All right, I think we're seeing attendance starting to level off here, so we can go ahead and get started. Good morning to the West Coast, and good afternoon again to those out East. Welcome back to the Post-Tensioning Institute's Monthly Webinar for December. My name again is Kyle Boyd, and I'm the moderator of today's session. I'm also the chair of the Education Committee for the Post-Tensioning Institute, EDC 130. And EDC 130, the Education Committee, is what sponsors this monthly webinar. For those of you who it's your first time joining, welcome. We offer this webinar every single month, and it's at the exact same time, so it's the second Wednesday of the month at the same time, which would be 1 o'clock Eastern, 10 o'clock Pacific. It's a reoccurring one, we do it all 12 months out of the year. We've already gone through and planned out all the webinars for 2025, so we've got a strong pipeline going into next year for it. For those of you who are repeat customers, welcome back, we're glad you're here. We've received a ton of requests for slab-on-ground design materials, and last month we did the first webinar based on slab-on-ground, which was more focused on the geotech side. This month we're excited to present part two of the two-part series, which is more focused on the structural side. So obviously we had to do the geotech side as a little bit of a primer before we get into the structural aspect of it. If you missed last month's webinar, you can go online, you can watch it. If you watch it, you take the quiz, you can get the free PDH for it, so we highly recommend that, and you can do that for any of the other webinars that we've presented in 2024 so far and into 2025. So before we dive into this month's webinar, we do have a couple of just general house keeping slides that we always have to go through. The first one is continuing education on there. We offer one continuing education credit for being part of this webinar from the start to the finish. All you have to do is be logged on under your name, your email registered, and you'll automatically get that at the very end. Once again, if you miss it, we have all this stuff loaded online. You can go watch it online, take a quick quiz at the end, and get that same credit, which is great at this time of year when a lot of the renewals are happening and you need to prove those credits. The next slide is just copyright material. This is just one to make lawyers happy and say thou shalt not copyright, plagiarize, any of that stuff. If you do need any information, feel free to reach out to us and we'll see what we can give you on there. So from there, we go into the webinar protocol. You guys are all in listen-only mode. We can't hear you. We can't see you. If you have questions, ask them in the Q&A function down there. We've talked about how this thing's already recorded on there. So with that, I can go in and introduce today's speaker. So today's speaker is Tony Childress, another industry expert and leader in Slab on Ground. He has over 30 years of experience and he's the owner or president of the firm that he founded. He does design and he does forensics. He's the past chair of DC10, Slab on Ground Committee, which last month we heard from Dean Reed, who's the new incoming chair of that committee as well. He's on the executive committee of the Post-Tensioning Institute. He's on the technical advisory board, so that's the board that really looks at all the technical content before it goes out to the general public, and he's a board member. He's obviously very well-established and respected within the Institute, and last month, Dean was the most qualified person we could possibly find out there in the industry to present on geotech. I'd say this month, Tony's the most qualified individual we can, more on the design side. So with that, Tony, I'm going to hand it over to you and let you get started. Thank you, Kyle, and thank you, everyone, for joining today. I'm grateful to be here. I'm battling a bit of getting over a cold. So any apologies for any coughing or delays, but yes, today, we're going over standard requirements for the design and analysis of shallow post-tension concrete foundations on expansive and stable soils. It is called the standard. If I use the word the standard, I'm referring to this DC10.5-19 document. I'm not going to be reading my slides. I have those because they come right out of the standard, so you can refer back to them. I will just be discussing primarily what the standard states. I will be giving you some personal opinions that aren't in there, or recommendations, but most of this today will be right out of the standard. So as we go on, the standard discusses three types of foundations. There's a PTI type 1, a PTI type 2, and a PTI type 3. The PTI 1 is a flat slab, not a uniform thickness foundation, but these are on stable soils. This is where we're only having to design for thermal or concrete shrinkage, so that's what PTI 1 is. These are these flat slabs. PTI 2 is reinforced and stiffened slabs. This handles more of the foundation movement, so we'll go into that in more detail. And finally, there's the uniform thickness foundations. Uniform thickness foundations are where you take a ribbed slab design that's conformant to the requirements of the standard, and you convert it into a uniform thickness foundation. We'll be going through all three of those per the standard. What is not in the standard? Compressible or collapsible soils, perimeter loads exceeding 1,500 pounds per square foot or per foot. Again, I'm not saying you can't do a post-tensioned slab if it has more than 1,500 pounds. You just have to do more of your own work, especially in bearing, to make sure the soils can handle those loads. But the standard was based upon one and two-story typical loading. The standard doesn't address soil bearing. Soil bearing has nothing to do with post-tension. So how you handle soil bearing in a conventional reinforced slab or any slab on ground is the same. So the licensed engineer or whoever's using it must do their own soil bearing. It doesn't address suspended post-tension foundations. This is all slab on ground. It also doesn't address high concentrated loads. If I've got a two-and-a-half-story CMU fireplace, you've got to design that locally. You've