Introduction to Engineering Mechanics

Engineering Mechanics

* Experimental findings developed around the states of rest and state of motion of the bodies by

Archemdes, Galilea and Newton is known as classical mechanics/Newtonian mechanics.

* Albert Einstein put forth the theory of relativistic mechanics to explain the behaviour of high speed

bodies.

* Schrodinger and Broglie put forth theory of quantum mechanics to explain behaviour of particles

when atomic distances are concerned.

* The basic terminolgies in mechanics are

1. Mass

2. Time

3. Space

4. Length

5. Displacement

6. Velocity

7. Acceleration

8. Momentum

9. Continuum

10. Rigid body

11. Particle

* The fundamental laws of Newtonian mechanics are

1. Newton’s 3 laws

2. Law of gravitation

3. Law of transmissibility of forces

4. Parallelogram law of forces

1. Newton’s first law states that every body continues in its state of rest or of uniform motion in a

straight line unless it is compelled by an external agency.

2. According to Newton’s second Law

Force µ Mass × Acceleration

3. Newton’s third law states action and reaction is equal and opposite.

4. According to Newton’s law of gravitational acceleration the force of attraction between the

bodies of mass m1 and mass m2 at a distance d is

F =

where G is the constant of proportionality.

5. According to the law of transmissibility of force, the state of rest or motion of the rigid body is

unaltered, if a force acting on the body is replaced by another force of the same magnitude and

direction but acting at any other point on the body along the line of action of the replaced

force.

6. Parallelogram law of forces states that if two forces acting simultaneously on a body at a point

are represented in magnitude and direction by the two adjacent sides of a parallelogram, their

resultant is represented in magnitude and direction by the diagonal of the parallelogram which

passes through the point of intersection of the two sides representing the forces.

* Triangle law of forces and polygon law of forces are the laws derived from parallelogram law of

forces.

* Unit of force is so defined that the constant of proportionality in Newton’s second law becomes

unity. In SI system 1 newton of force moves 1 kg mass at an acceleration of 1m/sec

2

.

* 1 kg-wt = 9.81 newton. In practice 1 kg-wt is simply called 1 kg.

* System of forces

1. If all forces do not lie in a single plane, it is system or forces in space. If all forces lie in a single

plane it is coplanar force system.

2. If all forces in a system pass through a single point it is concurrent force system otherwise it is

non-concurreat force system.

3. If all forces in a system are parallel to each other it is parallel force system.

* Scalars and Vectors: A quantity is said to be scalar, if it is completely defined by its magnitude

alone and it is vector, if it is completely defined only when its magnitude as well as directions are

specified.

RESULTANT AND EQUILIBRIUM OFSYSTEM OFCOPLANAR CONCURRENT

FORCES

* If F1 and F2 are two forces acting on a particle and the angle between them is q, the magnitude of

their resultant is

R =

and the inclination of resultant to the direction of force F1

is

=

* If a force F makes angle q with x-direction,

Fx = F cos q

Fy = F sin q

* If a system of forces are acting on a particle,

R =

and its inclination to x-axis a is given by

a =

* Self-weight (W = mg) and reactions from the bodies in contact with the body under consideration

are non-applied forces.

* If body under consideration is freed from contact surfaces of other bodies and the forces on it

including self-weight and reactions from contact surfaces is shown, it is known as free body

diagram (FBD) of the body.

* Lami’s theorem states that if a body is in equilibrium under the action of only three forces, each

force is proportional to the sine of the angle between the other two forces.

=

* If contact surfaces are smooth, reaction between them is normal to the tangent at contact surfaces.

* Equilibrium equations in planar system are,

SFx = 0, SFy = 0.

Resultant and Equilibrium of Coplanar Non-Concurrent Forces

* Moment of a force about a point is the measure of rotational effect of the force and is given by

M = F × d

where F = the force and d is perpendicular distance of the force from the moment centre.

* Varignon’s theorem, also known as principles of moments, states the algebraic sum of moments of a

system of coplanar forces about a moment centre is equal to the moment of their resultant force

about the same moment centre.

R × d = SFidi

* Two parallel forces equal in magnitude and opposite in direction and separated by a definite

distance are said to form a couple.

1. The translatory effect of a couple on the body is zero.

2. The rotational effect about any point is a constant.

* Magnitude, direction and the distance of resultant force from the moment centre are given by

R =

a = , and

d =

* x and y intercepts of resultant of non-cocurrent system of forces in a plane are

x = , y =

* Equations of equilibrium of non-concurrent system of forces are

Rx = SFx = 0, Ry = SFy = 0, SMA = 0

If points A, B and C are not collinear, the following equations of equilibrium may also be used:

SMA = 0, SMB = 0, SMC = 0

line AB is not in y-direction, the following set of equilibrium equations may be used

Ry = SFy = 0, SMA = 0, SMB = 0.