Seismic: Diaphragms 2

So let's talk about diaphragms. Diaphragms are horizontal structural members. Basically, they're the floor. When the floor gets a gravity load, be it dead load, life load, or a combination thereof, we call it a floor. But the same member, when it receives lateral wind or seismic forces, we call it a diaphragm. So it's basically your floor with a lateral load. So diaphragms come in two varieties, a flexible diaphragm that is made of pieces, plywood, or whatever it is, versus a rigid diaphragm, which has to have cast in place or monolithic concrete. So flexible diaphragms are ones that are made of pieces, such as plywood, metal deck, precast members. So let's look at this animation very quickly. It's just showing me what makes a flexible diaphragm. And it has an error in that cast and placed concrete should not be in this animation. That's for rigid diaphragms. But if we think of metal deck, that's a bunch of pieces. Plywood, OSB, they're all a bunch of pieces. all your wood frame is typically flexible diaphragms. In a two-story shopping strip, for example, the floor could be metal deck plus concrete, cast-in-place concrete, which ties all the pieces together, but the roof is just going to have metal deck and insulation. That's a flexible diaphragm. Very good. So the aspect ratio is another important consideration. If the proportion of the dimensions of the diaphragm are greater than 3 to 1, that's it, it's flexible, doesn't matter if it has concrete cast in place or not. So to be a rigid diaphragm, the aspect ratio must be less than 3 to 1 and it must have cast in place concrete. So in a flexible diaphragm, the vertical supports are more rigid than the diaphragm itself. So these guys are stronger than the horizontal, that's the definition of a flexible diaphragm, and when a lateral load comes in, the diaphragm gives, it deforms, there's gaps between the pieces and they close and they open accordingly. So we have collectors that are in, that are parallel to the direction of the lateral load and they take the load from horizontal diaphragm down to the foundation. So collectors is the first component that we need to know. Another thing that we need to know in a flexible diaphragm we have a compression cord which is the first cord that lateral load hits and there's another tension cord in the back just like with white flange the top goes in compression, the bottom goes in tension. Well, in a flexible diaphragm, the front cord goes in compression, the back cord goes into tension. Very good. That dimension over there is called the in-plane deflection of the diaphragm. And let's see what the bullets say. Vertical supports are more rigid than the diaphragm. Yes, the diaphragm bends and racks. This corner is no longer 90. None have not deformed as much as the diaphragm. So the verticals don't deform. Tributary spacing of walls determines the load distribution from diaphragm to verticals. Give me a minute on this one. I'll explain it in a little while. The load distribution. Okay. So let's keep going with this animation here. Now, if you have two laterally enabled shear walls, for example, and they're by a drag strut, what happens is the diaphragm sends its load to the drag strut, and the drag strut sends the load, the lateral load, to the two shear walls, for example, or moment frames, or what have you. Okay, so those are the terms I wanted to go over, collectors, and compression chord, tension chord, in-plane deflection of the diaphragm, and a drag strut. Very good. So this This next animation shows me what happens when a lateral load comes in and hits a flexible diaphragm. It bends it and it acts, this diaphragm acts as two simply supported beams. What happens here is the tributary spacing of walls determines the load distribution from the diaphragm to the verticals. It's clear what's happening here. This red load, which is from wind or what have you, is split between these two collectors and the same for the next one. So what happens is this much tributary width is going to... What happened? I didn't mean to do that. So let's see what happens with this animation here. When the lateral load comes in and it pushes on that diaphragm, it does tributary load distribution and it's as if this diaphragm made of several pieces. Let's start over again. Okay. Zachtig baby. So let's look at this animation here and see what happens when we have two bays underneath a flexible diaphragm. Let's see how it responds. When the lateral load comes in, it pushes on that diaphragm and it deforms it basically because it's flexible. And so it acts as if it were two simply supported beams. And now this bullet says tributary spacing of walls determines the load distribution from the diaphragm to the collectors. What happens here is this bay here, this first bay, the lateral load from that first bay is going half here and half here. And the same for the next one, half to the middle and half to the end. And so what ends up happening is tributary load wise, this half goes here, this