Live 64 -Continuação complemento da live Muro de Arrimo - Cálculo da Fundação

Added: 2026-05-30

[00:00:00]Good morning everyone. Good morning everyone. How are you all doing? We're starting another live stream, our 64th live stream, right? Live stream number 64. We'll be doing a continuation, folks. Continuation, supplement to the live stream about retaining walls.

[00:00:23]Okay, let's calculate the reinforcement of the block and reinforce some very important concepts. Hey, Antonio. Good morning, Antonio. Everything's fine here in Curitiba. Nice to meet you, Antonio. Awesome!

[00:00:40]That's good. It's very cold there in Curitiba.

[00:00:43]It's quite cold here in Rio do Sul.

[00:00:46]And we'll continue from there. We've improved the normal flu, right? I, at least, catch a cold every winter, there's no way around it. So we 've already started off well on YouTube. How is the audio quality? We're doing great. Audio.

[00:01:03]Oh, great! Legal.

[00:01:06]We're doing well with the audio, everything's fine on YouTube, Instagram folks, just a reminder that the live stream and all the content are being generated on YouTube, where I can do drawings, where I can explain all the concepts necessary for us to progress and evolve in order to do the dimensioning, okay?

[00:01:41]Without further ado, let's get started, shall we? Let's begin today's live stream here. Just a reminder, everyone, that this is very important for those who don't know me. Well, I'm a professor, I'm a structural engineer with over 1000 structures that have had their technical responsibility formalized within the CRÉ (Regional Council of Engineering and Agronomy), not counting those that we end up not removing from the technical responsibility list, because the cost is high, whether we like it or not.

[00:02:09]Well, among other works, structures that we've been designing throughout our careers, right?

[00:02:18]Ah, I'm the creator of the structures and foundations community, which is an environment where we have the evolution of engineers through content to generate more safety and efficiency for engineers, you know, through content for the calculation of foundations and structures. The community today has a gigantic technical collection, and we are improving and updating it whenever possible.

[00:02:47]Alright, guys? So, today the community is embracing Foundations from Scratch, which is our foundations course. Okay, let me just take a look here at how many classes there are... uh, foundations from scratch.

[00:03:03]Well, just so we have an idea of what it would be like. Let me open the other file I have here. Ta- da! Ta-da! Ta-da! Ta-da! Ta-da!

[00:03:15]I think this is it. Well, for example, just so you guys have an idea, okay? The Foundations from Zero course consists of 300,336 lessons, okay? 336 lessons, 49 hours of step-by-step content.

[00:03:37]Reinforced concrete from scratch, 19 hours of content, 217 step-by-step lessons to teach you reinforced concrete from the very beginning. Library of live streams, we're now approaching 64 live streams, okay?

[00:03:55]Well, an exclusive WhatsApp group, spreadsheets, updates, a technical community—that's everything that encompasses the structures and foundations community.

[00:04:06]What's going on, guys? We had, over time, it was a product that we call perpetual, which is basically a product that the student can access at any time, okay? But we've decided to close community registrations, okay? We will close community registrations and only reopen them for a limited time, which will be after an event.

[00:04:35]Probably the first event we're going to do, which I have scheduled for about a month from now, will be about retaining walls, by the way, okay? So, uh, there's going to be a week where we'll have a special offer for students to enroll and everything. So, initially, the community has closed its registration, right? And we're going to open in a short period of time, just a little while from now, okay? So, for now, only the content that's available there, through the platforms. And if you want to be part of the community, you have to wait a little while until we can get the registrations open and you can join the community group, okay? From the community group, structures and foundations. So I'm going to end the Instagram live here, okay? Hey Instagram followers, follow us on YouTube so we can continue and do our dimensioning of this foundation block, okay? A big hug to everyone there. Thank you, everyone.

[00:05:49]Let's go, then. Let me share my screen so we can remember the efforts we had planned, right?

[00:06:01]Let's share the screen here. Our software. Nice. Legal.

[00:06:07]Let me move Streamyard over here so I can see it a little better. Awesome! That's awesome.

[00:06:16]So, folks, we have a foundation block, right, where we have a compressive load on the pillar of 2.3 tons, which is what we had already calculated, okay?

[00:06:33]It's a horizontal load, which is precisely the thrust acting here, right, of 5.34 tons of force, correct?

[00:06:46]This is the horizontal load acting here.

[00:06:49]So we can put it back here, right, redo it here, put it back here so we can remember the efforts, right, everyone? So here, look, 5.34 tons of horizontal force, right?

[00:07:11]In our case, we have the bending moment acting here, right?

[00:07:16]So, bending moment here, remind me, the calculated bending moment of 6.64 is a 4, I think that's right, isn't it? Let's see here. Let's go back up here.

[00:07:30]So, 5.34.

[00:07:34]5.34, no, 5 points is 5.34, right? multiplied by h/bre 3, which would be 1, becomes 5.34.

[00:07:52]Uh, sure, 5.34 tons of force times met, right? But I still have to add the horizontal force times half the height of the block. So, 5.34 x 0.3 equals +1.60, right? Ton of force times meter. So it's going to be 6.

[00:08:13]Let's take a look here. So, 1.6. Ah, sure. So, -0.3, right? - 0.3 ton-force times met, which is the moment due to this eccentricity of the load, right? Vertical load. You ca n't see my mouse, of course, because I have to click here. So, look, this is exactly where we added up the bending moments, right? 664 here, which is the 534 of the soil thrust, 1.6 which is the horizontal force here, times half the height of the block, and 0.3 which is decreasing because it's reversed here, remember? 0.3 turning the force sideways at a meter, which is this tendency to rotate due to the vertical load that comes here at the pillar and is discharged off the axis of the pile. So this gives us 6.64 tons of force times m. So let's put here, 6 and 64 tons of force times m of a bending moment, right?