got to design enough concrete to handle that transfer of load. That's not something you put into the equations. All right, let's walk through the process a bit. So the PTI type 1, as I said, they're lightly reinforced slabs. The slabs are post-tensioned to eliminate joints. One advantage of post-tensioning, of the many advantages, if it's a rebar slab or what we call conventional reinforcing, you have to put relief joints and patrol joints through the slab. With a post-tensioned slab, you do not have to. So what you have to do then is design enough compression in the concrete to, you can't eliminate cracking. I don't care if it's conventional or post-tensioned, you will never eliminate cracking, well, without some really extreme measures. Concrete does two things. It turns hard and it cracks. So on these type of foundations, the standard gives you a very, it looks complicated, it's really not. This is an equation on how to space your tendons to put enough compression in your concrete. Your F sub E, this is your final effective force. We'll show you that later, but that's basically 27,000 pounds. It's 32,000 pounds when they stress the cable, but after it's set, which is what's called the seating loss, there's estimated 27,000 pounds of force there. The FP in the denominator here, that's your desired minimum average residual pre-stress. We'll show you later where 50 PSI is really the minimum, but 70 is a better number, more people designed for 100. The higher PSI you design for, the lower probability cracking will occur. I said lower probability, not no probability. So your H is your thickness of your slab, your weight of the slab, this is your density of concrete in pounds per cubic foot, so it'd be about 150. Your length of the slab you're going in, now I'm talking about the length that the cables are running in. Your coefficient of friction, show you that later, and that's the equation. They give you an example in the standard. It says if I've got a 60 foot by 120 foot slab, and it's five inches thick, so you put in the numbers. I've got my 100 PSI here. This is actually for a tennis court, which comes out of the tennis court, sport court document. I thought it'd be good to show, because the equations still apply for PTI type ones. And you end up with, in the long direction, 3.06 feet, short direction, 3.64 feet. What that's basically telling you is if I want 100 PSI as my residual pre-stress, I need cables roughly three feet, roughly 3.6 feet of center. That's how simple a typical stable soil thin concrete slab is done for, say, sport courts and things of that nature. We go on to the more commonly known, the ribbed slab, so it's reinforced different slabs on expansive soils. So geometry makes a huge difference. A nice square, something that's really square, it gets what's called two-way action. It comes from Timoshenko theory of plates and shells, where the forces are distributed in two different directions. The longer and the thinner it gets, the loaves get more and more into one direction. But then you take the shape, like here on the right, and you've got all kinds of twisting and turning, and that's where you have to have some experience in learning how to make this work. So in the standard, section 4.1.1, there's a section called overlapping rectangles. Overlapping rectangles, well, let me back up. The whole theory behind the standard is using rectangles. We cannot take a slab like here on the right and model that exactly into the standard. There are some finite element models that can do it, but that's not part of the standard. So the standard is based upon taking rectangles, but you are able to overlap these rectangles to get an overall mesh. So what it defines is primary design rectangles and secondary rectangles. So if I look at a shape, a shape's got all kinds of pieces to it. You can have more than one primary rectangle. What is a primary rectangle? A primary, you want it to grab, and I'm going to go back here in a little bit, you want to grab as large as possible the area that encompasses the foundation. You can include voids, you can exclude parts of the slab, you're just trying to grab a rectangle that's most contiguous with the foundation. So if I look at this one here, I've taken this one, I may have it on the next page. My primary, I have this one right here that I can use. What primary says, this is going to act pretty much like a rectangle. It's going to act in this direction the way it's going to act. I have another rectangle I grab right here. The idea behind this is if I design for this rectangle, if I design for this other rectangle, that's kind of the minimum. That's the starting point. That says that we should not be any weaker than what that section is required. Any changes to it will make you have to go deeper or closer beam spaces. So as it's defined here, it's a design rectangle encapsulating the most contiguous portions of the foundations. And again, I don't like reading it, but that's what it is. Then you look at your areas that are your secondary rectangles. These are areas that protrude away from the primary rectangles. This is very important. A lot of this is common sense, but it all depends on which side of the fence you're standing on for that common line. If I look at this rectangle in this long direction, so up and down, that's pretty contiguous. In that long direction, it's going to act a lot like it's laid out there. But in the short direction, it's assuming it's only the width of this rectangle. So it's going to want to have a lot different forces than what's really there because it's really going on and on and on. So the secondary rectangle breaks away from the primary rectangle, but the primary rectangle should only be looked at in the long direction. You don't look at it in the short direction because the short direction is not similar at all to how the actual structure is going to act. So we're going to go through another one to be more specific. These are easy, right? You have one rectangle. When you do this rectangle, you're allowed to leave out areas of void. You have to be smart how you choose your rectangle. I've got a beam right here, and it truncates up to here. Assuming my beam is at the very bottom is more conservative than assuming my beam is right here. So I could