half goes to the end member, and the one in the middle, the collector in the middle, is taking from left and right, so it ends up with twice the amount of lateral load as the end two. So x, 2x, x. So that's the meaning of tributary spacing of walls determines the load distribution from diaphragm to verticals. Excellent. The load distribution to verticals is independent of rigidities. That's significant. So of. They could be cast in place concrete, they could be OSP, or a moment frame. The rigidity does not matter. You're still getting X to X and X. Not the case with rigid diaphragms. That depends entirely on the rigidity, and less so on the spacing. Very good. So there is no torsion in a flexible diaphragm. Torsion is when the diaphragm twists in plan. Well, a flexible diaphragm bends. it doesn't cause torsion on the legs underneath it. That is for rigid diaphragms. Now, the final bullet says diaphragm deflection is greater than twice the wall drift. So, the amount of deflection in the horizontal plane is greater than twice the deflection or the drift in the vertical plane. Okay, so let's talk about rigid diaphragms. They are not made of pieces. They could be made of pieces, but then you put cast-in-place concrete on top of them, such as a metal deck, then they're all tied together and they're monolithic. Must have cast-in-place concrete if it's a rigid diaphragm. Also, the aspect ratio must be less than 3 to 1. The vertical supports this time are less rigid than the diaphragm. The walls will be the ones to bend and rack and their corners will no longer be 90. The verticals will deform and the tributary spacing of walls in multiple bays is not relevant. The load distribution to the verticals or to the collectors is totally dependent on the rigidities. So let's take a look at this animation here where there is something called the center of mass which is the geometric center of the diaphragm. And what happens here is if you take the two diagonals, intersect them, that's the center of mass. The center of rigidity or the center of resistance is basically based on the stiffness of the two legs. If the two legs are similar in rigidity, then it also happens to coincide with the center of mass. And there will be no torsion as long as those two arrows are pushing against each other. So here's the term that we saw a little while ago, drift. Drift is that dimension how much the wall deflects in its plane versus the deflection of the diaphragm. So as long as the legs are symmetrical in rigidity or stiffness, then the green center or the center of rigidity coincides with the center of mass, the geometric center. Okay, so no torsion if rigidity of the walls is symmetrical about the center of mass, the code requires us to account for an accidental torsion worth 5%. Let's not worry about the numbers right now. But what this is saying is there is no such thing in an earthquake, for example, as absolute symmetry and there is no torsion. There has to be an accidental torsion for life safety, an account of accidental torsion for life safety. Torsion not symmetrical about the center of mass, the center of mass and the center of rigidity do not coincide, you get torsion. And the definition of a rigid diaphragm is one in which the diaphragm deflection in the horizontal plane is less than twice the wall drift in the vertical plane. So we saw a moment frame under a lateral load in the, under a rigid diaphragm and a lateral load in the top animation. Now we're seeing the same but with a brace frame. The two legs are symmetrical in rigidity. The center of rigidity and the center of mass coincide. The diaphragm moves as a unit. It does not twist and move. Okay, now looking at two bays, the top animation is for a brace frame, two bays under a rigid diaphragm. All legs are symmetrical, so it's going to move as a unit. The animation. So they will each resist an equal amount of shear if they have the same rigidity and as long as the legs are symmetrical there will be no torsion, no twisting implant. Excellent. Now regardless what the materials are it doesn't matter as long as those legs are symmetrical in rigidity we will have no and the diaphragm just moves as a unit as long as there's symmetry of rigidity about the central mass. Excellent. So now looking at the bottom animation, I see a wall that is fatter than the two end walls. If it's fatter and the same material and same construction, then it's going to be more rigid. But there is symmetry because this fat wall, this more rigid wall, is in the dead center. And the two end walls are supposed to be the same rigidity. So we have symmetry of rigidity. And the plane or the diagram, the rigid diaphragm, moves in the same plane and does not twist. It just moves back and forth. Very good. So there was a slight graphic error in this animation, but my student graduated many, many years ago, and this is not something I can fix with quite out. So anyway, these three arrows should not be the same length. The one with more rigidity needs to be longer than the