So now we get to put all the pieces together. So we've looked at different elements of buildings. So we've looked at beams and columns, trusses, lots of different elements. But we need to put them together and look at structures overall. So we've looked at bridges a little bit. So we looked at truss bridges and cable-stay bridges. Those tend to have just single elements in them. So it's easier to look at those earlier. But now as we look at buildings, we're going to start putting beams and columns and things, trusses, buildings kind of take all those pieces and put them together. So designing a building or understanding and analyzing a building is just about really combining those elements. So first thing an engineer would probably do is look at the independent elements. So they'd first consider the different types of loads that the buildings are going to be subjected to. Vertical loads are some of the main loads and one of the first things an engineer would look at. So a vertical load will come from the self-weight. That's what we refer to it as, but the materials themselves. So building is made of concrete or steel or some other material. But that has a certain weight and that vertical load from that weight has to get down to the ground. We also get applied loads from people, furniture, everything that's in the building, all the equipment, whatever materials are in the building. Those again are all vertical loads. In addition, on the outside of the building, you get snow, which is a big vertical load. Rain can sometimes pool up on the roof. And those are things we'll look at. So those are vertical loads. So as we analyze and design for those vertical loads, it would be a lot like we did when we looked at beams and columns. So we'd figure out first a load path. So those vertical loads would be either on the roof or on the floor levels. So where the people are generating the loads. Those would be applied directly to the beams. So those beams, we would look at the beams. Those beams, we would analyze to make sure they're okay. Then those beams would carry the loads out to the columns. And the columns would carry the load down to the ground. And we would call that a vertical load flow, or a load flow. We're figuring out where the load starts and how it gets down to the ground in a safe manner. So beams, if we're looking at just at the beam element, an engineer would, you know, just go back to beam design that we talked about. So a beam could fail in bending or it could fail in sheer. Those are the two main ways. So a longer slender beam would fail in bending. We would just reach too much bending, too much tension or compression. And then if it's a shorter, deeper beam, it would fail probably in sheer. So an engineer would look at that, make sure the beams are okay. Then move on to the columns. And check to make sure the columns are okay. They could fail in compression or in buckling. So they'd analyze and make sure that was okay. So that's the vertical load. The vertical load flow. So as the loads, we find out where they're generated. We figure out how to get them to the ground. We also have to deal with lateral loads or horizontal loads. And the two main horizontal loads that we deal with in buildings are wind and earthquake. So wind pushing on the side of the building. Earthquakes are a little different. They generate a motion in the ground, but that actually generates a lateral force as well. So how do we deal with these horizontal loads to a building? And what will they do to a building? So a wind load is probably easier to begin with to just imagine a wind load. So wind load on the side of the building will apply forces to the side. And cause the building really just to bend like a beam. So we saw that a little bit with the Eiffel Tower. So we analyzed the Eiffel Tower for a wind load when we talked about beams. And that Eiffel Tower behaved just like a beam. So if you turn your head, you have a can lever beam. In most buildings, we can actually do a first pass analysis for wind or earthquake loads by modeling them as beams. So instead of tension and compression being within a single member as it would be with a beam, we'll have tension and compression on different columns in that scenario by modeling a building as opposed to a single element. But the concepts will be the same. So a shorter wider building will tend to fail in shear, whereas a tall, more slender building will tend to bend more. So have more of a bending behavior. And then we'll look at where tension and compression is due to that bending. We'll look at those columns. See if those columns can take that extra compression. See if they can handle the tension. The other two failure modes for an overall building are overturning and sliding. So a building just toppling over or a building sliding along the base. These are really just a function of the connections at the base. So making sure we have strong enough connections to withstand overturning, to withstand any type of lateral sliding. So we're going to build some simplified models of buildings. And the engineers often do build simplified models. There's a lot of data if you're looking at a big three-dimensional model and trying to figure out what's happening. You can get buried in all the numbers. So coming up with a simplified model is very helpful. So we can take a standard three-dimensional model of a structure. And what I'll usually do is a first pass is come up with a two-dimensional model. So it collapses everything to two dimensions. And most buildings are pretty repetitive. So that's a fairly effective way to make it simpler. So collapsing into two-dimensional model means I'm going to take all the columns and just model the columns and the beams all along a two-dimensional plane. I can further make an even simpler model, which is referred to as one-dimensional model, by collapsing, further collapsing, all those columns together, and all the mass on the floor levels together. And so all the columns get grouped along one line. So that's where we get one-dimensional model. Everything's on one line. And then at every floor level we lump the mass. It does a really good job of actually predicting dynamic response. And lumping all the mass at the floor level is actually a good way to do it, since that's where most of the mass typically is. That's where the beams are. That's where the people are. All the equipment are. So if you have a one-dimensional model with a multiple, for a building with multiple floors, it would be referred to as a multi-degree freedom system. What I have here are us. Single-degree freedom system models. So these would represent the same thing. It's a one-dimensional model. Everything's collapsed along a single line, but it's for a one-story structure. So it's just one-story tall. I have two different versions to represent a taller building and a shorter building. And that's one of the things I want us to experiment with is, do they behave the same? Do they behave differently? So I tried to make them with very similar masses, but they have different heights. The different heights of the columns represent the stiffness. So stiffness, again, was how much is going to display for a given force? So if I apply the same force to both of these, one's going to display more than the other. So this one displaces more. The shorter one would be referred to as the stiffer system, as opposed to the taller one, which would not be quite as stiff. Hopefully you have a dowel or something you can use to build a single-degree freedom system model, or one of these lollipop models. It's just a wooden dowel in my case. You could also use a twig, anything long and slender, and a lump of clay on top. And what you want to do is experiment with how it tends to want to behave. So as I pull it back and release it, how does it want to oscillate? And will it oscillate different if it's got a different height or different stiffness? How about if I took all this mass and put it on a single lump? Would that make any difference? So you're trying to experiment with heights of columns and amount of mass and figure out how the building wants to respond. If you don't have materials to build a physical model, go ahead and use the online simulator to experiment with different masses and stiffnesses of columns virtually.