Everyone, and thank you for waiting, and welcome to Mathcad for Civil Engineers. I'm your moderator, David J. Newman, and before we begin today's live presentation by PTC Technical Expert Angie Severino and Professor of Civil Engineering at the Royal Military College of Canada, Dr. Pat Heffernan, I have some rules and expectations to establish. Today's webinar will last 60 minutes. Angie shall discuss what PTC Mathcad Prime is and its use cases for civil and structural engineers, while the bulk of our time will be dedicated to Pat going into two detailed example problems solved using Mathcad, the type of problems that civil engineers may face in the field. The remaining time will be dedicated to a live question-and-answer session after those demos, featuring the questions that you submit into the Q&A box throughout the presentation, including now. The webcast is being recorded, and the full replay will be available on mathcad.com shortly following the event. All registrants will be emailed this replay link as well. We'll also make the first of Pat's demo worksheets available for download on that replay page. You can continue interacting with Pat following the webinar by subscribing to his YouTube channel located in the resource library. There, you can also find the official Mathcad YouTube channel, our 30-day trial of Mathcad Prime, our monthly Mathcad Minute e-newsletter, and a free library of civil and structural engineering Mathcad Prime example worksheets. After the webinar, we'll have a very short survey asking for your feedback. Your feedback continues to be important to us. If you enjoyed this webinar, then PTC will have more webinars in this style in the future. I am excited to give the floor to Angie Severino. Angie, the time is now to amaze us. Thank you, David. Hello, everyone. This is Angie Severino, and I'd like to thank all of you for joining us today. We're going to get started with a quick overview of what Mathcad is, what makes it unique, and why civil and structural engineers choose Mathcad over other applications for their design and analysis calculations. Effectively, Mathcad is engineering calculation software that is purpose-built for engineers. It has a document interface with a math engine that runs under the surface of the document. As calculations are written and entered into the document, it performs those calculations and at the same time captures design intent, meaning that it has a documentation component that enables engineers to very naturally capture or document decisions, assumptions, methods, thought process as they're doing their work. The math engine is a robust and powerful engine. In addition to sequential calculations, it has capabilities to analyze, solve, optimize, and all of the calculations are completed within an environment that's conducive to showing your work so that Mathcad documents or Mathcad worksheets can be shared with other stakeholders such as colleagues, clients, or technical partners to communicate the calculation work that's been done. In simple terms, we can think of Mathcad as an application that combines the ease and familiarity of a readable document with a powerful math engine. As I mentioned, Mathcad is purpose-built for engineers. It was designed right from the start specifically for engineers with the goal of providing engineers with an application where they can perform calculations in a natural way, reduce errors that creep into calculations and mathematical models, and show and document their work. What we see here is a picture of a Mathcad document. One of the things that differentiates Mathcad from other calculation software packages is that it captures all engineering math in natural math notation, all of it. All math expressions, equations, formulas are represented in the document using the same notation used in technical publications and textbooks. There is no confusion around what the formula or the equation is supposed to do. The application is very intuitive, and the document interface resembles a whiteboard. Anywhere within the worksheet, we can enter math, text, graphics, plots to create a comprehensive engineering document. Again, all of the math is live. As variables are changed or formulas are modified, the calculations, plots, tables all update accordingly. It's important to point out here as well that the math capabilities are quite powerful. First of all, Mathcad has two engines, two math engines. It has a numeric engine and a symbolic engine. I also want to point out here that Mathcad has a comprehensive, best-in-class units intelligence capability. Mathcad manages all engineering units throughout calculations. It effectively takes the burden off of managing and carrying units off the engineer. It understands what engineering units are, how they relate to one another, how units simplify, dimensional compatibility, and has built-in conversion factors for all units, even going between different unit systems. On top of that, there's a programming capability to incorporate programming logic into the calculation workflow, solving and optimization functions, support for vectors and matrices, and the ability to write