L2 Gravity Load Paths contd

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[00:00:00]okay now that we have covered the types of loads that buildings are designed for and talked a little bit about the general process of Designing a structural system I wanted to dive deeper into how Structural Engineers actually Trace loads through a building and this example is going to go into specifically how we Trace loads from beams to girders into columns this example is going to be pretty high level not very detailed from the perspective of a structural engineer but will certainly be more detailed than what would be required for an architect so your homework problems and your exam problems will not be as complicated as this but I figured it's always best to be more detailed in the lectures so that you have everything that you need to do the homeworks and exams so for this example we are going to be using the same pretend steel set of drawings that I've been using in past examples and we are going to as I said take down some loads for a typical roof beam typical roof girder and a typical column for the sake of this example we will say that the building is located in Boston and that the occupancy is retail on all floors so let's get started with laying out the loading criteria for this building and this is the information that would be placed on the general notes page the first page of the structural set so let's start with the roof loads of course on the roof we are going to have some dead loads the self weight of the structure itself which includes the beams the girders The Columns and the decking will be our first category of load and for this we will say that the roof deck is going to weigh about two pounds per square foot and the steel framing itself will be about 10 pounds per square foot of course we could get the exact loading from the set itself by looking at the weight of all these steel sections but for now we're going to assume that the building hasn't been fully designed yet and in fact at the beginning of the steel design we would of course not know what any of these sections weigh yet and so we would have to have some kind of allowance for the self weight of the structure and this 10 pounds per square foot is generally pretty conservative for a steel roof assembly in addition to the self weight of the structure we also have all of the MEP equipment the finishes the ceiling of the Architectural Components and whatnot that will be permanently installed within the building so we call that a superimposed dead load so on a roof you will typically have some kind of fiberboard or substrate material rigid insulation perhaps more fiberboard a weather barrier all that kind of stuff all assembled on top of the roof deck and also the superimposed dead load includes all of the stuff that's hung below the just below the floor level so that includes the MEP the hung ceiling if there happens to be one which could be your typical acoustical ceiling tiles or gypsum board Etc also lights have weight and they're hung from the structure so that will all be included in the superimposed dead load and the allowance that we typically give for superimposed dead load is about 15 pounds per square foot so all together the self weight here will be 12 pounds per square foot and the superimposed dead load will be 15 pounds per square foot and so our total roof dead load will be 27 pounds per square foot or we'll just round that up to 30.

[00:04:14]again to be conservative so our roof dead load we will use 30 pounds per square foot for our floor load on the other side here in addition to the deck we now have concrete poured on top of the deck and that concrete has a significant amount of weight to it so over here this concrete and deck will weigh about 70 pounds per square foot and floor framing tends to be a little bit heavier than roof framing so we'll use 12 pounds per square foot giving us a total of 82.

[00:05:02]superimposed dead load will still use the same 15 pounds per square foot allowance for all of the hung MEP and Architectural finishes so that gives us a total of 97 pounds per square foot and we'll round up to 100.

[00:05:19]next for our loading criteria we have our live loads and for the roof we have a code prescribed minimum roof live load of 20 pounds per square foot and that 20 pounds per square foot is intended for maintenance workers so people who are maintaining the rooftop equipment or the roof assembly itself that 20 pounds per square foot allowance is not intended for any kind of public assembly live load so if you are intending to design a roof for public occupancy say a green roof you would definitely need a higher roof live load than 20 pounds per square foot but for this building we are going to assume that it is not open to the public on the roof of course the rest of the floors on the building will be open to the public and they are retail occupancy and so given this retail occupancy we will turn to chapter 16 of the IBC and scroll down to our live load tables which start in section 1607 and we will look for an occupancy that matches ours if I scroll down here see we have stores retail first floor is to be designed to a hundred pounds per square foot minimum and upper floors are to be designed for 75 pounds per square foot minimum now let's say we want to design all the floors to the same live load criteria this will help simplify the design and also give the owner a little bit more capacity to their building so let's design all of the floors to 100 pounds per square foot live load and it's important to note here this little footnote n and you can see that there is this footnote on basically every load that is over 100.

