Shear & Bending Moment Diagrams: 1a. Toys Wood Member Holes And Notches

So where's the best location to cut a hole for a 2-inch pipe on this span of this depth beam? So I have these holes in there. This one is at location 8. This one is at location 9 on the bottom at mid-span. And then this one here is at location, let's see, bottom at the support, location 3. So, let's see what happens here. At the support, the shear is very high. And so taking out area doesn't leave enough area for shear where down meets up. So any loading here is going to cause this beam to fail in shear. It's not going to bend and deflect. But suddenly, if I put a load here, it's going to fail right there. Because there was not enough area there. to handle that amount of shear. So any of the locations near the support, locations 1, 2, 3, are not very good location. 4, 5, 6 are middle of the road. Let me skip them. 7, 8, 9, let's see what happens with 7, 8, 9. I have these two toys. One of them has a pretty big cut located where 9 is. 9 is high tension. And so when I load this beam here, it's going to bend and it's going to deflect up to a certain point. But then if we exceed the allowable stress in tension on the bottom at this location, it's going to fail. That's not true if it's on the compression side because that hole is closing and it still might fail there. But I wanted this toy to illustrate a hole location bottom tension. So when I load this beam here, it bends, it deflects, oops, it just failed in bending at this location on the tension side below the neutral axis. It just gave in bending. Unlike the other one, the first one failed in shear at the support. This one failed in too much bending. It failed on the tension side versus location eight, which is the correct answer. It's where shear is low. We don't want to be at 1, 2, 3, where shear is low. But then 7 or 9, no, 8 at the neutral axis has no tensile stress or compressive stress in this Y axis. So this one should be able to survive. Even with the hole in there, it's still capable of taking bending and shear without failing. So, in response, the best location to cut a hole is at mid-span, where the shear is low, and in this direction, at the neutral axis. So, best location is at the neutral axis, at mid-span. None of the ones at the support are good, because they all have high shear, and you're taking out area. Shear is dictated by area. Bending and deflection really depend on the depth of the beam. The depth of the beam meaning section modulus and moment of inertia versus area. Area is necessary and very critical at the support. Okay. Bye. Продолжение следует... Продолжение следует... Продолжение следует... Продолжение следует... Продолжение следует... Продолжение следует... Продолжение следует... Продолжение следует... Продолжение следует...