your own custom functions. Okay. I mentioned earlier that Mathcad uses natural math notation for all the math. Mathcad is a very visual application. Both the math and the text can be fully formatted using rich text formatting options. You can really call out equations, highlight critical engineering formulas, equations or formulas that have been approved and validated. Those can be made to stand out in the document. Data can be visualized through 2D and 3D plots. We have full control. Ultimately, we have full control over what actually gets displayed and published in the final worksheets for distribution and engineering reports. Aside from working in the Mathcad worksheet itself, Mathcad integrates with other applications. It has seamless out-of-the-box integration with Microsoft Excel. Data can be imported from Excel or CSV or a flat text file directly into Mathcad. Data can be exported from Mathcad to Excel or another destination. We also have an API, the Application Programming Interface, that enables integration with other applications as well. Of course, Mathcad does integrate out of the box with PTC Creo and PTC Windchill. Aside from that, we integrate with Excel, with Word, and then through the API, other integrations can be put together. Finally, because of the transparent nature, Mathcad worksheets are perfect for standardizing on approved workflows, methodologies, and calculation best practices. Okay. Very quickly, at the individual engineering level, engineers can perform calculations with transparency and precision. All of the calculations in Mathcad are completed with 64 bits of floating point precision. They are precise. Engineers can document and share their work with others, create worksheets that can be reused to save time, reduce the errors that unintentionally could creep into calculations and into the calculation process. At the teams or organizational level, teams benefit from retaining knowledge, retaining intellectual property, standardizing on best practices and approved methods, standardizing on workflows, on formulas, on equations that have been validated, that have been approved, and reusing calculation templates, again, that have been validated and approved. All of this enables engineering teams to ultimately produce higher quality work, free of errors, free of calculation mistakes in shorter periods of time. Let's talk just for a moment about spreadsheets. Historically, engineers have gravitated towards using spreadsheets for engineering. There are a few reasons for this. First of all, spreadsheets are readily available. They're on everybody's desktop. They're on every engineer's computer. They have a very low cost of ownership at initial perception, right? There's a perceived low cost of ownership for using spreadsheets for engineering. They're not purpose-built for engineering calculations or engineering design work. Spreadsheets were initially created for business purposes, where Mathcad was initially created and designed for engineers. That's a fundamental differentiator in terms of the concept. One was created for one purpose and one set of users, and the other was created for a different purpose and for a different set of users. When we use spreadsheets for engineering calculations, we enter a slippery slope. Spreadsheets are error-prone. It's easy for mistakes to creep into the calculations. There's no visibility into the actual formulas. There is no transparency. We actually have to click into a cell to see the formula that is populating the result in that cell. They're difficult to validate, and they're risky to reuse. Here we can see the formula that's highlighted in yellow for the Reynolds number. In the spreadsheet on the left, the result is 19.172. And on the right, or 19.172, and on the right, we can see the equivalent Mathcad worksheet. Okay. This is the same problem. On the left is the problem represented in Excel. On the right is the problem represented in Mathcad. It's the exact same problem. On the right-hand side, we have visibility into the calculation for the Reynolds number. We can look at that. We can see how it was generated, how it was calculated, what the drivers are, what the variables are. We can see everything. The same applies for the friction factor. Okay. This is a good visual that shows the difference in what a problem looks like in Excel or in a spreadsheet and what that same problem looks like in Mathcad. Okay. Just to put a finer point on it, on the left here, we have two formulas. On the right, we have the same two formulas written in spreadsheet format in this case. We can easily see the difference, right? On the left, we have natural math notation. We have transparency. We can validate it. Any engineer can look at the left-hand side of this slide and understand what those equations are doing, what those formulas are doing, how they're being calculated. On the right-hand side, to validate those expressions that are constructed with parentheses and special characters and carets and forward slashes and reverse slashes, to validate that is going to require a lot of reverse engineering. It's going to take time. It's going to require