Support Conditions: Support Conditions

In this video I would like to talk about support conditions and structures, and I would ask you to consult another video or watch another video that I've produced on the same topic using the plastic toys. Okay, we have three types of support conditions based on their rigidity. The first one is a roller or a rocker and is represented with these symbols on a free body diagram. The next group is a pin, also called a hinge. A roller is called a rocker, a pin is also called a hinge, and it's represented with this symbol on a free body diagram. And finally, a fixed end or a moment resisting or a monolithic or a rigid support is represented with this symbol, and clearly the fixed end is the most rigid and the roller is the least rigid. So what happens when we load these beams supported on this type of support? How does the support respond? That's the topic of this video. So a roller support is capable of resisting loads in the vertical direction only. It has one vertical reaction. It is unable to resist horizontal movement and unable to resist a change of angle at that support or rotation due to bending. So a roller support has one reaction in the vertical direction versus a pin support. A pin support is one step stronger or more rigid than a roller. It has a horizontal reaction in addition to the vertical reaction. So it has two sets of constraints, one in the vertical, one in the horizontal. Still, it cannot resist rotation, as I will illustrate in the next slides. Very good. So a pin is a little bit more rigid because it can resist horizontal and vertical versus a roller that can resist only vertical. And a fixed end support is stronger than a pin. It can resist what a pin resists, which is basically vertical and horizontal. but in addition, a fixed support will also resist bending at the support and maintain the 90-degreeness of this angle, or whatever the angle is, doesn't have to be 90 degrees. A rigid connection prevents rotation at the support. So let's understand this a little bit better. Here's the roller, and it's capable only in the vertical direction. it'll move horizontally, and it'll rotate at the support. So let's understand this through the example of a free body diagram with a uniform load. And under this uniform load, the beam is going to respond as such. It's going to bend. The top is going to go in compression. The bottom is going to go in tension. And what happens is exaggerated. It deflects a little bit. Now, the pin has a vertical and a horizontal reaction, so it doesn't budge. But that angle has changed. It has rotated, so it's unable to resist moment or rotation. But the roller itself is going to be pulled in a little bit. It has no horizontal ability at all, but it has vertical ability. So the beam ends up pulling on the roller a little bit. the top goes in compression, the bottom goes in tension, and in this case, both supports the angle change from 90 degrees. So, no rotation resistance whatsoever. Looking at the next example that gives me a fixed support on the left and a pin on the right, the pin is going to do what it did earlier, so it cannot prevent rotation. It has a vertical and a horizontal reaction. Now the fixed end, how is it going to deflect on this side? It's not going to do that because the fixed end prevents rotation. So it's going to keep its 90-degreeness here, and then a little bit later, it's going to start to bend. So the deflected shape for this one is going to look like this. Here, there is rotation, because a pin support cannot prevent rotation. But on the other end, it remained 90 degrees. So instead of rotating, it fought back with a reaction, a moment reaction. And it prevented up-down, and it prevented the beam from pulling in at the support. So it also has a horizontal, it has a vertical, and it has an anti-rotation, or a moment resistance as well. So, when we have two fixed ends, it's not going to do what a simply supported beam on a roller and a pin would do. It's not going to do that. Instead, this 90 degree shall be maintained, this 90 degree shall be maintained. And so, it's going to do something like that. Minimizing the deflection and having one reaction and two and three on the right end, a moment reaction. a vertical and a horizontal. And then the same on the other end. It's going to have another vertical. It's going to have another horizontal. And it's going to have a bending moment reaction as well. So we'll talk about statically determinate and indeterminate in another video. This one I'm just trying to focus on the three kinds of supports and show you pictures. So here we are with roller supports. And let's remember that a roller, let's look at this image a little bit. It has a plate, a bearing plate, and it's anchored or embedded in concrete or masonry. And coming on top of it is this bottom cord of a truss. And there's this upside-down T that is attached to it. And this beam, this truss rather, cannot go down because this wall is going to support it back. So there is a vertical reaction. But in this direction, it is free to move. And what they would really do is put some Teflon here to encourage it to glide so that for thermal expansion and contraction, this allows horizontal movement. There is no resistance to horizontal, and the Teflon is encouraging horizontal movement, but vertically it cannot move. So these are rollers or rocker supports, and you can see on this ball here that some rocking is possible. That's the design of the support. We want it because it's a long-span steel structure, responds a lot to temperature, increases and drops in temperature so we gotta allow it to move a little bit. The same with this image, it can rock a little bit on this rocker. And the same here, I'm gonna talk about these two images in a short while, but let me also illustrate this one here which is just a 4x4 sitting on two layers or rather two concrete supports and it has vertical resistance that 4x4 cannot go down. It has vertical resistance on each end. But when loaded with this concentrated load and this concentrated load, well, it bent, and the top went into compression, and the bottom went into tension. And what happened at the support? At the support, it rotated. That angle is no longer 90 degrees. Remove the load. It'll go back to horizontal. So this support here is resisting vertical, but if you push it this way or that way, it moved a little bit because of the load. It's