[MUSIC] Okay, this is Module 34 and we're going to finish up the design of the beam to be used in this real world engineering problem. Here is our beam model with a load and we selected a wide flange I-beam shell. We've done some critical checks. We've looked at the maximum flexural stress at the outer fiber. We've looked at the maximum transverse shear stress experienced at the neutral axis, point C. And, today we're going to check the last point, which is point B, where we have a combination of normal stress and sheer stress. And, we said that the junction of the web and the flange simultaneous high normal stress due to the bending and large fexural stress make it a critical point for investigation. And so, we're looking at point B. Question becomes, since it's a combination of normal stress and shear stress, where along the beam does the highest combination of bending moment and shear force occur, and what are those values? So, we're going to look at our sheer force and bending moment diagram and I'm going to eyeball to find the largest combination, which is going to occur right here where I have 175.5 kilonewtons for the sheer force and a large bending moment, as well as 105.3 kilonewton meters. Okay, so we now have those values and we can now solve for the sheer stress experienced at point B using our sheer stress transfer sheer stress formula. And so, what we do need to is, we need to find the first moment of outward area at point B. So, I make my cut at point B, y bar, out to this outer area is 166.2 plus 9.8 divided by two times that outward area which is 171 times 9.8 millimeters. So qB, the outward area at point b ends up being, the first moment of outward area point b ends up being 286,730 millimeters cubed. And, so now I have my Vmax. I have my first moment of outer area, I've got my I. I know what my B is, and so at point B we can solve for the transfer shear stress and it ends up being 60.3 megapascals. Now we also have to find at point B the flexual stress so the normal stress and so to determine that we take that moment value at that cross section, we have our I we know now that the Y is the distance on the cross section from the neutral axis to this point, and in this case the y is going to be 166.2 to point B. If I substitute that in I find that my normal or flexural stress experience at point B is 144.6 MPa. And so now I have my tower B, my sigma at B. And I can draw my stress block, which has got a combination of normal and shear stresses as shown. So we have our shear stress at point B, our normal stress at point B. And what we can do now is we can draw Moore's circle. And I'd like you to do that on your own. Find the maximum sheer stress experience because that's what we're designing against. And so here's my Moore's circle. I can find in the center, I can find the radius and therefore from the radius I know that my maximum shear stress at point B is 94.1 megapascals and that is less than the maximum, or excuse me, the allowable shear stress that we were designing for which was 104.6 megapascals if you look back at the previous modules. And so again, we're okay. We've now checked a, b, and c critical points and all of them are good enough for our design and so we have now arrived at our final answer. And, so we are going to select the 356 x 45 wide beam, wide flange I-beam, with that section modulus and it will work to carry the load that's desired. And, so you now have a very nice procedure for designing a real world engineering beam and so that's where we'll finish this module. [MUSIC]