dissecting the spreadsheet in order to really understand what's going on. That's risky to reuse because it's difficult to understand if it's being done correctly or not. Okay. Finally, I'd like to wrap up here by just going over some of the areas where Mathcad is used in the AEC industry. AEC is really a primary industry for Mathcad usage. We have a lot of customers in this industry. We have customers that are using Mathcad for design and analysis of building structures, facilities. Concrete is very common. Pavement, easements. We have customers using Mathcad to design bridges, highways, roads, retaining walls, columns, pillars, footings, water drainage, and waste disposal systems and pipelines. Those are just some of the areas where we see heavy use of Mathcad in the AEC space. The types of calculations that we see that are fairly common amongst these customers include beam analysis. That's incredibly common. We have a lot of customers using Mathcad for beam analysis. Calculating and modeling things like torsion, deflection of a beam, shear, slope, moments, all of those things that go along with analyzing the behavior of a beam. Effective length factors, stiffness ratios, reduction factors, those are quite common. Rigidity, modeling the rigidity and strength and stability of different structures and different members. Member response to wind loads, seismic loads, uniform loads. The response that we see based on different loading conditions and loading types, maximum allowable stresses, very, very common. We see that all the time. Section analysis, okay? Analyzing different sections of a bridge or a highway or a road or a beam even. Also material trade-off analysis. That's another common use case where we see Mathcad applied in the AEC space. These are just some examples. These are just some typical calculations. There are many, many more. I did want to just take a minute to just point out some of the common calculations and common use cases that we see our customers using Mathcad for in the AEC space. Okay. I'd like to leave you with a quick overview of some of our global customers in the AEC space that use Mathcad. These are some of our customers that have implemented Mathcad in their calculation process at some level and that use Mathcad for engineering calculations around some of the areas that we discussed. At this time, I'd like to hand the presentation over to Dr. Pat Heffernan, who's going to walk us through some examples of how he uses Mathcad in his own work. Dr. Heffernan, over to you. Thanks, Angie. Yeah, we're going to get right into it. I have two worksheets that I'm going to present today. The first one I thought was really important was to start off with the design worksheet because it is so core to what we do as civil engineers. I'll start there, and then I'll go on and look at a bit of a section analysis with the second worksheet. Right off the bat, you're seeing my worksheet, my design worksheet. This looks at doubly reinforced rectangular concrete beam, and it figures out what the moment resistance is for that concrete beam. Hopefully what you're seeing is something that would look very similar to what you would do if you were doing this by hand. That is the intent because it communicates not just the calculations themselves, but also the theory, the background, the logic that goes through the resolution of the problem. I did want to start out with just kind of some fundamentals about what Mathcad is because I'm sure we have people in the audience that have perhaps never used it before. If you see my cursor, I'm hanging around the geometric properties here to the right of the image. I brought the image in from PowerPoint and saved it as a PNG because I like the transparent background. Very flexible choice of presentation. I have my two variables defined. I have the width and the height defined as B and H. You notice that there's a colon equal sign. That defines B as 250 mm. It defines H as 500 mm. I can now use those because they've been defined. I go just below it. If I wanted to know the area, I can define the area as B times H. In this case, I'm going to use a different equal sign. I'm going to use the calculate equal sign, and it comes up, and it's able to calculate that because B and H have been defined. I know there was a question about units, so it's choosing the base unit, meters squared. If I wanted that as millimeters squared, I could choose millimeters squared, and it will recalculate it. Because it separates calculation units from display units, if I wanted to go back in here and change that to square inches, I can do that, and it's going to do the conversion for you. That is not what this is about, but in understanding that, you're able to look at the sheet and kind of understand the logic and the layout that's doing it. Now, it does work on a sort of top to bottom, left to right topology. For example, if I was to take, let's say, our B variable here, if it showed up below the formula that uses it, it does not recognize B anymore because it's below it. It has to be top to bottom, left to right formatting. Let's get rid of that, and let's get into this a little bit. I'm