[00:09:19]Yeah, cool. And here we have this VK, which is the shear force on the pile, right, of 7.83.

[00:09:31]So, the shear force on the pile here is 7.83 tons. Okay, okay, okay. It 's OK. Oh, and we have the horizontal beam at the stake, right, at 2.67, okay? So let's put it here below the 2.67 per stake.

[00:10:03]We're summarizing the efforts we had planned in the last live session, in our last class, okay? And remembering here, right, that we also calculated the weight of the block itself, right, which divided by 2 is 0.8, 8 tons of force plus 1.5. 1.5 would be what? So, this 2.3 here is by stake, if I'm not mistaken, right? This one is staked, right? Its own weight is here, right?

[00:10:36]3,000 3078 kg, right? I believe that was it, right?

[00:10:43]Because here, 0.9 is the cornerstone, right? So here's the 570 kg of the pillar, and here's the beam.

[00:10:52]So, 1000 and 1140 kg for the beam. That. E 2 m² of masonry x 2 x 0.19 x 1.8 1368 kg. So the vertical load that reaches the block there and is transferred through the pillar is 3,078 kg. So let's put a vertical load here, right?

[00:11:20]Unloading in a block of three, 3 tons, right? 3078 kg, right? 3 tons by force, okay? Beauty? 3 pon a gente tá usando duas duas duas das na vírcía. 3.07, right? 7008, right? 3.7 3078, right? Beauty? So that's it, folks.

[00:11:45]These are the loads that we have acting on our block, okay? The first thing we need to understand, folks, when we're going to do a dimensioning calculation is this: Let me get a quote before I show it to you. Let me... Let me see if I can share it here.

[00:12:05]Eh, cha cha cha cha.

[00:12:07]Stop the screen.

[00:12:10]And I'm going to share with you the TQS screen, which is where I created the TQS window. Let's see if it shows up for you.

[00:12:21]Legal. Let me put it here. So, guys, look what happens, okay?

[00:12:27]When I look at this, even in the last class I said that this model of this block, it looks a lot like a beam, right? And really, if we look at it, it has bending moments, it has shear stress, right? But what matters most when I look at this, folks?

[00:12:49]I have to look at this area here. Okay? This region right here. My amoeba is huge. Let's go back here and set up this amoeba.

[00:12:59]Minimum radius. Let's set it to 0.1 to see if it improves a bit. It got a little better, but not much. 0.0.

[00:13:06]Oh no, but you have to set the maximum radius here, right? So, let's put 05. Let's see if now... Ah, now it looks good, see. Legal. So, here's my amoeba.

[00:13:17]Important amoeba, right? Oh, let's go.

[00:13:20]So, this region here, folks, if we look at it from the perspective of the standard's concepts, we'll remember that there are several regions within a structural project.

[00:13:32]And this here is a region that we call region D. It's a region of discontinuity.

[00:13:39]Well, and in this region, when we have a discontinuity, we can't, we can't calculate this point as a beam calculation model, we can't calculate this here as a beam calculation model, okay? So this is a region where we need to have better criteria to calculate this region. This is a concept of regional norms, right? Okay, let me see if I can open NBR611 and put it here so we have it in our PDF, okay? Let's put the region here in the PDF to see if we can find that graph of the regions, right? I think it's more towards the end of the standard, if I'm not mistaken.

[00:14:32]Let me find it here. Ta- da! Ta-da! Ta-da! Ta-da! Ta-da!

[00:14:41]further down.

[00:14:54]Just a little more. Okay. Puncture. Not yet.

[00:15:10]We're getting there.

[00:15:14]Here, look.

[00:15:16]Typical situations in region D. Now like this, look. This is pretty cool, right, guys? Yeah, right. Let me see. I'm going to copy this part here, see?

[00:15:29]Let me copy this into our PDF here.

[00:15:44]Let me move this a little further to the side.

[00:15:50]Let's go back to our painting.

[00:16:04]Pause screen, share screen. Scald. Now that's more like it.

[00:16:11]So here's the excerpt from 6118 for us to check the definitions, right?

[00:16:29]Legal.

[00:16:31]And here are the typical regions of discontinuity, okay?

[00:16:43]And here we're going to bring this image of our block over here, okay?

[00:16:52]So, look at this, guys, here's what's happening, right?

[00:16:58]When we look at Law 6123, folks, at Law 6118 of 2023, what does it tell us, right? She says, "Look, item 22, okay?" Well, in section 22.1, the specific symbology is specific to this section. The symbology presented in this section follows the same guidelines established in section four. Therefore, the subscript symbols have the same meaning as those presented in 4.3. Then he's going to talk about the stresses and verification resistance of the concrete FCD1, FCD2, and FCD3, okay? And here it's always closely linked, right, to the issue of connecting rods and tie rods, right? Uh, and then these FCD1, FCD2, and FCD3, he says, look. Well, in this section, criteria are defined for the design of elements with generalized discontinuity and elements in which geometric discontinuities or loads that affect the behavior of the structural element as a whole are called region B of a structural element, those in which the plane section assumptions, i.e., a linear distribution of specific deformations in the section, are applicable, and those in which this plane section assumption no longer applies.