[00:07:25]so if I scroll down to the footnotes here it says that live load reduction is only permitted in certain circumstances so if you have a live load that is over 100 pounds per square foot that generally will mean that you are not allowed to use live load reduction but if you are at 100 or below you are permitted to use live load reduction so in this case since we are using 100 pounds per square foot we will be able to use live load reduction so that's something that's important to keep in mind when you're designing your buildings and determining the occupancy so if you tell a structural engineer that you want to design a building for a certain occupancy and that occupancy happens to have a code minimum requirement over 100 pounds per square foot that means that the structural engineer will not be able to use live load reduction and you will likely end up with a much larger structural system next we have our snow load snow load is of course determined by the location of the building which we've decided will be in Boston so to determine the snow load on the roof we turn to this asce 7 document and we go to the snow loads section and from here we scroll down to the maps and you can see here that this map this figure 7.1 says ground snow loads PG so ground snow loads are not the same as roof snow loads however they are related so if I scroll back up to the top you can see that there's a formula here for determining the flat roof snow load PF and you can see that it is equal to this Factor 0.7 times the other variables times the ground snow load and each of these factors the exposure Factor the thermal factor and the importance factor for a typical building will be just 1.0 so the only factor that we really need to pay attention to is this 0.7 so we're going to take the ground snow load and reduce it by 30 percent to get our roof snow load so scrolling back to the maps these can be pretty difficult to read but if I zoom in on Massachusetts I think it's pretty safe to say that we are somewhere in this 40 pounds per square foot region and so that is our ground snow load now it's important to note that depending where we are in Boston and what neighborhood we are in there could be a local requirement for a Higher Ground snow load some of something higher than 40 pounds per square foot and that local code jurisdiction will control over this IBC reference standard but for now we're just going to use 40 pounds per square foot for our ground snow load and as I said we will reduce that by 30 percent to get our flat roof snow load so we end up with 28 pounds per square foot for our snow load so now we have our full loading criteria laid out for this building for the roof and all of the floors for the roof we will use 30 pounds per square foot dead load 20 pounds per square foot roof live load and 28 pounds per square foot snow load for the floors we will use a hundred pounds per square foot dead load and 100 pounds per square foot live load so with that loading criteria in mind let's now Trace these loads through the structural members starting with the roof beams and you can see I've picked out a typical roof beam here in the middle so as we saw in the previous video the tributary width of this beam is going to be equal to the beam spacing so there are three spaces here between grid lines two and three which means that the spacing of the beams is 20 feet divided by three so the tributary width is 20 feet divided by three or six foot eight now we said that the dead load here was 30 pounds per square foot we multiply that by the tributary width of the beam and we get 200 pounds per foot for the linear load across this roof beam next we have the roof live load 20 pounds per square foot multiplied by the tributary width and we get 134 pounds per foot finally the snow load 28 pounds per square foot times 6.67 equals 187 pounds per foot so now that we have all of these individual loads according to their type dead roof life and snow of course we need to combine them into an ultimate load to design this beam so for that load combination return back to the IBC section 1605 and we look here for the load combinations for a strength design or load and resistance Factor design lrfd which is how we design steel and concrete members and we're going to look for a load combination that we think is going to provide the largest load the maximum load to design the member for so first we have this 1.4 dead that could be the maximum load however there is no live or snow involved in this equation so it's pretty unlikely that this load combination is going to control next we have 1.2 dead plus 1.6 live plus 0.5 roof live or snow so this one may be our controlling load combination but this 0.5 seems to be a pretty low Factor so let's look at the next one next we have 1.2 dead plus 1.6 roof live or snow so this load combination uses both dead and either roof live or snow combined together so this load combination seems like it is going to be our controlling load combination it's important to note here that it's either roof live or snow and that's because if you think about it if there is a maximum amount of snow on the roof 28 pounds per square foot it's pretty unlikely that you're also going to be sending up maintenance workers onto the roof and so that's why this load combination is either or you either have the maintenance workers up there or you have your maximum snowstorm it's also important to note as I said in the previous video that the dead load only gets an increase of 20 percent because we're pretty confident about the assembly for the dead load however snow load and maintenance worker load is pretty unpredictable throughout the entire life of a building and so we increase those loads by 60 percent so our ultimate load combination will be 1.2 dead plus 1.6 roof live or snow of course in Boston our snow load ended up controlling over our 20 pounds per square foot code minimum roof live load and so we will