Principles of Engineering Mechanics

BASIC PRINCIPLES OF ENGINEERING MECHANICS:

Hello mechons, in this post we are going to explain to you all the basic principles of engineering mechanics. 

1. TWO FORCE SYSTEM:

 If a body is acted upon by two forces, then the two forces must be equal, collinear, and opposite to each other.

2. THREE FORCE SYSTEM:

If a body is acted upon by three forces, then the resultant of any two forces must be equal, collinear, and opposite to the third force.

3. FOUR FORCE SYSTEM: 

If a body is acted upon by four forces, then the resultant of any two forces must be equal, opposite, and collinear to the resultant of the other two forces.

Methods For Equilibrium:

• Analytical.
• Graphical

ANALYTICAL:

LAMI'S THEOREM:

STATEMENT OF LAMI'S THEOREM:

If three coplanar forces acting at a point that is in equilibrium, then each force acting at the point is proportional to the sine of the angle between the other two forces. 

(Representation of Lami's theorem) 

Let P, Q, R be three coplanar forces,𝝰, 𝛃, 𝜸 be the angles between them

Then,  P/sin 𝞪= Q/sin 𝜷 = R/sin 𝜸

GRAPHICAL:

CONVERSE LAW OF TRIANGLE OF FORCES:

If three forces at a point can be represented as three sides of a triangle, then they are in equilibrium.

(Triangle law of forces) 

CONVERSE LAW OF POLYGON OF FORCES:

If any number of forces can be represented as sides of a polygon, then they shall be in equilibrium.

(Polygon Law of forces) 

CONDITIONS OF EQUILIBRIUM:

1. Body may move in one direction.

2. Body may rotate itself but there should not be any movement.

3. Body may move and also rotate itself in one direction.

4. Body may be completely at rest.

By the above conditions, we get,

 1. If a body moves in one direction, a resultant force acts on it. If it is considered to be in Equilibrium, then it's horizontal (𝚺H) and vertical(𝚺V) forces are zero.

                            𝚺H~0, 𝚺V~0

2. If a body rotates itself without moving, then it has a resultant couple acting on it. If it is said to be in equilibrium, then the resultant moment(𝚺 M) is zero.

                                 𝚺M~0

3. If a body rotates and also moves in one direction, then it has a resultant force and a resultant couple acting on it. If it is said to be in equilibrium, then the resultant force(𝚺H, 𝚺V) and moment(𝚺M) are zero.

                       𝚺H~0, 𝚺V~0, 𝚺M~0

4. If a body is in rest, no resultant force or couple acts on it. 

                       𝚺H~0, 𝚺V~0, 𝚺M~0

TYPES OF EQUILIBRIUM:

1. Stable equilibrium:

    If a body returns to its original position after applying a force, then it is said to be in stable equilibrium.

Ex: A smooth cylinder in a curved plain, after a displacement, comes back to its original position to bring the weight back to the horizontal axis.

(Stable equilibrium)

2. Unstable equilibrium:

    If a body does not return to its original position, then it is said to be in unstable equilibrium.

Ex: A smooth cylinder in a convex plane, tends to move away from the initial position.

(Unstable equilibrium)

3. Neutral equilibrium:

    If a body occupies a new position after displacement, then it is said to be in neutral equilibrium.

Ex: A smooth cylinder in a horizontal plane. 

(Neutral equilibrium)

Conclusion:

That's all about engineering mechanics principles, for now, we hope that we covered almost all the principles of Engineering mechanics, also we hope that you understand the definitions. 

If you have any queries or doubts or need improvements in this article put that in the below-mentioned comments section we will reply and rectify as fast as possible. 

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