Span Types: 1. Toys Span Types

Music Okay, in this video I would like to go over different types of spans. To begin with, we have a simple span of a beam or a truss or what have you. A simple span means it's going from support to support. the support could be a roller, could be a pin, or any other combination of those two. So a simple span, when you load it, it goes down, the top goes in compression, bottom goes in tension, the roller or the pin cannot prevent rotation, so this angle changes. So a simple span, that's the first one. And with simple spans, here's three separate simple spans, It's totally independent of one another and when you load one, the others have nothing to do with it. We have a pin connection here so this is separate. These are three separate beams. If I load this one, the other two don't care and this angle changed from 90 degrees. The top is in compression, the bottom is in tension, the ends, sorry, the beam is supported at its ends. So that's a simple span versus an overhang. An overhang is where this beam spans between two supports, but then it overhangs a little bit. And whereas in a simple span, the bending is in one direction, it's bowed upwards, or it's like a smiley face. The top is in compression, the bottom is in tension. In an overhang, when we load this beam in the middle, the two overhangs go up. So that's the overhang number one, that's overhang number two. With the load in the middle, if I load the overhang, then we get something called the negative moment versus a positive moment. A positive moment is like a smiley face. When the top is in compression, the bottom is in tension. But in an overhang, you will also have a negative moment on that overhang. And so the top is in tension, the bottom is in compression when that is loaded. So we might see something like that with a negative moment on the overhang, a positive moment between the supports, and therefore it's doing this S, and therefore there's a point of inflection somewhere over here where the curvature is going from down to up. It's reversing. So an overhang is a second type of span. Simple span is the first one, second one is overhang. And please notice when I load this one, when I load between the two supports, the two ends go up, but then when I load the overhang, watch what happens here. It goes up a little bit, so the overhang is helping reduce the positive moment. This moment is positive, but when I put a negative moment over here, which is tension on the top, compression on the bottom, the belly here goes up a little bit. And then if there's no load in the middle and you load the overhangs, well, then the middle is going to go up, of course. And likewise, if I load in the middle, then the two overhangs go up. Very good. So overhang is the second variety of span. The third variety is a cantilever or fixed end support, where one end only supported, the other end is not supported. And we said with this one, we have a negative bending moment, which is tension on the top, compression on the bottom. And this support must be rigid enough, and you notice in this plastic model that it is monolithic with its support. So the beam cannot move up down. The beam cannot move left right. So there's a reaction to the vertical. There's a reaction to the horizontal. And furthermore, this angle shall remain 90 degrees. So when I apply a load here, this beam is not going to do that because this end is very rigid. and what it's going to do is it's going to provide a counter moment in this direction, a counterclockwise moment because you did a clockwise with the load. And so, this support responds with a counterclockwise moment in order to keep that at 90 degrees. So far, we have a simple span, an overhanging beam, a cantilevered beam, And then maybe both ends are fixed rigid, and this one is called the constrained or a restrained beam. This one is highly indeterminate. The others were determinate so far. So when this one is loaded, you notice what happens here. Over -- right here, there's compression on the top, tension on the bottom, but at the support, it looks like it's flipping. It looks like there's tension on the top, compression on the bottom. So whenever you go from positive moment, compression on the top, tension on the bottom, to negative moment, negative moment is tension on the top, compression on the bottom, there must be a point here where the curvature is reversing and where you're going from positive moment to negative moment passing through zero. That's called the point of inflection. The moment at the point of inflection is zero. And with a constrained beam, we have one point of inflection and another one on the other end. And so it's as if saying that the span is from point of inflection to point of inflection because it looks like the support is claiming part of the beam. The other support is claiming part of the beam. So it looks like the span is from here to here, not all the way to the ends. If it were simply supported, it would have been all the way to the ends. Okay, so far we have simple span, overhanging beam, and then cantilevered beam with a rigid connection, and then a constrained beam or a restrained beam which is rigid on both ends. And then another type of span is a continuous beam where a beam such as this one runs on top of multiple supports, in this case, four supports and three bays. But it's one beam running on top of all of them, so it's definitely not simply supported. And now, one bay is going to affect the other bay, unlike this problem. With this problem, it was three simply supported spans, totally independent of one another. This is one beam with three spans. And when the middle bay is loaded, you notice what happens here. Over the support, we're getting a negative bending moment. Between the supports, we're getting a positive moment with tension on the bottom, compression on the top. And what just happened was very good because if you load the middle bay, then -- come on, now it doesn't want to do it. There it goes. That end wants to go up and so does this one, just like we saw with the overhang. So this reaction has to be a tie down. It's got to bring this point down and keep it down here so that when this is loaded, that stays, this reaction is downward. And the same with this reaction, it's also downward. What it has to do is prevent that from happening, so it's got to be a tie down. But these two reactions are basically supporting the load. whatever that load is, it's going here and here. And then these two supports also have to take that additional load that is downward. So we have, currently we have four downward, sorry, three downward loads, one here, and then two is this one. And then, sorry, this is getting a little cumbersome here. Two is downward, and then this one also wants to go up, so it needs a downward reaction. So these two have to carry the load I put in the middle plus this downward plus this downward. So these reactions are a little bit bigger than the load because they have two tie downs also going down. So total vertical load should equal to zero. So whatever this uniform load is plus a downward load here plus a downward load here should equal to these two because the beam is not going to move up down. Very good. So that concludes the segment on the different types of spans. They are a simple span, an overhang, a cantilever, and then we have a twice fixed or a restrained beam, and finally we have a continuous beam. And by the way, anything that is cast in place concrete has to be a continuous beam. Anything that is precast will be simply supported. And then anything which is wood construction is also typically pinned. You cannot make a moment connection with wood to wood. Steel could be either a pin connection. Steel connections, steel to steel could either be pinned or fixed. Okay.