Design Issues for Structures

The two big issues of any structural design are gonna be the shape and the material. So, when we talk about material, we're talking about steel, we're talking about concrete, we're talking about wood, any of these different materials are gonna have different aspects to them that will be more ductile, more strength, more brittle, more strong. Those are all different terms talking about kind of similar sets of issues. So, we're very concerned about the specific material choice. Is it robust enough?

Is it helpful enough? Does it allow enough movement in a high wind or an earthquake to not tear itself apart, but to be able to withstand that earthquake? So, what are the issues that this particular project in this particular location needs, in terms of that material choice. Plus, the material choice has a lot to do with financing, it has a lot to do with finishes. So, a whole bunch of other aspects, fire ratings, and things like that, that all tie in together. So, the material choice becomes a huge, important question.

The shape becomes an important question. So, it sounds sort of weird when I say the word, shape, but we're really talking about there is the idea that we want the material to be in the most useful locations. So, for example, if we're talking about steel, you're probably talking about like a wide flange. Right, that's that shape that you all know well. So, there's our wide flange.

What's going on there? Well, I've got a bunch of material up here and way down here. What that's doing is it's putting as much of the steel as possible exactly where I want it, and, then, it's just holding it apart from each other. So the web is just holding the chunk of steel that's up at the top as far apart from the chunk of steel that's down at the bottom as far apart from each other as it can, and, then, that way when we have something that's spanning across...

So, we've got our steel beams spanning across. It's a very short steel beam, and it wants to sag. As it does that, I have a lot of compression in the top as things are sort of pushing inwards towards each other, and I have a lot of tension at the bottom where things are stretching out, away from each other, and then I have this neutral axis in the middle where it's staying the same.

So, what I want is I want the steel at the top to deal with that compression, and the steel at the bottom to deal with that tension, and I'm then just holding those apart and I'm hoping that will keep it nice and square and stiff. So, that's that whole point of a shape is I'm just trying to push those parts apart in order to get as much depth as possible.

So, when we talk about shape, we're really talking about the depth, trying to push that material as far apart as we reasonably can fit it, and, then, we're combining that with the question of material and how robust and how flexible that material is and is it the right material for that particular use. So, while I used the wide flange, the steel wide flange as the example, we could look at any number of different materials and we would see the same kind of discussion.

So, I'll give you a quick example, something like a glulam beam. Let's say this was a glulam beam and it was made of lots of different layers, different laminations, glulam, and each of those laminations is a bit of wood, let's say two-by-sixes, all sort of trimmed down and glued together. If we actually looked at that in cross-section, it would look something like this.

And if we looked at the specifics of which species were where, we would find that the top few and the bottom few are gonna be the best structural species and then the ones in the middle are really gonna be just filler species. They're just gonna be spacers to hold those good species apart from each other. Now, for reasons of color mixing, and kind of the look of the thing, they may choose to do it all out of the good material, but they don't need to.

They would find that in the same way that the wide flange wants to be heavy on the top and heavy on the bottom, the glulam, the structural capacity, what I'm really trying to do, trying to get a bunch of material up at the top and a bunch of material down at the bottom and it's gonna go through that same sets of issues in terms of the compression at the top and the tension down at the bottom, and I want the material where that's really happening the most.

I want the best material to be fighting that particular set of issues. So, when we talk about these design issues, when we talk about kind of the structural systems, we're really talking about both the material and the shape and how they combine together. When we talk about material, we're talking about the modulus of elasticity, and the modulus of elasticity is just a mathematical way of understanding the robustness of that material.

So, it's all about the material, itself. When we talk about the shape, we're talking about the moment of inertia, and sometimes the radius of gyration, little r. Those are useful ways of thinking about how to document the shape. So, if I have shape that is where I have a lot of material at the very end and very low end of the depth, that will have one type of I, one type of moment of inertia. If I have one where it's squeezes it all together and becomes very close, and it's all very dense, well, that will give me a totally different kind of inertia and what we already know is the moment of inertia we want is the one that gives us a lot of depth, that's gonna be stiffer and stronger kind of no matter what the material is.

So, the moment of inertia and the radius of gyration are ways to describe the shape. Once we know what the E is, the material is about, then we also know what the I is, or what the r is, that allows us to start putting these pieces of information together and we can start to really understand what the capacity of the material is.

So, if I have steel, I have very, very high E, it's a very high modulus of elasticity, and if I then, also, am using something like a wide flange, it has a pretty good I because that shape is really designed specifically for the kinds of uses that we that we have. And so, we're finding that we put those together, we get a very robust system.

If I'm doing the exact same thing, but out of wood, well my E is gonna be much lower. It's not gonna have the same robustness. It'll still be pretty good, but it's not gonna be anything near as robust because the E is so much lower. So, I took that wide flange steel and I crushed all that material down into one sort of, say, square section, something like that. So, it's the same amount of steel, and it's the same E, because the steel has the same modulus of elasticity, but my I would now be totally different.

Well, that's not gonna be anywhere near as effective a combination of shape and material. It's gonna not work as well. It's gonna have a lot less capacity. It'll be a lot less robust. So, both of these issues are really important, both the material and the shape, and we represent those through the modulus of elasticity, through the moment of inertia, through the radius of gyration, and a few other things which will show up along the way, but these are sort of the main ones to kind of keep in your head because they're the faster ones to really get at that set of issues.

We can't really think about structural systems without thinking about these particular issues. when we talk about the idea of shape, we talk about how much span something has, we're also going to be very interested in the idea of bracing, because that's where we're really saying, this is not just a material out in the world, by itself. We're now saying it's part of an overall system, and when we put it into an overall system, there's a lot more things going on than just a beam or just a column, just the material, and just the shape.

We're now connecting it into the world of this particular building, and so bracing also becomes a key element of the discussion. But, the main focus is really gonna be the material and the shape and then these secondary elements about how often it gets connected in and, therefore, what the span systems are like.

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