Shear Walls: 4 Sw Discussion

So the last lateral system I would like to discuss is the shear wall. The post and beam we said is totally useless in the lateral direction. The moment frame has rigid connections between horizontal and verticals, which gives it some lateral stability. And then we discussed the brace frame with diagonal connecting two joints, which gave it even more stability. A little bit less ductility, but a little bit more stability. Finally, the shear wall. The shear wall comes in wood. You put plywood or OSB on top of studs, you have a shear wall. Or masonry, as we see in this image, CMU making a shear wall. Or else maybe on the campus of Rice University in Houston, the Caesar Pelli buildings as an example, are also doing a shear wall, or anything Tadau Ando is going to be a shear wall, cast and place concrete. Very good. So, looking at the load path for a concrete shear wall, if you have a concentrated load, then it goes down a 45 until it reaches the foundation. And if you have this uniform load, each one is going to do what that concentrated load is doing. This one will do this much, and this one will do this much, etc. So the load makes it down to here, and my 10 kip load, or whatever it was, is spreading to the foundation. Same with CMU. The same idea. It's a little bit less rigid because it's made of pieces versus cast-in-place concrete. Here we have mortar joints, and the mortar is supposed to be a little bit weaker than the CMU, or the brick rather. Looking at the lateral load, which is really what we need to focus on, if this wall is 10 feet tall and 20 feet long, then the 12 kips is going to each foot of the length. Unlike brace frames, it was going wherever the diagonal sent it, to one of the two supports, versus moment frame, there was two equal legs, and they carried half the load each. In a shear wall, the 12 kips is spreading over the length of the wall. So that turns out to be, how much is that? 3/5 0.6 kip per every linear foot or 600 pounds per linear foot. So here's 600 pounds, here's another 600, another one, another one, another one. Turns out 600 pounds per every foot. So 12 feet later, you're getting 600 pounds per foot multiplied by the length of 20 feet, and you get 12 kips. Okay, so that's it. The base shear is taken care of. The 12 kips went evenly to every linear foot of the 20 feet. there is still the problem of overturning. And with the overturning, here is the pivot. And this wall wants to do that under that load. And the overturning moment is clockwise about the pivot. And its magnitude is 12 kips. Here's the line of action. And the 12 kips is at a distance of 10 feet from the pivot. So 12 kips times 10 feet is 120 kip times foot of clockwise overturning moment. So who's going to resist the overturning moment? Let's see. We don't have two points the way we did with the brace frame or the moment frame. Here, what we have is rebar, and the rebar is anchoring to the foundation. And unlike a brace frame in wood or in steel, or a moment frame in steel, this wall has dead load. So it has a certain weight. I don't know how much the weight is, but there is a certain weight. And that weight is going to give me a counter moment. So the attack is 120 kip foot of clockwise. The response needs to be 120 kip foot of counterclockwise rotation to prevent this wall from rotating. Now, if the wall doesn't weigh enough, guess what? There's some rebars here, and they're anchored to the footing. And the wall might be bending a little bit so that the rebars to the right of center are going to go into compression, to the ones left of center are going to pull up. So there's anchorage to the footing I'm going to add the weight of the footing to the weight of the wall and make sure that the overturning moment is significantly less than the dead load moment Very good Now if you have a stud wall this example here if you have a stud wall and there's a bunch of studs and on top of them is OSB and let's say we anchor at three locations, A, B, C. There's an anchor bolt A, there's an anchor bolt B, and there's an anchor bolt C. Now, what's happening here is the wall still wants to do that, wants to rotate about point C. So, anchor bolt B needs to be a tie down. Let me fix it. Here's a tie down at B. Sorry, at A. and it wants to push back at C, and these two are going to make a couple. The attack is clockwise. The counterattack is counterclockwise. And anchor bolt B is doing nothing because it's in the middle of A and C, so it cannot participate in rotation. But it still is doing shear. Let's figure out the shear. So 12 kips is going to 3 anchor bolts, Each bolt is going to take 4 kips. So I'll fight with 4 kips. I'll fight with 4 kips. And I will fight with 4 kips. So the 12 kip of shear is taken care of. Each of ABC anchor bolts has to handle 4 kips and tie the sill plate to the foundation. And uplift is happening at A, but there's a tie-down, an anchor, at A. And anchor bolt C is being pushed into the ground. Very good. With concrete, of course, there is a major dead load. So there is a dead load. And we have to remember here that concrete weighs 150 pounds per cubic foot. And so if I can calculate the volume of this wall, given its thickness, its height, and its length, then I know the dead load. And when you throw a 12 kip lateral load at me, there is rotation about the pivot clockwise for the overturning moment. And there is a counterclockwise moment generated from the dead load. Just the dead load of the wall that doesn't exist in wood, doesn't exist in steel. In concrete, it's very heavy, and that is called a stabilizing moment. So the stabilizing moment needs to be significantly larger than the overturning moment. Stabilizing moment. So the stabilizing moment, let's call it SM. So the code requires that the stabilizing moment in a structure be at least 1.67 times the overturning moment. So I need to make sure that the dead load provides enough moment, and we'll do numbers later, provides enough moment, dead load moment, to counter by 1.67 times at least the overturning moment due to wind or whatever that 12 kip load is.