 Hello students, I am Bhargesh Deshmukh from Mechanical Engineering Department, Valkchian Institute of Technology, Solapur. This topic is on design against fluctuating load. We are going to see the charts about the stress concentration factors. At the end of this session, the student will be able to use the standard charts to calculate the stress concentration factor. We are supposed to use the charts developed by R R Moore which can give us what is a stress concentration factor for different cases that are understood. We have seen that there are some fundamental equations. You may revise that we have used some of the equations. The basic equation is sigma t equals p by a then sigma b equals bending moment divided by the section modulus. We have seen these equations. Then what is the issue? What happens when it becomes a fluctuating load? Here in this case, we are dealing with the static load. This load is static. This bending moment is based on the static load. That means the load is not going to change on the basis of time or with respect to the time. However, if the load is going to change with respect to time, if there is a variation in the load magnitude, then we need to discuss something. But before that, let us move to the stress concentration. You may think upon what will happen if I am going to cut a sugarcane. Where do we cut? If I am using a sugarcane to cut, if this is a sugarcane, I will check for the node and I will put it at some support and then we will apply the force on this sugarcane so that it breaks readily at this zone. It is a node. What happens? If you check it, there is a change. Here we can find, there are the fibers. However, at this location, it is a brittle somewhat or the material changes at this location. Then what happens when you change the material at this location? It causes a stress concentration at that location. If I say that the stress concentration, then what is the stress concentration? This concentration, if I say that if this is a plate which is loaded under tensile load, tensile force which causes sigma t to develop in the material. If the plate is having a hole over here, whatever is the magnitude of sigma t by regular equation, we have the regular equation, whatever is the magnitude over here, it has been seen that at the location near the discontinuity, discontinuity means the hole. If this value is sigma t, same value is over here. If I assume it is wrong assumption, it is observed that this value exceeds the normal stress value. That means this is sigma t, this is sigma t max and hence there is a need to define the stress concentration factor. Then the stress concentration factor is defined as k t, k t is given as sigma max upon sigma 0 or sigma 0 is obtained by the nominal equation, this equation sigma 0. Sigma max is observed stress at this location, either you can use the photoelasticity method or some modern methods but RR Moore has used the photoelasticity method to obtain this k t value by using sigma max because under photoelastic analysis, we can find out what is sigma t max and hence we can get what is the value of k t. Therefore, k t is defined as the maximum stress at the discontinuity divided by the nominal stress obtained by the regular equations. If I proceed further, there are various cases about the stress concentration. If I check a few cases, if the component is going to change its shape, the abrupt change in the cross section, if this is the case, I am looking at the component, the component is changing its shape, there is abrupt change in diameter at this location on the left end and the right end is different. If I apply a force on it, there exists then the stress concentration lines and what is going to happen over here, there are the stress flow lines initially if I draw a straight line, this is the stress flow line at the inner zone, other lines if I show, I am interested in this line when there is a abrupt change in the cross section, you can find that this stress flow line has abrupt change in its direction. The second nearer line will have then again a sharp change in its direction, therefore at this location, the stress concentration phenomena is observed, we are interested to reduce this then what can be done. I can then use a component with a modified style, if this is a component step then I will be using a fillet like this and then the component can be again made as like the earlier component. Here what will happen to the line, this line I am explaining the stress concentration line, this concentration effect is over here, I need to mitigate that effect, I cannot however eliminate the effect of stress concentration, I need to mitigate it. Now you can see that this stress flow line will gradually change its direction, the other line will also gradually change its direction, therefore the concentration, the flow lines which were coming together is now mitigated and we can get relief from the stress concentration or the effect can be reduced, here the effect was maximum, I could reduce this but I cannot eliminate thoroughly the effect of stress concentration. The reason is if I need a discontinuity, this discontinuity is essential because I need to put a bearing over here, I need to mount maybe a gear, maybe a pulley, then I need to change the shape, I need to have these geometric irregularities as a functional requirement. I cannot reduce it beyond some limit, I cannot eliminate it but reduction is possible. We can see some other case also, if I have a threaded bolt, let us see this bolt, this is a bolt which is under axial loading, I will draw a thread over here for representation so that you will understand how the stress is going to flow, here the stress flow line, the stress flow line is going to pass straight, this is how we can reduce the stress concentration effect. The problem can arise if I use a component where this bolt, the similar bolt if I design it like the shank diameter is less than the outer diameter, you can see that now what is the effect. If I prepare the further part like this, here the shank diameter is equal to the core diameter, same case but in case if I prepare it equal to, if this is the case now, what will happen the stress flow line over here will get immediately deviated, I need to reduce that and the effect has been obtained over here, this case I can reduce the effect, the line can go straight therefore, the effect stress concentration effect has been eliminated. Therefore, I need to use some chart, let us see one of the chart, how we can use the chart, let us see one case, how to use this chart, how to get the KT value, you can see that the component is mentioned as a plate, wherein the diameter of this hole is mentioned as small d, you can see over here and the outer the other dimension of the plate is w, this dimension is small d, then how to get this KT value, I need to check what is the ratio d by w, I need to calculate d by w, look at it over here, let us say it is 0.4, draw a vertical line which is going to cut the line shown by this curve, from this point draw a horizontal line, this is what is the value of KT that you need and therefore, KT from KT what you can do, KT equals sigma max upon sigma 0, you can get sigma max using this chart, this is what is the use of the chart, thank you, you may use the book of VB Bhandari for this, thank you very much.