 Hello students, I am Professor Bhagyaj Deshmukh from Mechanical Engineering Department, Valchain Institute of Technology, Solapur. In this topic, the failure of machine elements Part 2 will be discussing failures of simple machine elements. After completion of this session, you will be able to write the design equation for typical machine elements. These are the primitive design equations. If you learn these equations, then it will be easy for you to design the components which are having the combination of failures of these primitive failures. Let us see the next case. Now the straight bar is changed. Let us use some different type of rod. I will call it as a stepped rod or a stepped bar. It is a solid bar, however it is stepped over here. The diameter at the smaller zone is D. The cross section over here is having small d as the diameter whereas the larger portion represents capital D as its diameter. This component is loaded under tension. It is pull force P. It is to be understood that the force is in the line of axis. It is axial loading. Therefore, it is a pull force. The component is going to be stretched. Now it is interesting to write the design equation for the component. One may need to think whether the component will fail at which location, whether this or this. Then you can check our regular equation force P equals two brackets. First bracket is area which is resisting the failure multiplied by the corresponding stress. Here it is sigma t. There can be two locations. Either the component will fail somewhere over here or at this junction and second this is the first case and here at the larger diameter there may be the second case. This is the second plane where the component may fail. However, if you look towards the equation if area is going to get increased the stress is going to get decreased. Therefore, at larger area the stress will be definitely less and therefore the failure is going to happen at the weakest cross section. Therefore, when there is a variation in cross section or there is a change in cross section one need to identify where is the weak section and weak section one can find over here. This is the weakest section here somewhere because it is a junction. But we will take that the failure is going to happen at diameter D and the section will be like this. It is a circular cross section which is going to resist the failure. Then I need to write on the basis of this p into a p is equal to a into sigma t on the basis of that I need to write the equation force p equals pi by 4 into d square I am taking this small d because at larger diameter at capital D failure is not going to happen multiplied by sigma t is the corresponding stress. Therefore, the component is going to fail over here therefore, I need to write the design equation for this section. This is a case of a stepped rod or bar which was loaded under tension. I need to use sigma t we can try with our rule just extend this axis you will find that the force applied is perpendicular to the area which is resisting the failure as per my thumb rule I can attribute this failure to tensile failure. Let us move further we will see the next case now the component is bit changed I am changing the component let us see the component in some modifications I am doing some modifications with this component this is a solid rod or a solid bar which is under tension I have drilled a hole which is perpendicular to the axis of the given rod. We can see the other views also this top view in the top view you can find it very correctly if you project these two then you can get the top view of the hole which is drilled in this solid rod the diameter of this circle is small d one can see in the side view also this represents the hole the outer circle diameter is capital D and this hole if I see this dimension it is small d I need to write the design equation for this component we need to begin with the area available for this component the weakest section I need to identify the component is not going to fail at this section the component is not going to fail at this section it is going to fail somewhere over here because the area you have removed this material from the component one need to identify that area see what is going to happen with that area this is a circle which was earlier fully filled but you have drilled a hole over here and hence the material is to be removed from this component therefore effectively this much material only is available I can show it over here this is only the material because it is by drilling a hole in this rod you have removed the material therefore I need to find out what is the area outside circle area is pi by 4 d square therefore p is equal to pi by 4 capital D square is the established equation minus I need to reduce this area of the rectangle which rectangle I am talking about this portion because we have removed this material then how much is that area height is d because the diameter of this rod is d and this dimension is small d therefore I need to reduce capital D into small d is a rectangular area from this component and then this is the net area available I need to multiply with the corresponding stress I am going to use sigma t as the corresponding stress because here again if I check the force is perpendicular here you can see the force acting is perpendicular to the area which is resisting the failure therefore it is a typical case of tension or the failure is going to happen due to tension hence it is mentioned as tension and corresponding stress I am going to use it as sigma t ok let us move further let us make the earlier component more complicated now we have seen a bar which is loaded under tension we made that bar a hollow the side view of the bar was like this inner circle and outer circle the top view if I try to indicate it is like this I need to make this component hollow then further due to additional need we drill a hole in this component in the front view you can see it like this there will be no hole over here the reason is already the material is removed in the side view also I can show the component this is the change in the component if one try to identify the area one need to think upon it the force is p the component is loaded thank you