have made this rectangle smaller, and if you do that, that beam really should run continuous across, if that makes sense. So if I look at another section here, here's a section where, again, you have a primary rectangle, and unfortunately, I just changed colors. It should be in green. This red is my primary rectangle. I'm trying to represent this beam coming across here, this rectangle. It'll check it in the short direction. It'll check it in the long direction. And whatever design I get, I'm going to write that down and say that's a 10-inch by 24-inch. This is the design. Then I'm going to run this next section this way, and I'm going to see what it tells me in the long, because obviously, I'm bringing a lot more forces into the slab here. In the short direction, I'm bringing no more force into this area than what was considered from the green edge to the red edge. So your first analysis, your primary rectangle, your next analysis is rotated sideways. Again, I pick this rectangle. So this is the theory of overwrapping rectangles. If I found out that in this long direction, I needed 28-inch beams, I would then go back and make my whole design 28-inches. Even though this primary may have said 24 or 26, you have to design on what controls. But if the short direction says it fails or if the short direction says you've got problems, when I say you ignore it, if you do your rectangles right, you ignore it. You've got to be careful that you don't have a rectangle that's going out there 50 feet, 80 feet all by itself. They can truly get that short direction bending. In that case, you'd want to run it as a primary rectangle. This is one where it's more complex. You ran a primary rectangle across here. Again, you'll notice that I left out some concrete here. You're allowed to. You're allowed to exclude concrete or include concrete, but it's got to be reasonable. But what I'm grabbing is this beam line right here. I've got the majority of this beam line coming across here, which, again, is conservative. If I grab this line here as my rectangle, my rectangle is going to think that I'm actually smaller in width and give me different results. We'll discuss overlapping rectangles in a questionnaire later. The next thing we look at is shape factors. Shape factors are the foundation perimeter. You take the perimeter of the foundation, and you square it, and you divide it by the area of the foundation. What are we looking for? We're looking for when a house looks like this, which means we're really comfortable how it's going to perform, at least in theory, compared to a house that looks like this one here, where there's so many irregularities, so many bump-outs and changes. I hope I'm not making people nauseous when I flip through the slides, but I've got fancy bass fingers. We're looking at, like I said, I went too far, my apologies. You take that, and you divide it. There's what's called a simplified shape factor. A simplified shape factor is your primary rectangle, making sure that it's also you take the perimeter, square, divided by the area. What we're looking for is if the shape factor exceeds 32, or if the simplified shape factor exceeds 24, the user ought to consider something. I know that everybody would like to have a nice button that says, add a beam, do this, do that. We don't have that. This is where you have to say, okay, do I modify my foundation footprint? Well, how many owners want to get rid of a fireplace, or how many owners want to change their footprint? But one of them is to simplify the footprint, or you've got to strengthen the foundation. You can add stiffening beams. You can add ribs. In areas of high torsion, you might want to add some reinforcing, some non-free stress reinforcing. And there's geotechnical approaches, moisture barriers, moisture conditioning, and again, all of this is listed in the standard. What we're trying to do is let engineers be real engineers. Once we have a complicated shape, make an effort to do something more than just the minimum, because considering how irregular the shape is, it's nothing more than guidance. All right. Some standards. Minimum slab thickness is four inches. For a post-tension slab on ground, it's four inches. You can be five inches, you can be six inches, but the minimum is four inches. The minimum concrete strength for a post-tension slab on ground is 2,500 PSI. To be able to stress the cables, you must get at least 2,500 PSI. So that's the minimum. If it's a sport court, which is covered under a different publication, it's 3,000 PSI. So your sport courts are 3,000 minimum, your slab on ground is 2,500. In the Dallas-Fort Worth market, where I do most of my work, the average is 3,000, which is used here. Be careful. A lot of people out in the field use two, they don't do it as much. They will put it in a three-and-a-half-inch slab, because they have their cushion sand. They'll say that the cushion sand will compress a half an inch to get to your four inches. That's a no. If you're out inspecting these slabs, it's got to be four inches. Rib depth. The depth, the rib depth is from the top of concrete to the bottom of the beam. It's not from the top of the brick ledge. Now be careful. If your brick ledge is deep and it goes way down, then it is from the top of the brick ledge because it's really about this meat that we're looking at here. So we've already said the thickness is a minimum of four inches. The rib depth is a thickness plus seven inches. So if I've got a four inch slab, I need a minimum of 11 inches. Again 11 inches is not very common, but that just is what the standard gives you. Now there's a ratio between your beams. A lot of times your beams will be deeper. They'll be 36 inches and your interior beams may only be 24 inches. Maybe you have to extend your beams down because of drops or other things. In the standard, you should not consider anything more than a 1.2 ratio. Now again, be careful. I'm not saying you can't have a 24 inch wide beam on the interior and a 36 inch wide beam on the exterior. You can have it, but you should only take the 24 inches times 1.2 and use it in your perimeter for your calculations. The reason behind that, and I'll try to address it again later, is the standard assumes the entire foundation to be a uniform foundation. All of the ribs counted together make one unified stiffness. So you'll take the depth of a 36 inch plus the depth of 24 inches, you'll add it together, and that's going to give you a false typical consistency within the rate remainder of your foundation. So again, certain softwares out there will do that automatically, but if you're doing this to Excel or your own stuff, just make sure you understand that your variance between beam depths is no more than 1.2. The rib widths, the bottom of these rib widths, minimum of 6 inches, no greater than 14 inches. As I just said, the minimum is the minimum. Again, 8 inches and 10 inches are pretty common. Well, 10 inches is common in down in Fort Worth, 12 inches more in Houston and other areas. 