nothing we see with the naked eye, but it moved horizontally and it rotated at the support. These are two roller conditions. Let's look at this animation for, just to illustrate, this animation is of these two images here. So we're going to animate these and understand how a roller works and why it's there in the first place. So, we have several steel beams and they're sitting on this contraption, which is the support. And it has a cup, the bottom of it is curved. And here's the steel beam and it's sitting on this rocker. And as the temperature drops, it moves horizontally. As the temperature rises, it also moves horizontally in the opposite direction. Vertically, it cannot move. And when it expanded or contracted, that angle with the support is no longer 90 degrees. So let's go back here and let's look at this one. And let's understand that it is vertically capable. It's not letting the beam move up-down. horizontally, it wants it to move up-down, so there is no horizontal resistance. And rotationally, once this expands or contracts, that angle is no longer 90 degrees. Okay, so roller support, basically vertical resistance only. Let's look at a pin or a hinge. The pin is capable vertically and horizontally. It will not allow movement horizontally, unlike a roller. But rotation at the pin is possible. So let's look at these images. But before we do that, I have wood, I have steel, and I have examples in precast concrete. So the steel is taking over a little bit the third row because it's nice and the connections, the details are quite nice. So before going on, let me say that wood-to-wood connections or wood-to-wood supports are typically pinned. The same with precast concrete. You cannot make a fixed connection with precast concrete. You cannot make a fixed connection with wood. You have to intervene with steel or concrete or cheat a little bit to make a moment connection with wood. But let's go through these images. Looking at the first one, it looks like it's some kind of glue lamp structure, and it looks like it has some kind of plate here that must be anchored in the foundation. And the plate prevents horizontal, prevents vertical, but if it wants to rock a little bit, just a little bit, this detail allows that movement. The second one has a steel plate that is anchored in the concrete. It probably has some kind of base that is sitting in the concrete. And then there's this wood glulam member that has a shoe plate. And the shoe plate has a pair of blades that surround this plate that's coming out of the concrete. And then they're pinned together. And there will be no vertical movement. The concrete and this contraption prevent that. If the column wants to move this way, no, we're not going to let you. There is horizontal movement. If it wants to move in that direction, we're not going to let you because the connection prevents horizontal movement. So this one on a free body diagram will look something like this. The next one is very similar. It's not wood to concrete directly because the termites, the moisture, the humidity, will eat it up, so there's a transition to steel. The steel plate itself is anchored monolithically in the concrete, it's embedded, but then the wood to the steel connection, wood has moisture, wood has grain, wood has direction, wood is squishy, so it's not going to be able to make a rigid connection. This is also a pin connection. Looking at the next one, similar, we have two by sixes and they're making a column and there's a steel contraption and this is a pin connection. Whenever the area of a member is tapered down or reduced, that is because it's a pin connection. When I look at this member, it is that dimension over here, but then it gets tapered down, and it gets tapered another time, must be this pin connection. Now, this steel plate is anchored in the concrete, and then there's a pin here, so that this cannot move up-down, it cannot move in the horizontal direction, but if it needs to, it can rotate just a little bit. So, this is a pin connection. I talked about this in another video that is on rigid bends. But basically, this image is repeated here for one reason. This is a fat area. This is a fat area. This is very skinny. This must be a pin. This must be rigid. When you have a lot of area, you're making a rigid connection or a rigid support. When you taper down or you reduce the area, you're making a pin connection. So this is a pinned frame, and it's pinned in two locations, and this is a two-pin frame. Very good. Now, looking at the next image, the area is being reduced here. It's a lot fatter up here, and down here, it's a lot thinner. So that must be a pin. And then I talked about this with the video on bends. If your anchor bolts are between the two flanges, then you have a pin connection. So this one is clearly a pin connection. It will not tolerate movement in the vertical direction. You cannot move it this way in the horizontal direction. But it's okay to wobble a little bit with temperature, to move horizontally, or to rotate rather. Okay, so here's this monumental pin. It's at the Dallas Cowboys Stadium in Texas. And it's pretty hefty over here. And then what happens at the support? It goes down to a point. It must be a pin. This is a very long span arch, if I remember well, it's like 1200 feet. It's going to expand and contract a lot, especially that it's steel. So we need a reaction here, which is both vertical and horizontal. But if this thing wants to rotate a little bit due to temperature, then we're going to allow it. That's why it's pinned. Excellent. Here's another example of a pin where we have something anchored in concrete. There's like two plates. And I noticed that this is being reduced in area. Must be this is a pin connection. No vertical movement, no horizontal movement. But rotation is possible. Here's another example. A huge ball and there's an arch sending a load here. and there's a reaction, and it has a horizontal, it has a vertical, but if it wants to rotate a little bit, that's perfectly fine. That's what it's designed for. Looking at these, they're more of the same. Again, fat, and going down to slimmer, and then connected. No up-down, no horizontal, no horizontal. So this one is a pin connection, rotation is allowed. Again, once it is tapered like this, it used to be that diameter, and now it's been tapered down to just a plate. This one is a pin connection, and so is the one next to it, where a column