a structural engineer. This is about civil engineering, so it's bigger than just structural engineers. I hope you can look at this sheet, and you can see that the nature of the calculations are really the same regardless of which subdiscipline of civil engineering you're working in. I've laid out my sheet. I think the communication aspects that Angie was highlighting really come across between the images, the text, the labeling, and then the way the math components are actually laid out, and we see material properties and everything else. I tried to lay out my worksheets to do the best of that. The first thing I do is I use the collapsible areas quite a bit. You'll definitely see it in the second sheet, and that is shown here by this line. That's a collapsible area that has a whole lot of calculations going on inside of it. What I've done is I've hid what are some things that you don't have to see all the time, but you can open it up and see it when you need to. I've put the summary information just below it so that if that's all you're interested in, you can leave it collapsed and focus on the part of the worksheet that interests you the most. I'm just going to pop it open here by pressing the plus sign, scroll up so you can see where we came from. Now you see this collapsible area opened up in front of us. In this collapsible area, we're going to select the reinforcing bars for the beam and compute the effective depth. As you will see in all of my sheets, I always put my references to the right. You see the code reference here. Now, I'm using the Canadian code, so CSA 23.3. If you're using ACI code or Eurocode, it really doesn't matter. One, they're fairly similar. Two, you would just build your worksheet to reflect whatever code is in force in the area of jurisdiction that you're doing your work for. A couple of features that I wanted to point out. The first one is a dropdown combo box. Where I'm using it here, I have a variable. EXP is a variable for the exposure. On the dropdown box, I'm assigning it to one of three conditions, which the code allows for and changes the amount of cover that we need depending on whether it's exposed or not exposed. Having done that, the next feature is this logic box, right? We have a logic box which is using some very, very simple programming to assign to the variable cover the amount of cover required depending on what the string is that is assigned to the variable EXP. I finish that off. I go down right to the bottom here. The other thing we have to account for is that it's not just the cover based on the exposure, but it also has to be the greater of that value or one and a half times the maximum dimension of our aggregates. We are able to take into account those types of multiple code requirements by using either a logic box itself or these inline functions where I can say maximum of cover or one and a half times the area max. That returns the value based on this logic, and we get a cover value. It works out really quite nice to be able to compactly build the fundamental requirements of the code in one spot. I'm going to keep scrolling down. I use another combo box, and I use it multiple times. Here, I'm using a combo box to assign the reinforcing bars. This list basically gives us all of the metric standard reinforcing bars that we use. If you're working in imperial units, then you would just build yourself a different combo box. I want to go into the edit mode just to show you what's behind the scenes. If I go into edit, this is the data table that I put in to be incorporated into this combo box. We select the bar. That's what's in the first row. What shows up is, or what it does, it assigns to the array of the variable that is tagged to it two elements. The first element will be the number from the first row or first column, pardon me. It's going to be the area in millimeters squared. Now, I'll go back in a second because I created a custom units here, and I want to point that out just because the combo box doesn't really like exponents in its columns. This is 500 mm squared, so it's picking that up if you would choose a 25M. In the second element of the array, it's picking up the diameter, which is 25.2 mm. If I pop back out, you can see if I change this, it's going to come up with different numbers. What I'm doing in the subsequent equations is assigning the first element of the array back to the area of the bar used in the compression steel or the diameter of the bar used in the diameter steel for the second element of the array. It makes it a really nice, easy way to select from a data table. I had alluded, and I meant to mention it earlier. I'm going to scroll back up to the top. Up to the top here, great control. The first one is the origin. Any array or matrix, of course, you have the elements of the array or matrix, and they have an index. Now, by default, Mathcad chooses an index of zero, and you can find that up in the calculation tab if you like. I prefer to work with the first element having an index of one. I reset the origin of my arrays to have that. I like to put it here directly on the sheets itself so anybody looking at it can see that