14 inches are really for your softer soils. The more strong clay soils you have, you could go to 10 inch wide beams, the more sandy and soft the soils are, you go to the more wide 14 inch wide beams. Now I've got a fireplace sitting on the perimeter beam. I need to put a 24 inch or 30 inch wide spread footer or beam there. You can do that. You have to do that for bearing. Remember, post-tension doesn't address bearing. You can do a 24 inch. It's not that they say you can't, but your calculations for your stiffness should only assume 14 inches of that in your stiffness calculations. So even if you run a 24 inch wide beam across there, you should only consider 14 inches of it in your overall calculations. Rib spacing. This is the spacing between the ribs. Now these ribs are continuous ribs, not just a rib that's in between two beams. This is going to be your ribs that run contiguous from short or long. Rib spacing is a maximum of 15 foot. The standard made that pretty clear. You should not exceed 15 foot. Now when you talk about rib spacing, rib spacing is center of beam to center of beam, but it's also center of beam to outside edge. Some people try to say I'm 15 foot to the center plus half my beam. The standard gives you a drawing, it shows it to you. No, it's outside of beam to center of the first beam, then center of beam to center of beam. That's your rib spacing and it's a maximum of 15 foot and your spacing should not exceed a ratio of 1.5. You can exceed any ratio you want, but if your ratio exceeds 1.5. So if I go from eight foot wide to 15 foot wide, my ratio between those two spacing is greater than 1.5. You can't use those average beam spacings. You don't get to count up all those beams and average them for your stiffness. You actually take your largest spacing at 15 feet and you take a ratio of 0.85. Now I really hate this. Again, I'm talking Tony Childress here. I've been doing this a long time and I've done a lot of analysis on failures. You can sit there and put all kinds of beam spacings into an equation to prove it works. That doesn't mean it's going to, you have to know what is really going on. So we'll show you an example of that. But your moment and shear equations cannot be less than six feet. What that means is you may put beams in there at five feet or at four feet for whatever purpose, but your equation should be limited to six feet. So let me show that in a second. So this is just a quick check. You're doing a shape factor check here. I'm doing my spacing check here. This one at 15 foot spacing, my minimum was 12 foot. I'm at 1.3, therefore I'm less than 1.5. I can use my average beam spacing. This is my other direction. So you check it in the short, you check it in the long, but that's just a simple check. All right, let's talk about space. What you really want when you can is equal space. You want it to be uniformly rigid. Whatever it feels here, you want it to feel here, you want it to feel here. And I apologize, I don't think, I just realized you aren't seeing my mouse. So whatever you feel here, whatever you feel here, you want it to be consistent. And now I could model this, and you have the same number of beams, and I enter that into a spreadsheet or through the standard, and I'm going to get the same result. Now granted, this wide spacing right here compared to the small spacing, I will get a reduction, which will help. But you really want to try to think about your design and to make it as uniformly rigid as you can. Well, that makes it hard. What happens when you have shapes like this? Well, again, if I'm looking in this direction, if I'm looking in the short direction, I'm trying to keep my ribs, if these ribs are at 10 feet on center, I try to keep these at 10 feet on center. Again, this is Tony Childress talking, not the standard. Same in the long, I try to keep it as consistent as possible. I want to make sure that as these forces are transferring through, it's as consistent as I can be. I never vary my beam depths in the long and short, and I never vary my beam depths as I go from one section to another. In fact, I don't want to see that being done. So again, that's something important to talk about outside of the standard. Minimum pre-stress force, again, this is the minimum, and if you understand the equations that are given in the standard, what it's really telling you is 50 PSI is the minimum. If you really are bored and you like reading a lot of stuff, you'll find out that 50 PSI is the minimum strength required to help with shrinkage cracks or what we call RCS cracking. So that's why 50 is the minimum. 70 used to be kind of a standard. I don't know many that do anything less than 100. 