[00:18:30]In general, the boundary between these regions B and D can be considered to be located at a distance H from the considered structural element of the effective discontinuity section.

[00:18:46]Figure 22.1 illustrates typical situations in region D with nonlinear deformation distributions, geometric discontinuity, static discontinuity, and geometric and static discontinuity. And then he says, look, where are these regions, you know, so we can check them out.

[00:19:12]Regions of change, for example, here he gives examples, right? A sudden change of session, right? Example of a portal frame node, one here, right? A sudden change of session. It's precisely this first image where I have bending moment and loads, and normal loads here, right? Oh, there's a portal node too, there's a region of discontinuity, beams with openings, foundations, okay?

[00:19:42]Supporting a beam, right? With a concentrated load here, precisely, we have a discontinuity.

[00:19:50]Ah, concentrated loads on beams and the introduction of concentrated forces.

[00:19:56]So, for example, when I have prestressing, it would be a case of wall beams, where I have a very tall element in relation to the loads, right, in relation to the supports. Transversine, constellation, tooth, Gerber, are regions of discontinuity.

[00:20:18]When we look at our case, folks, if we evaluate it very carefully, we'll see that we don't even have anything close to this typology that we have here, right? The closest analogy we could make would be with a connecting rod, where I have a load applied here, a connecting rod— theoretically, this is a connecting rod— and a tie rod at the top of our block. So, it would be equivalent, in general terms, to a consolation. Well, what's the problem here, right?

[00:21:10]When we look at this as a consolation prize, the consolation prize has a certain... it has... ranges, right, of nomenclature for it. So, we can classify a consolation prize as long, if I'm not mistaken. I don't know if that's the correct terminology, but it's long, short, and very short. Short, very short, I'm sure of it, okay?

[00:21:37]So, for us, the short and very short is what's important.

[00:21:42]So, which standard do we fall under then?

[00:21:47]We then refer to standard 9062, which is precisely the precast standard that will help us to have a calculation model closer to what this block requires. It's not a precast block, but we need a model similar to this to help us with the calculations, similar to our case, okay? So, look what's happening here, folks. Look, these are calculation assumptions according to law 9062, okay?

[00:22:32]We'll also put it here in our PDF. Calculation assumptions.

[00:22:44]When I have an A over D between 1 and 2, the dimensioning is done as a cantilever beam. What is A and what is D? Let's go back to the norm here as well. And let's take this definition of A and D, right? Because this is going to be very important for us. Just look.

[00:23:10]So, here's the diagram of the standard that will show us what A and D are, you know, for a consolation prize. Look, A is precisely the distance between the point where I have the load applied to the corbel and the face of the column. And our D is the useful height of our consolation.

[00:23:32]Let's take a look at what A and D would be in our case, shall we?

[00:23:38]So, uh, going back here, uh, let's zoom in a bit here? He has.

[00:23:44]Legal. So, looking this way, look at the distance.

[00:23:50]Look how interesting, everyone! Look at our case, what happens?

[00:23:55]We have a load applied here, and the face of our precast column, let's say, because imagine we had this here, the precast column here, okay? Our consolation is that I have load application and I have the face of the precast pillar. A represents precisely this distance here. But look, our point of load application is to the right of the face of our pillar.

[00:24:26]This means that our A is actually negative.

[00:24:31]He's negative, isn't he? If we consider A to be equal to zero, then what will our A divided by D be equal to? A negative zero means that we can't even classify this as a very short consolation prize. We're down on a very short tier of comfort. So here we are, look at the complexity of this, folks. We are in a DM region, which is a region of discontinuity, okay? where the calculation model that most closely approximates this would normally be a short consolation model, a very short consolation model, sorry. So let's go back. The closest model to this would be the lap-worn one, which is very short.

[00:25:27]However, when we look at the definition of very short consolation, remembering that we were between one and two here, right?

[00:25:37]Here, look, short consolations, okay? This would be a balance sheet, right? Because here, I'm reviewing what I said in the previous live stream to see how important it is to keep up with the content, right, everyone?

[00:25:51]Well, I had this concept of consolation, but a very short-lived one. I always remember calculating this type of block using these concepts. Remind me to calculate transition beams, for example, for columns that originate at the property line, where you have a beam that will connect that column to the property line and bring it to a centered footing. I remember using these concepts because they are regions of discontinuity, and we know that we can't apply the concepts in a crude way, like, "Oh, the bending moment here, I'm going to apply the beam formula, right?"

[00:26:30]Cantilever beam.

[00:26:32]So, if I have an a over d between 1 and 2, okay, cantilever beam. Nice.

[00:26:39]Among all the beam formulations, shear and bending moment. If I have between 0.5 and 1, I have a short consolation prize. What's the cool thing he's going to tell us here, folks? Look, he's going to say that when it's between 0.5 and 1, the dimensioning is done according to the mathematical model of a truss of bars with one tensioned bar or tie rod and another compressed bar or strut. And the rest, uh, like bars of uh, sewing reinforcement bars, right?

[00:27:23]Limitations must be established for the requirements of the constituent materials of the bars, tie rod steel, and strut concrete, as per the items.

[00:27:35]Then he will say what limitations he wants to impose. But what is he telling us, right? So when I have between 0.5 and 1, look what happens here, right? Here I have my comfort, right? When I apply the load here, I have a connecting rod, right, a compressed bar, and a tie rod, okay? And there's a tie rod that goes through here. Nice.

[00:28:01]When I have between 0.5 and 1, it's like this. Then I can calculate it using the strut-and-tie method. OK? Very cool. I have no problem with that. When I... and then I ask you, when I have less than 0.5, what happens?

