L10 Sizing Steel Elements contd

Added: 2026-05-30

[00:00:00]now let's move on to beams and girders and it's important to note here that steel gravity framing is often one way meaning that the load travels in One path from left to right across the deck and then north to south along this beam and then again left to right along the girder down to the columns and to the foundations this is opposed to a two-way system where the load would travel in two directions across the slab and we'll get more into two-way systems when we talk about concrete but for now simple gravity framing in steel is most often a one-way system and so the first question we should ask ourselves is does the span direction matter so if we have a rectangular Bay like this with one length clearly longer than another does it matter if we place the deck span left to right and the beams north to south and the girders left to right again or should we flip it the other way and it turns out that this second orientation is way more beneficial for a number of reasons first being that there are fewer connections so if we look back at the one on the left you can see that we have many connections here that need to be made between the beams and the girder in total we have eight whereas on this side we have only four connections connections of course means bolts or welds and additional supplemental Steel all of which adds up to more cost and more time so from a cost and Time Savings perspective just looking at connections this orientation on the right is much better also this orientation on the right is more economical and it will often lead to less structural depth meaning that the maximum depth of these members will often be much shallower compared to this orientation on the left where the girders will be very very deep so now let's ask ourselves a further question of why this orientation on the right will be more economical and have less structural depth and we should be able to answer this question based on our discussion of analyzing beams earlier in the course so let's recall Our Moment equation for a simply supported Beam with a uniformly distributed load and that equation was the maximum moment at Mid span is equal to WL squared over eight where W is equal to the line load over the beam and L is equal to the length of the beam and it's important to note here that loads on girders are actually Point loads the loads on the beams will be a uniform load because the load comes from the slab but then once the load is picked up by the beam it travels to the girder and Frames into the girder as a point load but for now we can simplify our discussion by only considering this uniformly distributed load formula so the actual load on that girder that we just saw will look like this and the actual moment diagram will look something like this but we can reasonably approximate it by looking at something like that for this discussion anyway so let's look at what the demand loads will be on these members given these two different orientations note that this is the same base size in both cases 18 by 30 but in one case we have the beams running north south and the other east west so let's start with the girder in this top orientation and we're going to have a given live load of a hundred pounds per square foot the tributary width for the skirter is going to be half this distance and so it will have a line load of 900 pounds per foot and it has a length of 30 feet and so 900 times 30 squared divided by 8 will give us 101 foot kips next let's look at the beams these beams have six foot spacing and so their tributary width will be six feet and they will have a line load of 600 pounds per foot they have a length of 18 feet and so the moment 600 times 18 feet squared divided by 8 will be 24 foot kips and so that's quite a difference between the moment on the girder and the moment on the beams and so the girders will be much larger than the beams significantly larger making the overall structural depth much greater because after all the structural depth is dependent on the deepest member so even if we have very shallow beams here since our girders are so deep the overall structural depth will also be very deep let's compare this to our second orientation here in this case the girder has a tributary width of 15 feet so it has a line load a 1500 pounds per foot which is more load than we had before but it's applied over a shorter length only 18 feet and if we look at our equation here the length is squared and so it's the length Factor that's more important when determining Our Moment so let's see how this new orientation affects our moment here for the skirter so we have 1500 times 18 squared divided by eight and we get roughly 60 foot kips much lower than our 101 foot clips that we had earlier almost half as much now let's look at our beams our beams have the same spacing of six feet apart so they have a line load of 600 pounds per foot once again their length has changed however to 30 feet and so the moment for the beams will be equal to 600 times 30 squared over eight which is roughly 68 footcaps and so the moment for the beams has gone up significantly but now you can see how the load is more evenly distributed across the beams and girders and so even though the beams are getting a little heavier were significantly saving on the depth and the size of our girders so hopefully now you can see how this orientation is much more economical and leads to an overall more shallow structure of that as the size of the beams and the girders will be much closer together so this leads to a general rule that we can apply for steel gravity framing and actually this general rule also applies to concrete and wood gravity framing and that rule is that girders should typically span the short Direction and beams should typically span the long Direction but note that there are some exceptions to this rule one would be if we are spanning to walls on either side rather than girders it would not make sense for us to try to frame girders like this and beams in the long Direction that would not be an economical choice rather it makes much more sense just to frame beams to these walls assuming that they are load bearing or if the wall is not load bearing we could vary columns in it and very a very deep girder in it as well and if these are solid walls from floor to ceiling then that very deep girder would simply be buried inside the wall and these beams could be very shallow and so there are some cases where we want the beams to frame the short Direction but most of the time we want beams to frame the long Direction and girders to frame the short Direction so finally with beams before we get to sizing let's talk about what composite beams are so with steel beams we've already talked about how the floor slab will typically be made of concrete laid into a corrugated steel deck and so we're adding all of this area on top of our beam all of this massive material and concrete as we've seen earlier is a structural material and it's a structural material that has very high compressive capacity and we'll get more into that next week but for now let's consider what we learned earlier about shapes and bending and we learned how the moment of inertia the resistance to bending can be increased with this parallel axis theorem a D Squared when we have additional area that we add to our section A Certain distance away from the neutral axis of the overall section that we're considering and don't worry I'm not going to make you actually calculate moment of inertia is here but just consider how adding this area on top of the beam if we can somehow get these two sections to work together this area on top could actually increase our resistance to bending and so that's the idea of a composite beam we add these sheer studs on top of the beam that go into the concrete and allow the concrete and the steel section to work together compositely to resist bending but note that this is only true when we have a moment that creates compression on top and that's because concrete is very good in compression but has virtually zero tensile strength and again we'll get more into this next week so what are some situations where we might have tension on the top and compression on the bottom one example would be a cantilever beam so here you can see if we have a beam that is cantilevered from a support and we apply a load somewhere on the tip of this beam this beam will bend downward and so we will end up with tension on the top and compression on the bottom and if we applied Shear studs to this member to transfer some of that bending into the concrete we would actually be putting tension into the concrete which the concrete would likely not be able to handle and it could fracture like this and that's opposed to a simply supported Beam with a uniform load where we do have compression on the top and so the concrete will go into compression which is what it's designed to handle and the bottom of the steel beam will go into tension so adding Shear studs and creating composite beams is one way that we can increase the efficiency of our structural system we add additional strength to the beam section using materials that are already there anyway