100 to 120 is the most common to most of the structural engineers that I have a relationship with for slabs on ground. The higher the PSI, the better you're going to get restraint to shrinkage cracks. So that's kind of, again, the bottom part is my part. The standard pretty much gives you the 50 PSI, and the 50 PSI is really 0.05a when you run the numbers. If excessive shrinkage cracking is anticipated, you want to go to 0.1a. That's the 100 PSI, this is the 50 PSI, just when you run the numbers. Now, this will cause a stir. For 20 years, the PTI had a standard recommendation not to exceed 5 feet. It was in some publications that it's done, but it's not recommended. While we worked on the last standard, 2019, and while we're working on the next standard, which is going to be 2024, we realized that that's no longer in there. This is up to the user. People do 6 feet, people do 7 feet. As long as you get the PSI you're looking for, it'll work. I don't recommend going much beyond 5 feet. That's just, again, sidebar. That's what I and a lot of other people do. I'm not saying 5.0, 5.5 feet, 5.25 feet. I never go 6 feet. I do know others do, and I respect their decision to do that. The next thing we have to know is what kind of structure are we carrying? Are we sitting on just a framed structure, and there's not a lot of chance of cracking? Well, my edge drop, when my soles shrink and my edge drop, my ratio, my stiffness ratio is 240. For edge lift, that's when the edges go up, it's 480. Well, if I'm carrying concrete measuring units, well, those things don't handle movement very well. You got to make it a more rigid foundation, a more stiffer foundation, because CMU will crack easier. Here's your brick values, your stepover plaster, prefabricated roof trusses. Always pay attention to those little asterisks. If you have a house, say it's only 30 foot wide, and you have a truss that goes from outside of wall to outside of wall, and you don't use any of the devices that help transfer the load to the interior walls or help clear that movement, you're really limited on your movement. 1,000 for edge drop, 2,000 for edge lift. There are ways around that, but again, this is something you must consider when you design your structure. Again, I design for brick all the time. Even if it's stucco or plaster, even if it's just siding, I will not lighten my slab design for the elements. That's a decision I just push up on my clients. I tell them that. Yeah, it does help from time to time when they decide to add brick ledges, but I've just been successful at being a little bit conservative, and it's either brick or I design it for brick. All right, uniform thickness slabs on expansive soils. That's addressed within the standard, it's our PTI type three foundation. Section 4.3, we'll discuss it. They give you an equation. Your UTFs must satisfy all the requirements of section 5, 6, and 7 within the standard. First you have to design a conformance slab, so you design a ribbed foundation to meet the PTI design requirements, and once that's a conformant design, then you have an equation here that all this is doing, this H, this new thickness, this uniform thickness foundation doesn't say that a 7-inch or 8-inch or 9-inch slab is good. It tells you what's an equivalent stiffness, so it's going to take the stiffness of the conformance slab you designed and convert it to a thickness, so now at least we know we have a stiffness. We have to worry about moments, we have to worry about shears, we have other things to consider. So this is how you calculate it. The minimum uniform thickness foundation is 7-1⁄2 inches. Please do not get confused between a 5-inch thick sport court, which is a PTI type one, compared to a uniform thickness foundation, which is a PTI type three. So the uniform thickness foundation is designed to handle sole movement, minimum thickness 7-1⁄2 inches. Now in the design of this, which we're not going to go through today, you don't typically put your beams at 10 feet on center, 12 feet on center to get your conformance slab. You want to design your ribs closer together to get more, the closer you put your beams, the more quantity beams you put, the better initial estimate you'll get for your initial slab thickness. But even if you put your beams at two feet apart, well, the code says you can't, no. The standard doesn't say you can't. It says you put what you want in there, it's only going to consider six feet for the moments of the shears. But when you put your beams closer, it will consider that for the stiffness. And I hope I'm not going too fast. This is my first, I've done this presentation for 20 years probably, but this was brand new from scratch, and I've got an hour to get it all done. So again, your minimum three stress is still the 50 PSI, the 100 PSI is still the recommended by most users. All right. Now we're going to go into how to design a post-tension foundation. So this is not, you won't find this in the standard. This is now just Tony Childress. You want to start your design with the largest spacing and minimum beam depth. You can hurt yourself by just throwing a bunch of stuff in there, and then you find yourself fighting problems that you've created. You want to use the minimum number of PT cables to get started. Now any PT supplier hearing this will get mad at me and send me nasty grams because, you know, but the design will tell you how many cables you have to have. Don't put too many cables in initially. Run the calculations and review results. Now if you're a software person and you just want to tell you the answers, great, go for it. That's not what we're here for. We're engineers. We don't just put data in and take data out. You have to know what the results are telling you. So I'll show you that in a second. You want to find the biggest overstress or stiffness issue. Now what's the biggest issue? Attack one issue at a time. Don't try to look at all the problems and try to solve the world's problems with one sweeping issue. You have to understand what an overstress or stiffness issue is telling you. So we're going to do one. I'm going to pull up an app so it bears me one second. I've got this design. This is a real design, a real foundation, and we're going to run it, but I'm going to stop sharing for one second and I'm going to share a different screen. Here we go. Bear with me one second. Nope. Stop sharing. My apologies. Let me get my... I hear all the laughter. I can't hear anybody. Here we go. Let me share the screen. Let's go back to Zoom. Share. There we go. I've got my screen up. Kyle, if it's not up, I know you'll tell me. I'm going to share. So, this is a PT-ribbed example. You know, your soil information, we get that from the geotech. That's entered in there. Yeah, I'm trying to be funny. Subdivision, somewhere in the world, on some street. The builder, a good one, hopefully. And the plan, you want it to be as easy as possible. Your variables that you'll deal with. Some of this is my own personal stuff, but... So, one story. I've got 1,100 pounds on my perimeter. I've got 1,100 pounds on my perimeter load. That's only for edge drop. The standard... I'm not allowed to take questions during the session. Kyle, as long as the slide is up, we'll do the questions at the end. For edge drop, you want to use your largest perimeter line load. And that's in the standard. For edge lift, you want to use the smallest perimeter edge load. So, you don't want to consider... You want to consider worst-case scenarios. So, that's what this is doing. You've got the uniform load of 40 pounds per square foot. Your concrete weight. Your density of concrete. I'm calculating your creep. You can use 1.5. The standard gives it to you, or you can calculate it yourself. I don't believe I went over the subgrade friction. That's my apologies. If you're on natural ground, your subgrade friction is 1. If you're on poly, it's 0.75. The standard will give you different subgrade friction variables for what you're going on top of. My minimum cable is a half-inch diameter. 