[MUSIC] Hi and welcome back. In today's module we're going to continue going over fatigue stress concentration factors in fully reversed loading. So the learning outcome for today's module is to learn how to estimate a fatigue concentration factor for a component in fatigue loading. Again, today we'll be focusing on adding in stress concentration factors. So we'll be utilizing these equations for the fatigue stress concentration factor and the notch sensitivity factor. And again the fatigue stress concentration factor is reduced compared to KT, the static stress concentration factor, and it's reduced by Q, and that's because some materials have varying sensitivities to notches, so some materials are highly sensitive to notches and some are lower. So Q goes in there and reduces the stress concentration factor depending on how sensitive a material is to a notch in it. And this a chart for Q, so you can see it's dependent on both the strength and composition of the material and also the geometry, the radius of the notch. So here's our example problem. We can see we have a shaft in bending. It has a smaller diameter of one inch, a larger diameter of 1.5 inches and the fillet radii between the two diameters is .1 inch. And what the question is asking us to find, the fatigue stress concentration factor here at point A. And so the first thing we need to do is utilize this chart to calculate Kt which is the stress concentration factor before we adjust based off of the notch sensitivity of this particular steel. And in this case, for Kt, we have a shaft again, with two different diameters located or loaded in bending and you can see that we're going to need to calculate the r/d ratio and the D/d ratio. So, if we go ahead and start to do that, what we see is r/d is the fillet radius at the point of interest, right here, divided by the smaller diameter, right here, which is 0.1 and D/d is the large diameter divided by the small diameter which is 1.5 divided by one, which is 1.5. And so if we go ahead and look at this chart, we can see at 0.1 and we hit this 1.5 line right here, and that correlates to a Kt of about 1.7. So now that we have our Kt value, we can go ahead and calculate our Kf value, which is the fatigue stress concentration factor that we'll multiply our fully reversed stress by. So to do that, we're going to start with this Kf = 1 + q(Kt - 1) and then, we're going to have to go ahead and calculate Q. And so Q is going to be equal to 1 / 1 + the square root of a divided by the square root of r. So we already know r equals 0.1 and what we need is to calculate a. And a is going to be, the equation for the square root of a for a steel right, because we have a steel in bending is 0.246- 3.08 x 10 to the -3 times the ultimate strength which here was given to us as 240 ksi. So, 240 ksi, this equation is in ksi, so you can just leave the stresses exactly in ksi plus 1.5 + 10 to the negative fifth (240 ksi) and then -2.67 x 10 to the -8 (240 ksi). And this ultimate strength is cubed and this one I forgot to put in is squared. So if we go ahead and we solve this equation, we end up with the square root of a = 0.0075. And that gives us a q factor of 1 / 1 + 0.0075 /square root of 0.1, which is a q factor of 0.97. And that indicates that this material is very sensitive to notches, right? We're right almost at q equals 1. So, what we can go ahead at this point is calculate our Kf, which is our fatigue stress concentration factor and that's 1 + 0.97 (1.7- 1), and we get our Kf is 1.68. So it's just slightly lower than our Kt. And so then, when we knew the fully reversible stress at point A, we could go ahead and calculate the maximum stress that's happening here. So our sigma max reversible at point A will end up being Kf times our sigma nom reversible. Okay, so that's it for today's module. Next time we'll look how to add all of these steps together and solve the entire problem. I'll see you next module. [MUSIC]