forces without changing the effect of the original system. Action and reaction forces are equal but oppositely directed.
Scalar Quantity
It possesses only MAGNITUDE and can be added arithmetically.
Examples: length, speed, volume, mass, density, pressure, temperature, etc.
Vector Quantity
Possesses MAGNITUDE and DIRECTION. Can be added geometrically, usually called vector addition.
Examples: Velocity, Acceleration, Displacement, Momentum, Lift, Drag, Weight, Etc.
MOMENT OF A FORCE
Is the measure of the capacity or ability of the force to produce twisting or turning effect about an axis.
M = Fd
The magnitude of moment is equal to the product of the force and the perpendicular distance from the axis to the line of action of the force.
Varignon’s Theorem
Also known as the Varignon’s principle or the theorem of moments, is a fundamental concept in the field of statics and engineering.
Named after the French mathematician and physicist Pierre Varignon
The sum of the moments of a system of coplanar forces about any point is equal to the moment of the resultant force about the same point.
Varignon’s theorem states that:
ΣM = Mr
Varignon’s Theorem Equation