50 PSI is the minimum. I've limited my cable spacings. So, a lot of these are just standards. Here's my deflection criteria. All right. So, I've got a span of 34 foot 4 inches in the short. 61 foot. I want 4 inches for my depth. I'm putting my cables 2 inches from the top of the slab. So, I'm in the center of my slab. So, if I take 34 feet and I divide it in two, that is 17 feet. Well, 17 feet exceeds 15 feet. Can't use that, right? So, if I take 34 feet divided by 3, well, that's 11 feet. So, if I look here at my long direction, 61 foot divided by 4 is more than 15 feet. So, if I divide it by 5 spacings, which is 6 beams, my beams are at 12.2 feet. I've got cables here. I'll even go 5 feet. Let's go 5 and a half feet. I'm going to try a 20-inch beam depth, 10 inches wide. I've got one cable in the bottom of my beams, and I've got it at 5 and a quarter from the bottom of my beam to the centroid of the cable. Long, as I said before, I can't split 34 foot in half. So, I've got 11 foot 4 feet. Again, I'll say, let's go ahead and go 4.8. Same. This does my checks for my shape factor. What I'm seeing here is everything that doesn't work. I'm seeing bending stress in short direction, tension, edge lift mode. So as my edges go up, I've got a tension problem on the bottom. So now I've got to ask myself, and by the way, I can kick a button and fix this in a heartbeat. But that's not engineering, that's business. If I want to learn how to do this, well, if I add width to my beam, is that going to help? Well, your engineer should know that your width, your B is linear. So it's BD cubed for your stiffness. So adding width to my beam is not going to get me anywhere when it comes to bending stress. I could add more concrete. I could make the beams deeper. But when you add concrete, let's try that. I've got 110% right now. And I'm going to say, let's go to 22 inches. So I'm going to go to a 22 inch deep beam. And let's see. Yeah, went to 22 inches. And that didn't really get any better. Let's go to 26 inches deep. And let me make sure this thing runs. There we go. I'm at 64%. Well, I've started a bunch of concrete. But I still don't have it done. And I still got problems. So knowing what I do know is that this is controlled best by a cable. If I put another cable in the bottom, I just put one additional cable in the bottom. So we've got two cables in the bottom of the beam. Now I went from 110% to 23%. OK, but now I've got a stiffness. My biggest issue right now is 36% here. Stiffness and long direction. So I can add a cable. But the cable is not really adding any stiffness. I can add a width. But to make this work, I got to add 36% to my width. Because that's linear. So what's going to help is either beam depth or add a cable. So I mean, excuse me, add a beam. So first I'll try going to 22 inches deep. And with that, I've got to 19%. All right. Now I've got 24 inches. At 24 inches, OK. So my first run, I've got a 10 by 24. Double cables in the bottom. Beams are 11 feet, 12 feet. And I work. It's 4.6%, by the way, says. I still got 4.6% capacity before I get to my limits. And what I could do is I can look and see how much concrete yardage it's given me. And well, that'll be in the report. I will get the concrete yardage. And I can see, was that the best design? Or should I instead go back to 20 inches? And now I'm going to go in my long direction and add a beam. Which I wouldn't do. But I'm just showing you the difference. If I add a beam, now I'm to 17%. So I go to, oops, 22. I'm getting closer. So what I'm showing you is I can add a beam. And or I can go beam depth thickness. But so that's how you do these designs. You have to be able to know what the results are telling you. I'm going to go back here one more time and look at all these. So if I'm on edge lift and I got a stiffness issue, we discussed that. If I got a bending stress issue, short direction, tension, edge lift. My tension issue here means I got, I don't have enough tension down here. I got to get compression down here. Bending stress, bottom fiber, short direction, compression, you know? So this is now, it's trying to curl downwards. So you have to know what is telling you, whether it's uplift forces, downward forces, whether you have enough cables in the top, enough cables in the bottom. But that's the general process on how to design slabs. And just to finish this one, I'll go back to 10 by 24s. I'm going to put my beam at four of them, double cables. And there's my design. And there's my, there's my spacings. And that's what gets, all right. So stop sharing that, start sharing back to my presentation. Hopefully we're back. Let's see here. Apologies. If you're here, click. All right. So the question becomes, how would you handle this? You got an edge lift condition, bending stress, tension. So I got an edge lift condition. I've got compression, bottom fiber, short direction, tension, edge lift, compression, tension. So I got an edge lift condition and it says I got bending stress. So where's my stress is going to be, right? Do I increase my concrete strength? Do I add beam width? Do I add beam depth? Do I add beams? Or do I add slab cables? Again, edge lift, bending stress. You want to add slab cables. That's the answer. Edge drop, bending stress, tension. So now I've got an edge drop condition and my bending stress is tension. Where's my tension? The tension is the top of my concrete. So what would you do there? Well, again, there