I have reset the origin to one. The second one was, I assigned a custom unit, MMS, to be the same as millimeters squared, and that allowed me to draw that out from the combo box. That kind of was what that was about. This is all now going through the calculations. Of course, I'm not going through the math itself. I'm showing features of Mathcad that allow us to do our calculations as we go through. We get a lot of use out of this combo box because the same one is being used multiple times to set the bar for the compression steel, the tension steel, as well as the stirrups for the shear reinforcement. The only thing that's changing is the variable to which it's being assigned. Bar prime in one case, bar in the second case, and stirrup in the third case. I finish off this set of calculations really, again, by using one of these inline equations that chooses the maximum of 1.4 times the bar diameter or 1.4 times the maximum aggregate size or 30 mm, whichever is greater, and we get a different number. That's some of the features which I think are really great. I'm going to collapse that down, and we can carry on looking at our calculations. In 1B, we're checking the minimum tension steel, right, which is a code requirement. We have AS min being calculated here. What I wanted to point out here, obviously, you can see the equation like Angie was pointing out earlier, but in this case, it's an empirical formula. Units start to break down, and they don't work as nicely as you would normally like them to work when it comes to empirical formula. We have one pressure unit, so megapascals being the square root, and it's being divided by another megapascal below it. We're going to end up with a unit inconsistency here. What I'm doing and what you have to do in those cases is basically strip the units out on the way in and make sure that the units coming back to you at the end of the formula are what you would expect. That's what's going on here. This isn't about teaching you how to do it. We have other videos on my YouTube channel and elsewhere that would teach you how to do that in different circumstances. I wanted to point out that you do have to manage those units, particularly with empirical formula that we get in the codes. You'll see this in a lot of my sheets. I use flags all the time. Wherever there's a code requirement or an assumption that is made, I try to go and create a flag that checks to see if the code requirement has been met adequately. In this case, it's checking for the minimum steel, and it's coming back after the check and saying, "Yes, you've got the minimum steel requirement has been met." I do that just by setting up these flags using a very simple Boolean if statement behind it. We'll keep going down. Again, love the logic. I think Angie talked a lot about the combination of text boxes, images, and math components to build up a worksheet that communicates the calculations that are going on. Hopefully, that's coming across. I put a fair bit of effort into combining images and text to go with the calculations so that the logic flow of the calculation is completely obvious. Hopefully, when you hand it off to your checker for validation, they'll be able to find any errors that you might have let creep into it. We go down again. We're seeing all of these very simple Boolean conditions that allow us to fully put in the calculation, in this case for Alpha 1, not just the calculation of it, but the limit to it, which is stipulated in the code. We just carry on. We're getting to the end of this sheet. Again, looking at equations like we have for A, I think everybody that does reinforced concrete design would immediately recognize that formula so that the communication is not hidden. It's upfront, and you can very quickly find any errors or mistakes when you're trying to validate your worksheet and the calculation comes out of it. We go down. We have a couple more flags. Our compression steel does yield, which was an assumption up here. Following the flags, going down, checking them, and ultimately ending up with the calculation of our moment resistance for the doubly reinforced concrete beam coming out of it. Now, obviously, we can scroll back up to the top if we wanted, say, a different value. Oh, not getting rid of, sorry, 275. When I click out of it, you'll see the calculations start to scroll through it, and I can go down. I can check my flags and check the amount. Without getting into too much automation, I can use this to optimize my design as I like. I'm going to stop there on this one and pop over to the next sheet. It's going to allow me to show just a couple different features of Mathcad and how they might be usable to you. On this sheet, I put it together. It's basically going to look at the plastic analysis of a T-b eam, so looking at the section properties. Now, most of us will draw that in for standard sections. Most of us will draw that information from tables in the steel design manual or somewhere else. If you're using a non-standard section, you're going to have to do these calculations yourself. That's what this sheet does. It basically assumes that you're using a non-standard