[00:28:16]Look, he's going to say this: Let's bring it here.

[00:28:24]What happens when I have less than 0.5? Then he says, "Look." For a over D less than 0.5, Five. The dimensioning is done assuming rupture along the connection plane of the corbel with its support, and the favorable effect of aggregate interlocking can be considered, provided that the interface crossed by steel bars perpendicular to it satisfies items 7.3.1, 7.3.3 TR and so on. So, what exactly is he saying here in practice, folks?

[00:29:02]When I have it there, I'll use another figure from the standard that will also help us in this regard. Just look.

[00:29:11]Then he'll say something like this: Look how cool this is!

[00:29:21]That's why it's great for us to delve deeper into the concepts, right, everyone?

[00:29:25]Simply coming here and saying anything isn't our goal, is it? We need to say what is truly appropriate. Then I brought up this figure of the norm, okay? In item 7.3.3.13, right? Because that's exactly what she demonstrates.

[00:29:43]Look at this distance here, look at this tiny A, okay? Regarding D, right?

[00:29:50]If we're going to, let's think of A as being, let's say, 10 cm, and D as being 40, it will be A over D = 1 over 4 = 0, right? So less than 1.5. This would be a very short-lived consolation, wouldn't it? This would be a very short-lived consolation prize, considering these dimensions, wouldn't it?

[00:30:17]Then he says, look, for consoles with D greater than 4 x A + A0, the stitching S armature is unnecessary, right?

[00:30:30]And then he's going to talk about the armor arrangements here. But what is important? When we said here, that when he seeks this concept of the interlocking of aggregates, it's precisely thinking about a rupture that occurs on this plane. I squeeze this side here, I squeeze here with force, and that's precisely where the rupture happens, right here, in this part.

[00:31:00]Why is it that for very short comfort it tends to pull a little more armor up here? Because the tendency is to create a mini connecting rod here at the beginning, and this region down here, you see, will be used much less, right? With much less effort here in this region. So I have the connecting rod forming here in this region, right? Compression, the stresses are already passing through the pillar. These areas are closer to where the load is applied, and that's why this region is a little more heavily loaded with steel. And that's what he's asking for here with this item in the rule when I have a very short consolation prize, right? And how do we do this verification?

[00:31:45]through the items here, precisely from the verification of the concrete. And then there's R, right, which we'll see more about later, but R comes into play here precisely considering this reinforcement ratio that will help here, right, to overcome this rupture, it will help with the resistance along with this aggregate interlocking factor. Alright, guys? So this is really cool, what the standard brings to us. Of course, look, the potential beneficial effect of horizontal loads that compress the connection plane between the corbel and the supporting element is disregarded. It is assumed that the effect of horizontal loads that pull on the connecting plane between the corbel and the supporting element is fully absorbed by the tie rod, right? Beauty? That's awesome. That's awesome. We have several concepts here. What is important?

[00:32:56]Our case, folks, look at our case here. How does it work?

[00:33:01]We don't have, it's impossible to consider that in our case we have very short-term consolation, okay? But we have it, and it's really cool, this is important too. Look at this angle, everyone!

[00:33:16]What is the normal angle to use for connecting rods and tie rods?

[00:33:21]Something around 45, right? To recap, for example, what were the angle limits for calculating a block using blevo? Does anyone remember?

[00:33:35]I'll look it up in the meantime, because I don't remember. For a block to be calculated using the Blevö method, what are the limit angles between the connecting rod and the tie rod?

[00:33:57]So, something between 45, something between, uh, look, in the Blevö method, the inclination of the concrete strut in relation to the horizontal tie should be between 40 and 45, right, with a maximum limit here, right, of 55 to avoid excessive stress.

[00:34:24]So, for example, the blevot method, which takes into account, of course, the connecting rod and tie rod method, the maximum limit is 55.

[00:34:34]If I'm not mistaken, Fusco already has a little more opening in relation to more flexibility in relation to this tie rod. Yes, exactly. Oh, for Fusco, the recommended minimum would be 33º, 33.7 7 with the absolute minimum being 26º and the maximum being 63º.

[00:35:04]Approximately 63º, okay? So, guys, uh, look at our case here, right? If we're going to take the angle formed between the connecting rod and the tie rod, okay?

[00:35:26]Let me give you a quote here so we can get an idea.

[00:35:33]Doing the opposite here is different in TQS.

[00:35:37]The quote did n't work out. Let me, let's do it again. Wait a minute.

[00:35:48]Oh, it's showing 79.69º. I'll put it here.

[00:35:57]Let me put it here in our PDF.

[00:36:04]Look, 79.69º is giving us the angle of our connecting rod. Okay? So you see, it doesn't fit, for example, if we were to make an analogy with the boulevard method, it wouldn't be possible to calculate using the boulevard method if it were a block. It wouldn't be possible to calculate using Fusco if it were a block. In other words, it doesn't closely resemble the strut-and-tie method, right? And that's why we also have to do the calculation as a short-term consolation, right? Okay, so far we've only talked about what not to do, right? And we realize that we're not very supported by any of those places, right?

[00:37:02]If we were to evaluate it, we wouldn't have it; it 's not a beam, it's not a short cantilever, and it's not a very short cantilever either.

[00:37:10]So what do we have to do?

[00:37:12]Okay, everyone, I'm going to explain what I do here. Why? If we're going to evaluate this in practice, look, folks, if we're going to evaluate this in practice, look what we have here. Let's try to evaluate the behavior of this case, okay?