I would add more PT cables in the slab, get a higher compression in the top. Stiffness issue. So edge lift or edge drop, doesn't matter. I got a stiffness issue. Yeah, I can increase concrete strength. That's going to get me square root of F prime of C. So, wow, you know, if I go from a four square root to a three square root divide, I'm 15% stronger, going more stiff or going from one to the other. That doesn't do anything. Beam width is linear. Beam depth is to the third power. Add beams, that also helps. And cables aren't going to help. Beam cables won't help. Shear stress issue. Shear stress issue is controlled by concrete strength. But rarely would I increase the concrete strength to get shear capacity. Beam width will clearly help. Beam depth really doesn't do much. It does. Beams certainly help. Slab cables do help shear stress, believe it or not. Because part of your shear strength comes from your compression strength. And jack moment issue. That one, again, is going to be your beams. And last one. Does different climates affect the design? And I'm speeding up because we're running towards the end for questions. So, example. I have a dry climate example that will come out in a PTI publication shortly. That we came up with 14 by 24 inch beams with 15 foot by 12 and a half inch beam spacings. Single beam cable met a certain design. We took that exact same design and took it to another area that was considered an average climate. It had 10 inch by 26 inch beams with 10 foot by 10 foot beam spacings and double beam cables in the bottom of the beams. We took it to a wet climate and had 12 by 20 beams with 12 foot by 10 foot beam spacings and single beam cables. So, basically, the environment, the region you're in will control your design. Just because your guy in Texas has 26 inch beams with 10 foot spacing doesn't mean you're going to have that in San Antonio or Arizona or anywhere else. All right. I already went to that 2500 PSI. Does pre-stress cables increase strength? No, it only helps reduce restraint to shorten cracks. And can I eliminate restraint to shorten cracks? No, you cannot. Now, there are certain specialty concretes that can get you there. But most of your concretes, you can only limit your restraint to shrinkage or shorten. You cannot control it. If I use a slab thicker than four inches, does the location of my slab cables matter? Yes. There are eccentricities that will be considered. So, if you have a thicker slab, you've got to put in there where your centroid is, whether it's two and a half inches or two inches. And I'm done, Kyle. Hopefully, I left enough time for questions. Yeah. All right. So, we got a few questions. And I think we got plenty of time here on there. And I know you've got some slides you got to show too. Right. So, first one, this one has to do a lot with losses in the tendon itself. But can you talk about max minimum tendon length for a slab on ground structure? And then also kind of some guidelines for max and minimum lengths of the actual foundation itself? Sure. So, the maximum length of a post-tension cable that should be considered is going to range a good number of 225 feet is a very common number. You're not limited by design. You're limited that you physically can't carry a 250-foot or 300-foot cable across. It's just magically difficult. Now, if you have these very, any cable longer than 100 foot needs to be stressed at each end. So, a cable is dead end at one end. It's called a live end at the other end where they stress it from. But that's only if it's 100 foot or less. When you go beyond 100 foot, they will stress from each end. So, they will put a temporary anchor on one side. They'll stress one side. They'll set the wedges. And they'll stress the other side. So, but 225, 240 foot is a good range of about as big as you want to go with a single strand to post-tension. And then minimum strand length that you'd recommend or any advice for if you just had a narrow little? Okay, minimum. So, you can do strands 16 foot, but don't expect to get the elongation that you get from your standard. So, your elongations that we typically expect, and there are publications from PTI that can help you with that. When you have your cable from 35 to on up, these elongations are pretty consistent. When you get to shorter cables, less than 20 foot, you have a hard time getting the elongation you expect. It doesn't mean don't use it. Just understand what you're dealing with because you have so much, so little elongation that's coming out of a 16 foot cable that by the time you set the wedges and you get the seating loss, you'll never get the full elongation you expect. So, you may want to consider additional cables when you have, you know, so where you're 16 foot or I believe, and I can go look, I believe the minimum cable length required by PTI is either 12 foot or 16 foot. I'll have to go search that, Kyle. I don't have it memorized. Okay. There's a question that came in about dead ends that are in the middle of the slab somewhere. So, if you have a drop where you have a rib that dead ends into something else, and then you have those dead-ended tendons there, any information that you can elaborate on, on analyzing that best practices for detailing at the area where you're installing an added force mid-span? Yeah, maybe two conditions. Let's say you get a drop. You have a two foot or three foot drop. Now, you should drop post-tension cables through drops like that. Dropping at six inches, that's easy. Dropping at three feet, no. So, you want a dead end where the drop is at on the upper shelf, and you want a dead end on the bottom beam and have it live end at the opposite ends. There, you need Z-bars. So, you need conventional reinforcing Z-bars to make sure that area stays composite. If you want to put a expansion joint or a control joint, then you want to use what's called a keyway. So, a keyway is a piece of metal that you can set in your form, you can dead end to each side of it, but now you've got a control joint that you know is going to get when the concrete shrinks will open up slightly. So, you have a controlled area where you have a keyway joint, but those are called keyways. Okay, another question. Are these PTIA methods applicable for commercial townhomes or apartments, say, for example, three