section. You put in the geometry in terms of the flange and the web heights and widths, the material properties. We're going to go through now, and we're going to calculate the moment of inertia of the section and the centroid. You need those to go on to the rest. We're going to calculate the elastic moment capacity and curvature of the section. Then we're going to do the same thing for the plastic moment capacity. Again, you see how I'm using the collapsible sections and the summary outputs to be able to decide where I want to go look at my worksheet without getting overwhelmed. I build right into it. You see 3A and 3B down here. When we're looking at the plastic moment capacity and curvature, typical of a lot of the stuff we do, you have to start with an assumption. I'm going to assume that the plastic neutral axis occurs in the web. I'm going to go through those calculations, and then I'm going to verify whether that assumption is true or not. Then I put that into a flag. The flag is telling me, "Yes, indeed, the neutral axis does occur in the web in this instance." That assumption was correct, and 3A is going to control the calculations, whereas 3B is what we would do if that assumption was incorrect. We assume that the plastic neutral axis now occurs in the flange, but we see that that assumption is false. For all intents and purposes, I can ignore 3B in this case, and I don't even have to open it up. Let's see what we have under some of these. Let me open the first one. Here, we're going to calculate the centroid of the cross-section as well as the moment of inertia for the section. We're going to do that using the normal mechanics that we would have learned in school. We're going to break it up into two standard sections, the web and the flange. We're going to break that out. We're going to use parallel axis theorem to calculate what the I is. Now, this whole section, to show the flexibility of it a little bit, it came from a different worksheet that I already had done up because calculating this information for a T beam or an I- beam is pretty common. I was able to just copy and paste that and put it in here and then make sure that my variables match up. In this case, I'm using arrays to do it. Everything to do with the first section, the flange, is going to be the first elements of the arrays, and everything dealing with the web are going to be the second elements of the arrays. Now, you don't have to do this. You can just do the math directly, but it sometimes gets lost and gets a little bit harder to appreciate when you're checking it. The benefit of the array, when we go down to the calculation of Y bar here, we're able to see a formula using the summation, which is pretty much exactly what you would draw from your textbook or your notes for the calculation of Y bar from a reference plane. I went to the effort of building it up in arrays so that I can have this clarity of communication in the calculation, not just of Y bar. We see the individual components for I, but when it comes time to apply the parallel axis theorem down here for the calculation of I, again, you're looking at a formula which looks identical to what you would see in a textbook. I'm just going to switch over to draft mode here because our pagination is blocking our visibility of that formula. Now you're not seeing the pages laid out. You're just seeing a whole flat sheet. We can see that formula laid out a little bit better for the parallel axis theorem and go on to calculate the section modulus and other things. Let me close that. We're going to do the elastic moment capacity. I'm very quickly going to pop through these because it's not about the—it's about how it displays the logic. It's not about the logic itself. Of course, this uses a strain compatibility model, and then we look at the conditions. When we hit yield of our material at the bottom here, then we do a force equilibrium from the stress diagram, and that allows us to calculate the section modulus. That's what you're seeing here. Again, I go through a degree of effort to try to make sure that the logic is displayed both in images and in comments as well as the formula that go with it. Again, we're using a series of arrays to go through and to calculate the forces for the different components. This is where the force equilibrium is being established. We're checking for equilibrium. I have a flag that is going to tell me whether equilibrium has been met. We carry on to calculate the elastic moment capacity as well as the curvature of the beam. Having been satisfied that that is true, sorry, I'm going to go back to page mode. It's easier to deal with the sections. Close that. We're ready to go on and look at the plastic moment capacity. We know 3A is governing. I can open that up. You see the conditions shown in the diagram for the fully plastic. Our plastic hinge has just established itself in our strain and stress diagrams. We're going to go through this similar calculation using similar logic and determine what the plastic section modulus is here and the plastic moment and the plastic curvature. That goes down here. The logic is the same. It's just