[00:37:32]Let's try to assess the behavior of this case.

[00:37:40]What do you guys think is going to happen here? When the load starts to tighten around this block of ours, you'll agree that a good portion of the load will tend to move inwards towards the pile, right? All at once. It will generate a whole compression linkage here in this region, looking at our case.

[00:38:05]All of this, folks, is going to tend to generate a uniform compressive stress here, right?

[00:38:10]Uniform compressive stresses here. If we were to imagine what this model would look like if we were to apply a 3D finite element method model, right? Let's try to imagine how these charges would move inside the block.

[00:38:32]These loads would create a whole compression, a line of compressive load here all the way to the pile. And at the top of the block, in this region here, there will be a tie rod.

[00:38:46]So let's draw the compression lines here. Just look. So what will happen in blue?

[00:38:53]Compression, compression, compression, compression, compression. Legal. So, I have a connecting rod here in this region and I have a tie rod that will hold this, and of course, shear reinforcement that will withstand these forces here, right, folks. Hey, here. So, there are the connecting rod reinforcements that, of course, will withstand this tension to prevent rupture of the connecting rod, right? Connecting rod failure. The tensile stresses generated by this compression of the connecting rod are restrained by shear reinforcement and a tie rod that will help stabilize this compression, which is not actually vertical, right?

[00:39:50]Completely vertical, but yes, a little bit diagonally there, it goes from the pillar to the stake.

[00:40:00]What is the calculation method for this? Just a reminder of what our loads are. We are making an effort.

[00:40:12]Coming back to this point, folks, we have a vertical effort, okay?

[00:40:18]We have a bending moment, we have a horizontal force that will act on that point of the block.

[00:40:27]Let's take these loads down there and start the calculations. So, let's clear these charges here. Hey, I took a screenshot here. Let's copy, let's copy everything from there and transfer it here. Now that's more like it.

[00:40:52]Now yes. So we can delete it here, right?

[00:40:56]I can eliminate this vertical and horizontal strain here. Just look what's going to happen. So, let's actually begin our calculations, shall we?

[00:41:17]Let me grab my form here so we can begin our verifications. Awesome!

[00:41:49]Let's move this over here and let's put this one here too. Let's put it here. Let's organize things a bit here.

[00:42:19]Is that okay?

[00:42:22]So let's go. Look at this, everyone.

[00:42:26]Hey, what's going on, guys? When I do the check, I need to determine what the shear limits are when I have a very short cantilever.

[00:42:41]Look, I'll even grab the TQS article here; it will help us with this, okay? So, look what TQS is going to tell us. I'll put it here.

[00:42:55]Let me copy everything here.

[00:43:01]Because even though it's not a very short-term solution, we're going to have to adopt some kind of calculation model for these tie rods, right folks? So, the model that most closely resembles it is that of a very short dildo, right? So that's what we're going to adopt for our case here. Come on, we can do other checks like beam checks. We can do other checks, of course, absolutely. But initially, we'll understand, because we saw that although—and look, how these loads tend to travel almost vertically, directly from the column to the pile—using a very short cantilever is actually favorable from the point of view of reinforcement and stress. We're going to be in favor of security, okay? That's why we're going to adopt this model.

[00:44:03]Look, the first thing we need to understand, folks, is how these forces are going to act within the block, within the beam that I 'm designing.

[00:44:18]The tension here is compressive, so when I have the short console model, what will it tend to do? Remembering the consolation, I apply the load here, see, it tends to generate this rupture, right?

[00:44:37]So, that's precisely where the standard comes in, and it asks us to check here, the shear force, which would basically be 3.8, which is our vertical load, divided by the beam's shear strength (BD), okay? So, we're considering it as if there's tension on this plane here, look. Do you agree that we're even acting in favor of security, considering that, at the same time, in this case, I have a purely cutting-edge effort, right? In the case of the short console, I have a pure cutting effort. In this case, at the same time that I compress the force here by 3.8 tons and generate a certain shear force in this region, I also compress this region.

[00:45:29]So, this helps the particles stay aggregated because I have a cutting agent, yes. I agree that there's a stress at the rupture plane in the shear, but at the same time I have another component that compresses, so it causes the particles to be aggregated in our case. I'm talking about this, but we're going to calculate it as if it were pure shear, which would be a case like this one here, okay? And this is in favor of security. Is that clear to you? So, what would our calculated shear stress be? What would that be equivalent to? That would be equivalent to 3.8 tons of force.

[00:46:24]0.8 tons of force times 1.4 divided by our BD. What is the coefficient B of our beam? 60 cm, right?

[00:46:40]60 cm.

[00:46:42]And what is our D? We have to remember that for foundations, we consider that the pile here is going in 5 cm, and since there will possibly be soil, it's a difficult area to deal with in terms of concrete cover and reinforcement resistance. Therefore, we normally use 5 cm of concrete cover on the top of the pile cap as well.

[00:47:08]So it's going to be times 55, right?

[00:47:14]Our D is always the usable height of the block, which would be 60 minus the concrete cover.

[00:47:20]How much is this going to cost, guys?

[00:47:21]Considering a stress in kilograms per cm², I will have to multiply 3.08 x 1000 to convert to kilograms. Ton-force to kilograms.

[00:47:34]x 1.4 divided by 60 x 55. I will have a tension of 1 point 1.3 31 kg per square centimeter. This is our tension cm qu. This is our design stress, that is, the design stress requirement.

[00:48:09]And I have to check this limit voltage, this applied voltage, with three limit voltages in case of a short circuit, which would be here 3 + 0.9 R FD, okay?

