[SOUND] Hi and welcome back. In today's module we are going to finish up Random Varying Stresses and Miner's Rule. With that we will finish up Unit 3 on Fatigue Failure. The learning outcome for today's module is to be able to utilize miner's rule to specifically calculate the life of a part under a varying, fluctuating load. So last time we worked through this example and what we were able to determine is that the total damage on the part was equal to D = 0.00029. And that damage was caused in 10 seconds of these applied stresses. So what the question also asked us was to determine the life in hours remaining if this stress pattern continued to repeat for the remainder of the part's life. So this part, is going to see these cycles every 10 seconds for the rest of its life. So, you'll recall that when D=1, the part has failed, right? So, you have total damage and we know that the part, that 10 seconds of this causes 0.00029 amount of damage. So what we're going to do is we're going to take the number that would cause total failure which is 1 and divide it by 0.00029. And the idea is the part can repeat this 10 seconds of loading 3,367 times, right? So it can repeat these 10 seconds of loading 3,367 times before, the damage will equal 1 and the part will fail. So if we have 3,367 cycles and we know that each cycle is 10 seconds long so 10 seconds per cycle and they wanted us to find the time or the life in hours. So 1 minute per 60 seconds times 1 hour per 60 minutes, what we end up with is the life of the part is 9.3 hours. So this part can cycle for 9.3 hours of these stress cycles before it's going to fail. This is not a long life for a part and honestly you would probably have to redesign most components to live much longer. So there's some limitations to Miner's rule. What Miner's rule does is it calculates the life for each cycle, but what it doesn't do is it doesn't take in account, the order that the cycles are applied in. And specifically in this case, you had a cycle of very low stresses applied at the end. So sometimes what can happen is these initial cycles cause damage to the part and that damage can reduce the endurance limit. So here we're assuming that this actual cycle doesn't apply any damage and if it had been applied first in the part's life that would be true. But because of these other cycles that might have reduced the endurance limit it's possible that this cycle at a relatively low stress below the endurance limit actually does cause damage. So there's some limitations with Miner's rule involving when the cycles are applied. There's also some areas where you need to be very careful and if you look at the example that we used, the maximum and the minimum stress occurred in the same cycle, right? So this cycle had both the max and the min stress applied to the part. So calculating cycles or determining what cycles are occurring is actually quite a complex phenomenon. Especially when you have maximum and minimum stresses occurring across different cycles. In these cases, you can get something called hidden cycles where if you just were to calculate straight like we used to do. Or that we did across, counting cycles in a linear fashion across, you might miss some of the hidden cycles. There's a number of techniques you used to calculate cycles. The most popular might be or one of the most commonly utilized is the rain flow technique. These are really techniques for graduate level studies and so if you're really interested in fatigue. I encourage you to go on and take some graduate courses in it, so you can learn these complex cycle counting techniques. And just be aware, when you're in design, that these techniques exist, and some of your designs might require that type of technique, in order to properly do the analysis. So with that we're done with Miner's rule and done with Unit 3 and so I'd like to thank you for participating in this class. We've covered a lot of material from material properties in design to static failure theories and fatigue failure theories. And with that you should have learned a very strong foundation in the fundamental principles of machine design. So thank you for participating, I really enjoyed teaching this class, and I look forward to seeing all of you in future classes, and that's it. [SOUND]