stories in height? Absolutely. So, I'm doing all three stories, four stories, five stories, but be careful. I look at it differently. When I deal with three stories and more, I look at it differently. I will design the foundation first, based on the geotechnical parameters for soil movement. So, I'll design myself. It's a 12-inch wide beams, and I may have a 24-inch wide beams at 12 feet on the center, whatever. I design it. Then I take my load, my gravity loads, I take all my gravity loads down, and then I start seeing, do I have to keep my beam widths? Now, remember, if I increase my beam widths, I'm still not really changing my, I'm making my slab-on-ground stronger. I'm not making it weaker. So, yes, it's absolutely applicable. What I said was, you as the engineer have to take those 3,000, 4,000 pounds per foot, and as long as the bearing handles it, then the rest is carried by the post-tensioning, which is really the movement. If the bearing fails, your foundation is going to move. But if the bearing doesn't fail, if you do your job right, the soils are still going to want to move, and those ribs will take those forces. But yes, we do them on commercial buildings, on residential, on everything. Okay, another question. Can you elaborate a little bit more on considerations when you're trying to choose between a uniform thickness or a rib slab? Everything comes down to money, Kyle. Everything comes down to money. Now, when I say that, when you go to parts of Arizona, many people do different things. There's really two things that control that. One is, what are people used to? So, out in East Texas, or West Texas, you know, Averillo, certain areas, you know, they do things a certain way, even though there's better technology out there. But if they're only used to doing things one way, they'll continue to do it that one way, even if there's better ways of doing it. We probably shouldn't have said Averillo. They're doing it better now. But when you get to an area, we have a choice. So, like we get, we'll get to an area where I'm trying to get ribbed beams into a bottom of a basement, and I'm concerned about hitting rock. I'm concerned. I will analyze it as a ribbed foundation. I will look at how much concrete I'm using, the cost of it. Then I'll go to UTF. And so, if I go to a 10-inch slab at the bottom of that basement, am I less concrete, less labor than trying to dig all these beams? So, it's a money issue for the most part, because in theory, they're both going to act the same, because you converted the thickness as an equivalent stiffness, and you gave enough cables to handle the moments and the shears. So, it's really what the area is used to and what's driving cost. Right. All right, probably time for one, maybe two more questions, even though we have a bunch of really great questions here. So, for longer foundations, are pore strips a typical thing as they're used in elevated slabs? Do you see that as a common solution to help with the shrinkage mitigation? No, not pore strips. You know, leave-outs are really common in warehouse slabs and large slabs. Here, the user, the engineer, has to decide on how much shrinkage he's going to get. So, if you have a ribbed foundation, you can't get a lot of shrinkage, okay, because the beams are socketed into the ground. When you have a uniform thickness foundation or a flat slab, the potential for cracking is a lot less. When you put beams, and I'm talking purely just ribbed foundations in the ground, as your concrete cures, those beams are stuck in the ground. They will shrink a little bit, but as it shrinks, you get what's called curling. Curling is this twisting up effect, and that's where you get the curling cracks, shrinkage cracks. So, we did a huge one in San Antonio. Yes, we did do a leave-out, but the leave-out was for a jacking gap. Where we left three foot out, so after the slabs were stressed, you could stress both sections of it, the shrinkage could occur, and we poured a strip back. You can't do that, but we did that because we had 500 or 800 foot of length, and we wanted, we had to have jacking gaps so we could stress 250 feet to the left and 250 feet to the right. All right, we have, like I said, we have a lot of questions. We've had a lot of interest in this topic as a whole. We're not going to be able to get to all of them. We'll see if we can't provide some answers to them either online or another source there, because there are some very good questions that are still out there on that, but we do need to look forward to the next few presentations that we have and talk about that some. January, we go into electric vehicle weight and the design considerations for elevated parking structures, so that's becoming more and more of a hot topic as we see EV vehicles more present in urban areas where we have garages there. Then February, we change topics away from design considerations more into evaluation of existing post-tension concrete structures, so we're going from design to more how do we do the evaluation or repair type topic in there. Then March, bridges. We really haven't done that many bridge presentations. We did one last year, and so we're looking forward to get away from the building side and into bridges into March. Then as far as more slab on ground presentations, we do have a lot of them scheduled for 2025. I believe we have three of them on the books right now, just because the amount of demand and questions we've been getting on this topic. It's one of the biggest topics within the Post-Tension Institute as well, so we do look forward to doing a lot of them in 2025 on there. With that, if you guys do have any additional questions, you can see how to get a hold of Tony on the screen right there. You can see his email address to get a hold of him. You can also get a hold of the Post-Tension Institute through that info at post-tensioning.org on there. We look forward to seeing you guys on the future webinars. Like I said, it's the same time every single month, which is the second Wednesday of the month at one o'clock Eastern. See you guys next month, and thanks so much for joining, guys. Enjoy the rest of it.

post-tensioning

concrete foundations

expansive soils

structural design

PTI types

bending stresses

shear stresses

slab thickness

geotechnical