[00:48:30]So, the tension at LWU, right? It will be 3 + r. But look, folks, if we disregard the aid component here, right, from our armor, because the R is precisely that, right, it's how much armor we put into the session. So, we'll have at least three. Three what?

[00:49:05]This is MPA, okay everyone? 3 MPa.

[00:49:10]What is 3 MPa? That would be 30 kg per centimeter of body weight, right? So, 30 kg per cm² would be AW 1, let's say, because we're going to take the smallest of the three, okay?

[00:49:32]When I have to check the AW2, which would basically be our second verification here. Let's put it this way: 2 will be equal to what? It's going to be 027.

[00:49:51]This is precisely where the connecting rod breaks, right? Regarding the compression connecting rod, whether you like it or not, folks, these formulas come from the connecting rod and tie rod method. It 's not an exact application, okay? But these are limits that the standard helps us to establish, which are in favor of safety, right? So, it's difficult for me to tell you here that this is the most accurate model, right? It 's not the most accurate model we can find, but it's the most suitable way I've found so far to calculate this model, this discontinuity, okay? Well, it would be interesting to see if other engineers have different perspectives.

[00:50:47]It's very important to put this down here so we can evaluate it together and maybe do a future live session with an even more refined method, but within my knowledge, this is the most appropriate way.

[00:50:59]So, for example, let's imagine a concrete with a strength of 25 MPa, right? I'll have 0.27 x 1, but FCK always enters here divided by 250 times, ah, 25 here, okay? 25/1.4, right? 25/1.4 So how much will this be? 027 1 - 25/ 250 decreases. 25/ 1.4 divide. This all multiplied together gives 1 point, sorry, 4 points, 34 MPa, which will be equal to 43.4 kg.

[00:51:54]por cm qu, is that right?

[00:51:59]And the tension of three is a limit that the standard sets, right, related to the fact that we should never imagine, for example, a high-strength concrete with a lot of reinforcement within the section. So she sets this limit of a maximum of 8 MPa for the concrete's resistance, which is 80 kg per cm².

[00:52:30]So, within these three values ​​here, we always select the smallest one, which in this case would be 30 kg per cm², and compare it with our applied shear stress, which is 1.31.

[00:52:46]Guys, we're way below where we were in this session. Logically, folks, we have 3.88 tons of load force acting on this section, and we have a 60 by 60 section, okay? So, to actually have a crushing of that connecting rod is very difficult, right, folks? And remembering that this first item here, look, is what matters most to us, really, because if we're going to remember what it means, let me even grab a little help here to help us remember the concepts.

[00:53:36]Yeah, okay. It's a little further down here, even to help us with our reasoning, right?

[00:53:48]This first item would be the RD1, right? The number three, this number three here, MPA, what does it represent? It represents the basic resistance and interlocking of aggregates, but also the cohesion at the interface, even without reinforcement.

[00:54:10]So, you see, this is the most important item in all of these calculations.

[00:54:16]What does he put here for us? that the concrete resists 3 MPa, at least the retention of the aggregate interlocking and the cohesion of the aggregates here in this region. And what is 3 MPa? It is 30 kg per cm². What is our requested voltage? It's 1.31.

[00:54:42]Alright, guys? Is that part clear?

[00:54:46]Because you see that all the other values ​​are above, right? 80 is the limit, okay everyone? This is the limit of what we can consider. And the 4, the 43.4, is precisely the crushing of the compression connecting rod. But our connecting rod is going to be quite large here, right, folks? She's going to be, she's going to be really, really robust here, okay?

[00:55:08]So this item doesn't apply in a clear way, imagine if it does apply, right, folks? The thing is, it's difficult because it's a model that wasn't designed for what we're calculating here, but in a way, as I said before, it's the best way to calculate it that I've found so far, okay?

[00:55:31]It's complicated, but that's how it is. No, there's not much to do. So, let's move on to the next one, folks. The tie rod's armor is right here.

[00:55:46]Let's calculate the tie rod reinforcement now, everyone.

[00:55:53]What happened here? Ta- da! Ta-da! Ta-da! Ta-da! Ta-da!

[00:56:00]Why isn't it working?

[00:56:05]Opacity.

[00:56:07]Ah, now that's better.

[00:56:10]I adjusted the opacity here, right? But if I want to change the size. Ah, here's the size. Beautiful. I didn't understand this. Okay. So, tie rod armor. What's going on here, folks?

[00:56:25]Notice that we have a moment of 6.64 and a horizontal force of 5.34 tons at the top of the block. If we're going to check this section of the block, folks, what's going to happen here? I'll actually have a bending moment acting as if it were a couple, right? A combination of forces, where I will have tension at the bottom and compression at the top. So, look what's going to happen here.

[00:57:03]When he asks us to calculate the tie rod, he'll first ask us to check a component, to add a component of this tie rod that will be related to 0.8 8 x VD, that is, it's related to the vertical load of 3.8 that's up here. So, this first installment here is related to the 3.8, okay? And then he will add HD, which is the horizontal calculation effort divided by FD.

[00:57:43]So, just so you know, our 3.8 will actually generate a tie rod at the top of the block, right? But the moment, the bending moment, and the horizontal force will generate tie rods at the bottom of the block, right? It tends to compress the top part and pull the bottom part, okay?

[00:58:11]Well, it could be the resultant of the bending moments, right? Well, we could calculate the resultant of the moments and determine the tie rod only for the bottom part, which will certainly be greater than the one for the top part.

