Statics - Introduction to Engineering Mechanics
Fundamental definitions:
Mechanics: Mechanics is a physical science which deals with the effects of forces on objects that are at
rest or in motion.
Engineering Mechanics: Engineering mechanics deals with the principles of mechanics as applied to
the problems of engineering.
Rigid body: A body is considered rigid when the changes in distance between two of its points is
negligible for the purpose at end.
Deformable body: A body is considered deformable when the changes in distance between two of its
points cannot be neglected.
Particle: A particle will have mass but its size is negligible.
Note: In engineering mechanics we treat all rigid bodies as particles. When a body is
idealised as a particle, the principles of mechanics reduce to a simplified form.
Scalar quantities: These are the quantities characterized by only magnitude, such as mass,
temperature.
Vector: It is a Mathematical tool which describes those physical quantities in nature which requires
not only magnitude but also a direction for their complete addressing. Such as velocity, force.
Mass: Mass is the quantity of matter in a body. It is a measure of the inertia of a body, which is the
resistance to change of velocity
Matter: Anything which has mass and requires space to occupy is called matter
Mechanics
Mechanics of
Deformable
Bodies
Mechanics of
Rigid Bodies
Statics
Dynamics
Strength of
Materials
Kinematics
Kinetics
Fashion of
motion
Cause & Result
of motion
Mechanics
of Fluids
Statics: Statics deals with the action of forces on bodies at rest or in equilibrium.
Dynamics: Dynamics deals with the action of forces on bodies in motion.
Kinematics: It deals with the study of geometry of motion without considering the cause of motion.
Kinetics: Kinetics deals with a study of motion considering the course and result of motion.
Principle of transmissibility: The point of application of force may be transmitted along its line of
action without changing the effect of force on any rigid body to which it may be applied.
Principle of superposition: The action of a given system of forces on a rigid body will not be changed if
we add or subtract from them another system of forces in equilibrium.
Free vector: It is a vector, whose action is not confined to or associated with a unique line in space.
Only the direction and magnitude of the vector remains fixed. Example: Couple
Sliding vector: It is a vector, which may be moved along the lines of action without change of meaning.
For example: In towing a cart, we may apply the force anywhere along the rope.
Bound/fixed Vector: A bound vector is a vector with a well defined point of application. A bound
vector is, therefore, specified by magnitude, direction and its point of application.
Example: A vector representing force acting on a particle can be treated as a bound vector.
Equal Vector:
Two vectors are equal if they have the same magnitude and direction.
Equivalent or Equipollent Vectors: Two vectors are said to be equivalent or equipollent if, in a certain
sense, they produce the same effect on a rigid body.
External forces and Internal forces
External force: They represent the action of other bodies on a rigid body
Internal force: They represent the forces which hold together the particles forming the rigid body.
Force: Force is an action which may or may not change the state of a body. We cannot see the force,
but we can feel it. It’s not a thing, but it’s an act. It is a vector quantity.
Characteristics of force
•
Magnitude,
•
By the direction of action and
•
By its point of application.
•
Line of action
Force has many names and is called by that name in the context of mechanics
Wight
Compression
Buoyancy
Viscous
Pull
Repulsion
Push
Lift & Drag
Friction
Attractive force
Resistance
Centrifugal
Tension
Centripetal
System of forces: Several forces acting simultaneously upon a body
System of
Forces
Noncoplanar
Coplanar
(2D)
Concurrent
(3D)
Nonconcurrent
Parallel
General
Concurrent
Non-concurrent
Parallel
General
Coplanar System of Forces: Forces that acts in plane. They are also called 2-dimensional forces
Types of co-planar forces:
Non-Coplanar System of Forces: These are 3-dimensional forces or System of forces in space or Forces
that acts along x, y and z axis.
Types of Non-coplanar forces:



Concurrent forces
Parallel forces
General forces
Composition of forces: The replacement of two or more forces vectors by a single force vector having
the same effect is called Composition of forces. This is known as Resultant
Resolution of forces: A single force vector is replaced by two or more forces having the same effect is
called Resolution of forces. In 2D the force is resolved in to two components.
Note 1: If a force is away from the origin, the components of a force are also way from the origin
Note 2: If a force is towards the origin, the components of a force are also towards the origin
References:
•
Engg. Mechanics ,Timoshenko & Young.
•
Engg. Mechanics, R.K. Bansal , Laxmi publications
•
Engineering Mechanics,Fedinand.L.Singer , Harper – Collins.
•
Engineering Mechanics statics and dynamics, A Nelson, Mc Gra Hill publications
•
Engg. Mechanics Umesh Regl, Tayal.
•
Engineering Mechanics by N H Dubey
•
Engineering Mechanics , statics – J.L.Meriam, 6th Edn – Wiley India Pvt Ltd.
•
Engineering Mechanics , dynamics – J.L.Meriam, 6th Edn – Wiley India Pvt Ltd.
•
Mechanics For Engineers , statics - F.P.Beer & E.R.Johnston 5th Edn Mc Graw Hill Publ.
•
Mechanics For Engineers, dynamics - F.P.Beer & E.R.Johnston – 5th Edn Mc Graw Hill Publ.
•
www.google.com
•
http://nptel.iitm.ac.in/