Now we get to put all the pieces together. We have looked at different elements of buildings. We have looked at beams and columns, trusses, lots of different elements. But we need to put them together and look at structures overall. We have looked at bridges a little bit and so we looked at truss bridges and cable-stayed bridges. Those tend to have just single elements in them. It's easier to look at those earlier. But now, as we look at buildings, we are going to start putting beams and columns and trusses, buildings take all those pieces and put them together. Designing a building or understanding and analyzing a building is just about really combining those elements. First thing an engineer would probably do is look at the independent elements. They would first consider the different types of loads that the building's 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. It's what we refer to it as, but the materials themselves. A 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 will look at. Those are vertical loads. As we analyze and design for those vertical loads, it would be a lot like we did when we looked at beams and columns. We would figure out first the load path. 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. We look at the beams, those beams we will analyze to make sure they are okay. Then those beams would carry the loads out to the columns, and the columns carry the load down to the ground. We would call that a vertical load flow or a load flow. We are figuring out where the load starts and how it gets down to the ground in a safe manner. Beams, if we are looking at just at the beam element, an engineer would just go back to beam design that we talked about. A beam could fail in bending or it could fail in shear. Those are the two main ways. A longer slender beam would fail in bending, it 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 shear. Then, you 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. Then, analyze and make sure that was okay. That's the vertical load and the vertical load flow. As for the loads, we find out where they are generated and figure out how to get them to the ground. We also have to deal with lateral loads or horizontal loads. 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. How do we deal with these horizontal loads to a building and what will they do to a building? A wind load is probably easier to begin with to just imagine a wind load. 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. We saw that a little bit with the Eiffel tower. We analyzed the Eiffel tower for a wind load when we talked about beams and that Eiffel tower behaved just like a beam. If you turn your head, you have a cantilever beam. In most buildings, we can actually do a first pass analysis for wind or earthquake loads by modeling them as beams. Instead of tension and compression being within a single member as it would be with a beam, we will 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. A shorter, wider building will tend to fail in shear, whereas a tall, more slender building will tend to bend more. We will have more of a bending behavior. Then we will look at where tension and compression is due to that bending. We will 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, our overturning and sliding. A building just toppling over, or a building sliding along the base. These are really just a function of the connections at the base. Making sure we have strong enough connections to withstand overturning, to withstand any type of lateral sliding. We are going to build some simplified models of buildings, and 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. Coming up with a simplified model is very helpful. We can take a standard three-dimensional model of a structure and what I will usually do as a first pass is come up with a two-dimensional model. I will collapse everything to two-dimensions, and most buildings are pretty repetitive. That's a fairly effective way to make it simpler. Collapsing into two-dimensional model means I am 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 further, collapsing all those columns together and all the mass on the floor levels together. 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, it's 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. If you have a one-dimensional model for a building with multiple floors, it would be referred to as a multi degree of freedom system. What I have here, are single degree of freedom system models. 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. 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. Do they behave the same? Do they behave differently? I tried to make them with very similar masses, but they have different heights. The different heights of the columns represent the stiffness. Stiffness again was how much it's going to displace for a given force. If I apply the same force to both of these, one is going to displace more than the other. This one displaces more. The shorter one would be referred to as the stiffer system as opposed to the taller one, which should not be quite as stiff. Hopefully, you have a dowel or something you can use to build a single degree of freedom system model, or one of these lollipop models. It's just a wooden dowel in my case. You can 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. As I pull it back and release it, how does it want to oscillate? 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? You are 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 stiffness of columns virtually.