[00:58:25]But what would I consider most appropriate, personally?

[00:58:29]Consider it as if the moment, both the bending moment and the horizontal force, acted as a tie rod here at the top of the block. And then we duplicate that reinforcement for the lower part of the block as well, you understand? I think it would be something more, since we don't have an extremely precise calculation model, it would be more in the interest of safety if we did this calculation in this way. So, instead of doing what would be ideal, we can do what would be most appropriate in practice, which would be to make all these efforts in a way that is unfavorable to the structure, and then we can calculate what would actually be adequate, okay? So, for example, let's first calculate this installment here. The ASV due to shear stress will be equal to 0.8 times the VD. We have VD here, right?

[00:59:40]3.08 x 1.4 divided by FD, which is 5000 divided by 1.15. It's our fy multiplied by mi, where monolithically poured concrete is 1.4, eh for concrete poured over rough concrete is 1, and 0.6 for concrete poured over smooth concrete. So in our case it would be 1.4, right?

[01:00:24]Remember that here we still have to multiply by 1000 to convert to kilograms, right? Okay?

[01:00:31]So, 0.8 x 3000 is 80 times 1000 in kilograms, right? divided by 5000 divided by 1.15 x 1.4 divides.

[01:00:55]Let's try again.

[01:00:59]Uh, 0.8 x 3000 3.08 x 1000 x 1.4 5000/ 1.15 x 1.4 0.5 5 cm qu 5 6 here 57, right? 0.57. We're just going to repeat the calculation here to be sure. 3.08 x 1000 x 1.4 5000 divided by 1.15 x 1.4 divided by 0.57 57 cm². That would be our share.

[01:02:00]This would be our share due to this vertical effort that's being put in place here, okay?

[01:02:11]What's going on, guys? If we look here, at the second installment of the tyrant, it will take the HD over fy, right? But if we imagine this first tie rod, where would we place it? We would put it on top of the block, right? But our horizontal effort tends to compress that part. Then he would reduce that load on the tie rod. But as I said, we're going to start by verifying and calculating as if all actions were unfavorable. So, 5.34 x 1.4 divided by FD.

[01:02:55]The FYD will be 5000 on 1.15.

[01:03:04]How much will this cost? 5.34 x 1.4 5000 di by 1.15 5.34 x 1000 x 1.4 5000/ 1.15 15. This will give 1 point 1 point 72 cm².

[01:03:37]So, we'll call the first ASV, right? We'll call the second one ASH.

[01:03:45]ASH, right?

[01:03:50]And the third one will be AS due to the bending moment.

[01:03:55]Therefore, AS is due to the bending moment.

[01:03:59]Our bending moment is 6.64 tons of force times m. 6.64 ton force times m. If I divide this here, to generate a binary, and imagine that I'm going to compress the Z here below, let's consider that our Z is normally 0.9 times the height of our block, so around 54, divided by 0.54 here, right? This will do.

[01:04:41]We are, we are live right now. It seems like the live stream went down. That's legal.

[01:04:47]So, 6.64 / 0.54. What does this add up to?

[01:04:54]To generate our binary force, it will generate 12.29 tons of force, okay? 12.29 tons of tractive force, right? In this case, it would be tension from below; we'll consider the bending moment to be reversed. So, traction on top, right? And the compression at the bottom, uh, 12.29, okay? So, I have to multiply this by 1000 to convert it to kilograms, right? And I have to multiply by 1.4 to convert to calculation effort, right? And I'm going to divide that by 5000 divided by 1.15.

[01:05:53]So, how much would this cost?

[01:05:56]12.29 x 1000 x 1.4 5000 divided by 1.15 gives 3 points, which is 90 cm.

[01:06:17]We'll do it again to see if it's correct. 664/ z which is 0.6 6 times 0.8 0.9. Let's consider 0.9 0.6 x 0.9 54 divide 12 ton force x 1000 x 1.4 5000 di by 1.15 divide 3.96.

[01:06:48]So, what would be the 'as' of our tie rod, considering all loads with the unfavorable effect?

[01:06:57]So, it would be 3.96, 1.72, 0.57. We would have 6.25 cm².

[01:07:11]What is this equivalent to, folks?

[01:07:14]This is equivalent to how many of these armor pieces, right? If I take a 12.5 bar here, it gives 1.23, right? 6.25 divisions per half bar are 5/6, right? 5/ras of 12.5. So nothing too complicated for a 60 by 60 beam. I'd even have to check if this isn't the minimum, what would be the minimum for a 60 by 60 beam, okay?

[01:07:47]So, we would duplicate this armor, right? This applies to both positive and negative armor.

[01:07:58]Let's calculate now what it would be if we were to consider that the bending moments, right, both the bending moment and the horizontal force, act in a way that attracts the bottom part. Let's think about it that way.

[01:08:20]So, our armor due to the vertical load would remain the same at 0.57, right?

[01:08:28]However, our effort due to the horizontal load would be transformed into a moment that would be multiplied by the lever arm here, which would be the height of the block minus the cover.

[01:08:43]So, for example, here it would be 5.34 times 0.55.

[01:08:53]This would give a bending moment of 2.94 + 6.64. So the bending moment is compressing this region here, see?

[01:09:05]So, what kind of bending moment is that, right, everyone? So here I have a load of 5.34 tons of force, a bending moment of 6.64 tons of force times meters, okay?

[01:09:25]I have to convert 5.34 to binary, right? A rotational tendency, because it will act in relation to the bottom part of the block here, see. Okay, everyone?