was this dimension, and now it's sitting on four blades or plates. So these are all pin connections. The same with this one. It's a certain dimension, and then it ended up on a thin plate, You reduce the area. You used to have this much area. Now you have just a thin plate. That's a pin connection. Very good. Now, I said earlier, anything precast concrete is going to behave as a pin because it cannot be rigid. It could be a roller. I don't know. But never fixed. Precast is never fixed. Cast in place concrete is always fixed and rigid. So, looking at this image here, I have a precast column. I really don't know how it's attached down here to the ground, but it's precast. Therefore, it's attached in a certain way, which is not monolithic. And this beam here is sitting on a haunch of the precast member and another haunch. And it's not monolithic with the columns. It cannot be monolithic. So this one is either a pin and a roller, or maybe a pin and a pin, or maybe a roller and a roller. It's just not fixed. It's not rigid. The same down here. The column is probably pinned. The same with the double T. What happens here is they put a plate, and they either weld to it. If there is a plate embedded in the double T, then they would weld to the existing plate in the pocket. Otherwise, just a neoprene pad, which means it's a roller. It's just sitting on there. There's no connection with the pad. Okay, so pin connections. Let's look at the next slide. The next slide is about fixed or rigid or very moment-resisting connections. They are able vertically. They are able horizontally. And if you put a load on here, you're doing, let's say this is V, these must be equal. But you're also making a moment here, clockwise in this case, about this point. Well, this guy will not tolerate it. So it's going to maintain the 90-degree-ness of this angle and come up with a moment reaction. Whatever you do, it'll do opposite. You're doing clockwise. The reaction is counterclockwise to keep that angle at its initial set. So let's look at these. Here's some fixed supports. There's this beautiful fence outside the Nashor Sculpture Garden in Dallas. And it's cantilevered. And I don't know how this was constructed, but I assume that there's a plate here. Let me switch to white. There's a plate in here. And coming out of it are these things. And it's cast, it's leveled, it's plumbed, and then it's cast in the concrete. Very good. Versus this wood fence. The wood fence has these wood posts, and I don't think they're just sitting in the ground. That wouldn't make sense, because if it rains or something, they're going to shift. So probably they're going in the ground down to here, and then there's some concrete around them to keep them in place. And it's a counterweight, and it's rigidity at the same time. But, of course, that is a pin connection. No up-down. No, it's not a pin connection. It's a roller because it can move horizontally if need be. But it can move vertically. Yes, it can rotate. Okay. Let's look at steel. With steel, there is one key thing that we need to consider. Basically, where are the anchor bolts with respect to the flanges? We have two different conditions here. Condition 1 is the anchor bolts are between the flanges. Condition 2 is the anchor bolts are outside the flanges. And in this case, you have a pin connection. And if the anchor bolts are beyond the flanges, then you have a fixed connection. So looking at the images, it looks like this guy is tapering down. That's my first hint that this is a pin. The second hint is basically these anchor bolts are between the two flanges, which means definitely this is a pin connection. Looking at the next one here, down here, here are the flanges, and there are anchor bolts between. That makes it a pin, but as soon as I focus on these anchor bolts that are beyond the flanges, then I recognize that this is a moment connection. Looking at the detail here, I see a flange and another flange, and I see anchor bolts beyond the flanges. That means that this is a fixed-end connection. Versus if the anchor bolts were here, between the flanges, then that would have been a pin connection. Let's look at this image here, which says this guy is tapering down, must be a pin. This one is pin connected. Versus this one is not tapering, it's the same area, and this one must be a fixed connection. Let's look at these concrete examples. In this example here on the left, I have a concrete column cast in place and monolithic with its support. It looks like, it doesn't look like because we don't see it, but I'm sure the rebar is in there. They pour the foundation first, the pad, and leave the rebar sticking up, and then they pour the column monolithically after. So this one looks definitely like a fixed connection between the column and the pad. The same with this example where we have some kind of concrete wall and it's clear it's being cast in place and there's dowels probably sticking out from the foundation and then they add some rebar and they pour. So this one is monolithic with its support and this wall is fixed to its foundation versus if we look at the next two examples, These are precast. When I look at this column, it has four holes in the corner because there's a plate that is embedded. There's this plate here that has studs or something in the concrete anchoring it. But what happens here is they're leaving a little room for work to attach to these anchors here. But this one is more of a pin condition. Because of the way it's attached, the concrete column is massive, and the plate is not that thick, and the anchor bolts are pale. They do pale compared to the weight and the mass of the concrete. So I'm going to consider this as a pin connection. One more time, precast members are pin connected. They can't become monolithic. The same with the walls down here. I don't think this is substantial compared to monolithic construction. This wall is precast, and it's massive, and it's attached to a foundation with little stitches. So this one is considered pinned. And precast construction is not the same as cast in place, obviously. It's less rigid. And with low seismic activity, precast is fine. With high seismic activity, you would much rather have monolithic construction. Okay, let's recap very quickly. So, a roller is capable only in the vertical direction, one reaction. A pin is capable in the vertical and horizontal direction. Both of these cannot prevent rotation.