Shear & Bending Moment Diagrams: 5 Shear And Bending Moment Continuous Beams

Okay, let's look at shear and bending moment diagrams for continuous beams. Those are highly indeterminate. There will be no math. But understanding the shear and bending moment diagrams is still critical because anything concrete is going to look like these guys. Very good. Just recapping before starting, that's what happened with a overhanging beam loaded uniformly. And I expect the same to happen to these, only there's continuity, so one bay helps the bay next to it. Very good. Instead of starting with the shear and bending moment diagrams, I think I'd like to start with the deflected shape, because the deflected shape is going to tell me about the bending moment diagram. And the maximum shear is going to happen at the supports, period. So nothing new here. So the deflected shape, oops, is going to look something like this. And for this one, it's going to look something like this. Same idea. So looking at this and understanding that the bending moment is negative here over the supports is zero at the two ends that are simply supported. They're not fixed ends. And it's positive between the columns. And that there is a point of inflection where the curvature changes. From positive to negative, there will be a point of inflection where the moment is zero. So that's what's happening in this one. Same is happening in the previous one. There's two points of inflection. there's a positive bending moment between the supports, there's a negative bending moment over the supports, and we would have to flip our rebars in concrete. Now, let's look at the reactions very quickly. I don't have any numbers, but I need to acknowledge that this reaction and this one are larger than the two end reactions because this guy is carrying that much uniform load. versus the one next to it is carrying only that much. So if it carries more uniform load, then it's going to be a larger reaction. Same with the image on the right. This reaction, this one, and this one are larger than the two end ones. Very good. So let me draw a shear diagram very quickly. There is an upward reaction. There's a larger upward reaction. There's a larger upward reaction, and we have to end up at zero. With the next one, same thing. And I'll remind you, please, of the shear and bending moment diagram for the overhang we have down here, because the same thing is going to happen here. My shear diagram is going to do this, from here to here, from here to here, from here to here. And this one is probably going to do the same thing. And the reactions take me up. The uniform load takes me down. I'm not going to draw that anymore. But it's very much like this one. And when it comes to the bending moment diagram, I will remind you that zero shear is a critical point because it gives me a maximum or a minimum. All these values are where the shear diagram goes from positive to negative, or negative to positive, and that's going to give me a maximum or a minimum. I know that over the support is negative, so we're going to be down here somewhere. And between the supports is going to give me a positive moment. How much value? I don't know. It's indeterminate. I'd have to consult with tables and charts, but basically this diagram is going to look something like this. This is a little bit lower than the end moment because the two bays, 1 and 3, are helping bay number 2 a little bit. And the same happens here. We'll have a positive moment, a positive moment, a positive moment, and another positive moment. And this one will do something like this. Very good. So there is a point of inflection every time the moment diagram crosses zero between negative and positive. There's a point of inflection and the moment at the point of inflection is equal to zero. Very good. That concludes this one.