ES 202

Engineering Mechanics

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