We
have started a new topic in our previous post i.e. engineering mechanics. We
have seen there the basic concept of force
system, basic concept of truss
in engineering mechanics and we have also discussed there the process
to solve the truss problems using method of joints and method of sections with the help of our previous post.
Now, we will be interested here to understand the principle of virtual work in
engineering mechanics with the help of this post. We will see here, in
this post, the definition of work, .
So, let us start with the definition of work
Work
is basically defined as the product of force and the displacement in the
direction of the force.
Force
is a vector quantity but work is a scalar quantity.
Let
us consider that a force F is acting over a particle P as displayed here in
following figure. Let us assume that particle P is moving along the path C
under the action of force F. Let us consider that s is the distance of particle
at a particular point from a reference point.
Let
us find out here the work done by the force F over the particle P, when
particle moves by an infinitesimal distance ds under the action of force F.
dW = F.ds = Ft.ds
Complete
work done by the force F along the curve segment C will be given by following
equation as mentioned below.
Where,
θ is the angle between the force F and tangent to the curve.
Following
curve will provide the work done by the force F in moving the particle from one
point to another point. Work done will be determined by calculating the area
between the curve drawn between force and displacement.
Let us think here, when work done will be zero?
Work
done will be zero when either displacement is zero or force is zero.
Work
done by a force acting perpendicular to the displacement will be zero. For
example, in above case, the work done by the normal component of the force will
be zero as there will be no work by a force which is acting perpendicular to
the displacement.
Therefore,
we can say here that the normal component will not do any work and only the
tangential component will do the work.
Work done by a bending moment or a torque
We
have seen the work done by a force recently, now let us think that if we need
to find out the work done by a torque or moment then how we will determine the
work done. Here we have used term moment, this moment could be bending moment
or twisting moment.
When
a force will be replaced by bending moment or torque, we will also replace the linear
displacement with angular displacement.
Therefore,
we can formulate here the work done by a bending moment or a torque with the
help of following equation as mentioned below.
So,
we have just recalled here the basic of work in the subject of engineering
mechanics with the help of this post.
Do you
have any suggestions? Please write in comment box and also drop your email id
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continuous update from www.hkdivedi.com.
Further
we will find out, in our next post, positive and negative effect of friction and the different types of friction in detail in engineering
mechanics.
Reference:
Engineering
Mechanics, By Prof K. Ramesh
Image
courtesy: Google
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