other two in the proportion of rigidity. Okay, I cleared up that error. Let's move on. So now we have this side, the far side is double braced, and X-braced versus the near side is a single brace. That's the difference of rigidity. There's going to be torsion. So let's take a look at this animation. The center of mass is still in the dead middle, the geometric center. But the center of rigidity this time is closer to the X-brace versus the single brace. So there is, these two arrows have to be equal in shear, but they're not head-to-head, so they're going to make a moment, a torsional moment, in this case it's clockwise, because the center of mass is to the, the center of rigidity, I apologize, is to the right of the center of mass. Let's see another one. This time we have a brick wall and a brace frame. The brick wall is clearly more rigid than the brace frame of steel. So the center of rigidity is closer to the brick wall. There's an eccentricity between the two centers. Therefore, there's going to be a rotational or torsional moment in this case. So the load finds the center of mass. The two legs fight unequally but come up with the same amount of load, but it's eccentric and therefore there's a counterclockwise torsional moment in this case. And looking at the last animation on this page, we're going to see a long wall and a short wall assuming same material and same mortar and what have you. Then the longer wall is going to be more rigid than the shorter wall assuming same thickness. So it resists load in proportion to its rigidity because the diaphragm is rigid. Had this been a flexible diaphragm, it would have been based on the spacing. But no, it's a rigid diaphragm. Rigid diaphragms cause torsion. Flexible diaphragms do not. So different materials have different ability to resist lateral load clearly. In this bottom image, bottom left image, OSB on one side, CMU on the other side, they don't have the same rigidity. They're different. So the same with wood siding versus CMU, hollow core planks versus metal studs with bracing. They have different rigidities. So they're going to experience lateral load differently. So let me repeat this animation. We saw this one before. It has the fat wall in the middle and two symmetrical rigidity walls on either end, and it had the wrong graphics here. this green arrow needs to be longer than the other two. Anyway, this one is symmetrical. The center of rigidity and the center of mass are coincident, and therefore the diaphragm just moves as a unit. Now, if we take this more rigid wall and put it off on the end, and the other two have the same rigidity, now this is no longer symmetrical, and we will have some torsion. Now the green arrows are correct. Must be the student corrected them. So the center of mass is in the middle, but the center of rigidity is closer to the more rigid wall. And there is a large eccentricity this time. And so this wall, sorry, this diaphragm is going to rotate in the counterclockwise direction. Excellent. Looking at this animation, it has three equal stiffness walls, but their placement is non-symmetrical, and therefore the center of rigidity is going to be closer to the two that are near each other than the one that is out here in the front. The center of mass is still in the dead middle. The center of rigidity is way over there. Therefore, this is going to have a clockwise moment. It is very difficult to keep the diaphragm on top of the walls when you have an eccentricity and a torsional moment such as this. Looking at earthquake, let me, good. So this time, the load comes from the ground, and anything that has dead load is going to receive a proportional amount of seismic force. Due to the ground shaking, the forces will push the legs away from us, and due to its inertial force, the diaphragm will come towards us. And now the legs start fighting and the right leg is stronger than the left leg. So we will have torsion. And in a heartbeat, in an instant, it'll reverse and it'll do that. So I had two students do these animations and they had totally different perceptions. And one had a lot of fun with them. And so both of them did. So now we're looking at the second animation, again, due to earthquake load. So this student decides to have a lot more fun with this one. Anyway, so there's the earthquake. There's the ground fault. And if you'll notice, the lava is even moving. And the reflection on the legs. Anyway, the idea is there's torsion because the legs are unequal. And here's some bloopers from one of the students. I asked him to show me how this gets off the wall. and he decided it's like a frisbee. And then this other one was another source of error. I wanted the diaphragm to become disengaged from the wall and show how can that stay up there all this time. Anyway, we had fun with these animations, and these are the bloopers, and I hope you learned something from the previous ones. So, yeah, if it separates from the wall, that's it. It can't stay up there that way. Anyway, rigid diaphragm Bye bye