use snow in our load combination and leave out the roof live load so we have 1.2 times 200 pounds per foot plus 1.6 times 187 pounds per foot and all of that comes out to 540 pounds per foot so for every foot along this beam there will be 540 pounds of load and that load is what we need to design this Beam for now moving on to the roof girders for the girders of course they will be receiving the load from the beams and so rather than having a linear load across the member we will have Point loads in two locations and it's important to note for an interior girder like this it will receive load on both sides so the load will come from the beam on both sides of the girder and it will be half the load that it receives the other half will go to the girder on the opposite side but in total it will receive 10 feet from this side 10 feet from this side and so in total that will be 20 feet of load so if we go back up here to our roof beam we saw that there was 200 pounds per foot dead load so 200 pounds per foot of dead load times 20 feet that gives us 4 000 pounds or four kips next for roof live we had 134 pounds per foot times 20 feet that gives us 2.7 kips snow 187 pounds per foot times 20 feet that gives us 3.8 kips now for our load combination we have very similar loads here and so our controlling load combination will likely be the same 1.2 dead plus 1.6 roof live not Plus or snow and again it's the snow load that's going to control so now we calculate the ultimate load on the skirter 1.2 times 4 kips plus 1.6 times 3.8 gifts we end up with about 11 kips and note that that is 11 Kips here and 11 Kips there as well so that will be the load on the typical roof beam and typical roof girder between lines two and three of course getting the loads for the other beams and girders would be a very similar process and similar process for the floors below as well a lot of this work is not particularly difficult it's just very tedious and you have to make sure that you're keeping track of everything and so that's why we usually use computer programs to do this for us but we do still occasionally use hand calculations in a few key locations to verify that the computer has kept all of the numbers in line correctly now finally let's take a look at a column and here you can see I have the level one floor plan because we are actually going to be taking the load all the way down to the foundation so if you can recall in the set each of these floors looked basically the same there were no column transfers or anything like that this is a pretty simple building and so the tributary area for each of these columns is going to be the same on each floor and we are going to have a roof level three total floor levels and then the basement the loads from the basement however are going to go straight from the slab on grade and into the soil so they don't interact with the column at all so it's only this first floor level levels two and three and the roof that will pass load into our column so with that said let's take a look at a typical column the tributary area of course as I said in the previous videos is going to be halfway to each adjacent column and it's going to equal 15 feet plus 10 feet times 10 feet plus 10 feet 500 square feet so now the dead load on the roof was 30 pounds per square foot times 500 square feet the dead load on the floors was 100 pounds per square foot times 500 square feet and there are three total floors so that gives us 165 tips next for roof live we have 20 pounds per square foot times 500 square feet of course there is no roof live on the floor levels so this gives us 10 kips snow load 28 pounds per square foot times 500 square feet equals 14 Kips so the snow load again is going to control over the roof live now floor live load 100 pounds per square foot times 500 square feet and recall here that we are permitted to use live load reduction and we calculated previously that the live load reduction Factor was 0.44 and so we will apply that factor here and of course we have three floors but we're designing this column to hold so that gives us 66 tips now for this column we have both roof live load snow load and floor live load that we need to combine into an ultimate load so let's look at our load combinations again from the IBC we can see here that we have two options either 1.2 dead plus 1.6 floor live plus 0.5 snow or we have 1.2 dead plus 1.6 snow Plus 1.0 live this F1 factor is going to be 1.0 so either we apply the 1.6 to the floor live or to the snow load let's take a look given that we have a floor live load of 66 versus a snow load of 14.

[00:24:25]our ultimate load is going to come from applying that 1.6 to the larger load here the 66.

[00:24:33]and so our ultimate load combination is going to be 1.2 dead plus 1.6 floor live plus 0.5 snow so that gives us 1.2 times 165 plus 1.6 times 66 plus 0.5 times 14.

[00:25:04]and again we're using the 14 because our snow load controls over the minimum roof live load so in total our ultimate load for our column is going to be 311 kips so to summarize for our typical roof beam between lines two and three we had 540 pounds per linear foot of ultimate load for our typical roof girder between lines two and three we had ultimate loads to point loads of 11 kips and for our typical column at the foundation level we have a load of 311 tips and that is how we Trace loads through a building again from a structural engineer's perspective this is a very general high level load takedown but from an architect's perspective this is well above and beyond what you would be expected to do but I think it's helpful for you to know exactly what a structural engineer is doing as they are going through their process of designing your building and so we're going to continue to dive deeper into that process next week when we discuss lateral loads so as always I thank you for your attention good morning good afternoon and good night and I'll see you next time