[01:09:37]So, what is this bending moment, right, at 5:34 here?

[01:09:48]So it's going to be 5.34 because it's going to be added, right, everyone? He will add this here in relation to 6.64. 5,345 will give an increase of 2.93 tons-force times m. So the final bending moment will be 6.64 + 2.93 tons of force times meters, which in the end will give what? 6.64 will give 9.58 tons-force times meter. This is our final moment performing here.

[01:10:32]Let's divide by Z again. This here. So Z is 0.90% of the beam's height, right? So, 0.54 here, okay? Divided by 0.54.

[01:10:47]I'm going to have a compression here of 17 tons, 18 tons of force, practically, right? And a traction force here of 17.93 tons, okay?

[01:11:04]So what will our AS be? It's going to be 17 and 93 tons of force times 1.4 divided by 5000 divided by 1.15, okay? How much will that cost? 17.93 x 1.4 1793 x 1.4 x 1000 divided by 5000 divided by 1.15. So it's going to be 5.7 cm, right? So this would be the AS that we would place at the bottom of our block due to the bending moment and the horizontal force acting here. Alright, guys?

[01:12:08]Look how interesting.

[01:12:10]So, notice this, folks, that the difference between 6.25 and 5.77 is n't that significant, right? If we add these two together, it will give the same result. 5 3.96 plus 72. Yes, if we just add these two here, it gives 5 and 68. So, practically the same as 5.7, right?

[01:12:39]But in practice, folks, what would be appropriate here in my view, right?

[01:12:43]We'll add all of this up and put 6.25 cm², both on the positive and negative reinforcement of the block, okay? That's what I think would be the most interesting part, okay?

[01:13:00]And then he talks about the minimum armor here, right, folks? The minimum reinforcement that was going to be placed on the tie rod, right? So, for example, what could we calculate as the minimum reinforcement here? Ah, it could be the minimum reinforcement of a beam, for example, right? If we take this example and calculate the minimum reinforcement for this beam here, what will that be?

[01:13:38]Let me open this up for just a minute.

[01:13:52]So, if I take here, for a beam of 60 and 55 and a moment, let's take the largest moment we had, which was a moment of uh 9.58, right? 9.58 Oh, he would ask if I were to calculate it as a beam as well. That's interesting, isn't it, guys? We make all these comparisons, right? Because, look, this is the TQS software, right? For simple bending calculations, right? If we were to calculate it like a cantilever beam, right? Look what he's asking me, right? For a bending moment of 9.58, an S of 5.75, right? 97 9.58 to S of 5.75. So it means something very similar to what we calculated, right, everyone? Very, very similar. Even with the beam model, okay? So he calculated that tie rod as 5.75, right? So when I calculate it, I'll also add that rotational tendency due to that vertical force, then add another 5 cm², which brings it to 6.25, right?

[01:15:25]But let's reduce the bending moment here, just so we can see what the minimum AS would be. Yeah, the minimum AS is pretty close, right, guys? Here, I reduced the minimum bending moment a little bit, to five, the design bending moment.

[01:15:42]And the minimum area here, look, he calculated it for us as being 5.17 cm², right? So, basically, we're at the minimum armor for a 60x60 block, okay?

[01:15:59]We have minimum reinforcement in both positive and negative bending, okay? Uh, and then he's going to put on the minimum amount of armor here, right? He'll calculate it using that formula, but a minimum reinforcement can also be calculated as a beam; there wouldn't be a problem with that, because it's just a minimum reinforcement, really, right?

[01:16:24]Then he says that in relation to the constructive arrangements, right? Regarding the construction details, the diameter of the tie rod must be between 1.8 of the height and 1.8 of the width, okay? The tie rod must be less than 25 mm. Well, for the horizontal strap, for the vertical strap it has to be smaller than 16 mm. The tie rod spacing must be less than 15 times the diameter or the effective height, right, or D. Anchoring of the welded crossbar. Then he's going to talk about the welded bar frame. And then he'll also talk about how to calculate the shear reinforcement and the transverse reinforcement of this region here. Hey guys, how many minutes into the live stream have we been watching? At 1:17, okay? 1:17.

[01:17:24]It was a really intense, very conceptual live stream.

[01:17:28]It's really content that he demands, right? He demands it. It's difficult content, it's not easy content, it's not simple content, it's content that already has a great deal of depth. We couldn't even find a perfect model for this, but we've evolved, guys, right?

[01:17:55]So, what have we calculated today? We have the reinforcement for the top part of the block, the reinforcement for the bottom part of the block has been calculated, and next week we will calculate the shear reinforcement for this block and the transverse reinforcement for this block. Is it done, everyone? Look at that, it's actually quite interesting, isn't it, folks? It's difficult because when the content becomes difficult, we have less engagement, right? Engagement. That's interesting because it shows that people want things to be easy, right? That's an interesting question.

[01:18:41]Well, and then I even wonder, you know, if advancing this far is interesting, but I believe that for those who stay, for those who watch later, I believe it is interesting. I think it's content, for example, that I do n't know if it's on YouTube, this here. I've never seen anyone calculate this here.

[01:19:04]Never, there aren't even courses, I don't think anyone has ever gone into depth in this region here. It's always calculated as a beam, and that's it, right? Since this region isn't a region to be calculated as a beam, right? Okay? That's it, folks. What to do? It's part of the process. I appreciate the people who tuned in to the live stream, who were with us, right?

[01:19:30]Okay, let's move on to the next one.

[01:19:33]Thank you all, have a great day, and see you next time. Big hug, everyone. It cost,