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PRINCIPLE OF WORK IN ENGINEERING MECHANICS

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. 

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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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