L11 Sizing Concrete Elements

追加: 2026-05-30

[00:00:00]so sizing concrete elements note that we have the same disclaimer here that these are rough guidelines and are not intended to replace the full analyzes performed by a structural engineer now let's start with columns and note that with concrete columns we typically want them to be Square when they are gravity only columns when we have lateral columns that may change but for now we're just going to look at gravity Square columns and the width of the column is going to be equal to the length divided by 12.

[00:00:39]in other words the height of the column in feet should be equal to the width of the column in inches and note that with steel columns we select a dimension based on the unsupported length and so that gives us typically either a w 8 or W10 or maybe a W12 depending on how tall the column is but we didn't really talk much about the overall height of the building and that's because with steel sections when we add more stories we typically just add more weight to the section this number here and that analysis is a little more complex and it won't really have too much of an effect on the architecture so we won't really look at that too much in this course since it's an architectural course but for concrete we do have a general rule that we can apply that whenever we add an additional story we add one inch to the dimension of the column so with steel when we add stories we're typically adding more weight to the section with concrete for every additional story we add one inch so to look at an example if we have a 14 foot column supporting one story we're going to have a 14 inch by 14 inch column now if we add four more additional stories that's going to add four more inches to our section and so we'll end up with an 18 by 18 column at the ground floor here but note that the columns up here could be smaller as they're only supporting this one level and so that's basically it for selecting preliminary sizes for concrete columns pretty basic now let's move on to beams and slabs and this is where the discussion gets a little more complex because there are a lot of different ways of Designing beams and slabs in concrete and a lot of different concrete systems so first we need to differentiate between one-way systems and two-way systems and as the name implies with a one-way system as we saw in steel the load travels in One Direction along the slab so in this case here we have the load traveling roughly East West along the slab and then north south along the beams and then East West again along the girders and finally into the columns with two-way systems the load can actually travel either east west or they can travel north south through this lab and the amount of load that travels East-West versus north-south is dependent on the stiffness of the elements on either side and we'll talk more about that later the advantages of a two-way system is that the column placement can be more irregular also since load is able to travel in two directions rather than being forced to One Direction only the overall structural depth can be much shallower one disadvantage however as we discussed earlier is that MEP integration will become more difficult as now we have reinforcement in two directions that we would need to avoid in order to cut a penetration through the slab also with concrete systems we need to talk about end conditions for our members so when we talked about steel gravity framing we only looked at simply supported members that is all of these joints between elements were pinned and so we were designing for a deflected shape that looked like this with concrete however since it's placed monolithically we can have continuous members across supports and so the deflected shape will look more like this and what that means is that there will be less positive demand moment on these beams or if we look at the moment diagrams as you can see for simply supported condition we have very large positive moments here and here whereas with the continuous beam we have much lower positive design moments however we do also have this negative moment over the support and that negative moment is very important to consider when we look at the layout of the reinforcing of our concrete element so recall that concrete does not perform well in tension and so we need steel reinforcing at the tension face when we have simply supported beams that tension will always be along the bottom face and so we will only need steel reinforcing along the bottom however if we have a continuous beam such as this on the right the tension face changes from bottom to top and so we will need to lay out reinforcing both along the bottom face as well as at the top over the support note again that the continuous supported beam has lower design moments and so it can typically be much shallower than the simply supported beam and just in case you can't interpret my drawings here I'll place a picture for you to look at of the foam beam that I showed earlier note how the tension face changes from bottom to top in the continuously supported beam condition so now that we hopefully understand two-way systems versus one-way systems and simply supported conditions versus continuous conditions let's talk about the various concrete gravity systems so with concrete gravity systems we have five basic types we have the beam and girder system which is essentially a steel system but done in concrete it is one way and it has a typical span from 15 to 30 feet and note that in this case as it is essentially like a steel system we can more easily accommodate penetrations through the slab between beams next we have the panjoy system which is very similar to the beam and girder system however in this case we have a lot more intermediary beams or joists and they are typically much shallower than the girder the typical span for the panjoy system is 20 to 30 feet and it is typically the most ideal for controlling vibration now getting into our two-way systems first we have the flat plate so this flat plate system will have reinforcing in two directions through the slab and so the load will travel in two directions to these columns the flat plate system will have a Max band of about 25 feet and it is typically ideal when we are looking for the most shallow structural depth given that we have relatively light loads so if you are building a residential tower for example and you're looking to squeeze in one extra floor you may look at a flat plate system if we want to push the span further for our flat plate system say up to 30 feet maximum what will start to happen is we will have punching Shear issues around these columns and punching Shear is essentially exactly as it sounds this column will want to punch up through this slab as the slab is loaded and so to mitigate that we're looking at a flat slab system where we have these drop panels put in place which are just square or rectangular sections of concrete added above the column and we can also add these column capitals to further increase the capacity of the columns so flat slabs are ideal again when we want to achieve a very shallow structural depth but we may have either heavier loads or a larger span required finally we have the waffle slab our last two-way system and Waffle slabs are ideal for either heavy loads or large spans up to 40 feet and that's because we are providing a relatively thick floor plate but we're removing a lot of unnecessary material by creating these voids and so the slab itself will have lower dead weight allowing us to span further so for this course we're going to be looking primarily at sizing beam and girder systems as well as flat plate and flat slab systems and so we'll be looking more into sizing elements for these three systems next also it's important to note here that these typical spans can be increased through pre-stressing and again I'm not going to get into the specifics of what's pre-stressing is due to time constraints but I will add an additional video for you to watch if you're curious so in the next video we will get into sizing one-way slabs and beams