using the same components. I don't have to spend a lot of time on that. What I wanted to do is to show a couple other features. I started to create a section, which is to calculate the moment capacity and curvature at the moment when the entire flange becomes plastic. It's an elastic plastic condition. I haven't completed that yet. I didn't want anybody to be using it until I was completing it. Mathcad does allow you to protect the area. I've locked that area. It won't open unless I unprotect it. That hopefully is going to stop somebody from going in and using it when they shouldn't. It also allows you opportunities to protect your intellectual property or your calculations, stop people from breaking a validated worksheet by messing with things inside it. There are similar features that you would use in Excel if you were locking down different sections. What I wanted to do is to go down and look at section five. I created this condition so that I could show you some of the oh, don't want to do that. Undo, Control Z. It allows me to show you some of the numerical capabilities that Mathcad has. What we're going to do is we're going to assume a strain just when plasticity has started in the top of the flange. We're going to establish that and set it. We're going to go on to calculate what the elastic plastic moment capacity is at that moment, what the curvature is at that moment, and plot the stress diagram over the full height of the beam. Let me open that up. It looks really complicated. It really is just little bits carrying on. Certainly, it just builds on what we have done up until now, looking at the elastic section and the fully plastic section. I guess one of the things I point out, I use these clear statements so that I can reset a bunch of variables so I don't get a bunch of warnings that I'm redefining variables. I use that where appropriate. That's what the clear flag is there. We've established what the strain is at the top of the beam. We're going to get some shape, something like this for our stress distribution. It's plastic at the top, plastic at the bottom, elastic in the middle. Based on the assumption that the transition is going to happen somewhere in the flange, we're going to carry on. We're going to set up our diagram, our logic that we're going to then apply our force equilibrium to. Where does it get different from what we've done before? It gets different in the fact that we don't know, and nor do we have a quick analytical calculation for the height of the neutral axis. What I need to do is I need to do all of the same calculations that I've done before, only we're going to set them up as equations or as functions of Y bar, which is the height of the neutral axis. All of these heights that we have in here are now being set up as a function of Y bar. We can't get a numerical solution for them, but we are setting up their definitions. If we knew what Y bar was, we would be able to resolve each and every one of them. We go on, we do the same thing down here for each of our forces. We see the compression forces listed to the left. They're all taken from the diagram to the right and the various distances down here. Easy to see, easy to understand, but we're not getting a numerical output because they're functions of Y bar, which remains unknown at this stage. Same thing for our tensile forces here, T4 and T5. This is where the magic happens. What we've done is we've incorporated the solve block. I know in Angie's presentation, she showed you a solve block in the PowerPoint. Here we see it working. For it to work, basically, we have to give it a guess value, an initial guess value for Y bar. We don't know what it is. I'm going to give it 20 mm. I am going to set up the constraints that the solve block needs to satisfy. In this case, that is force equilibrium where all of the compressive forces have to be equal to the tensile forces. We're using another different equal sign here. We're using the comparison equal sign. This sets up the condition that the solve block needs to satisfy. We then go down and we say, "Okay, now what we want you to do is to find a value for Y bar such that this constraint is met." It is able to iterate numerically to find the value of 104.5 and change millimeters, which sets the height of the neutral axis. With the construct that I've chosen here, that is then assigning it to the variable Y bar. With the variable Y bar established, all of the formula that we had before are able to be accessed. Only in this case, it's C1 with Y bar known. It's able to give us the numerical calculation and value back with it. Same thing with all of the dimensions, all the heights of those various stress block components. Again, I'm using a flag to make sure that my assumption at the start was actually realized. The last thing I did, and this was more out of introspect, I'm just going to roll down. This is the calculation of the elastic plastic moment capacity and curvature. What I wanted to do was to plot the height or the stress distribution over the height of the beam for this condition. I needed to set up a couple of functions for the strain distribution as a function of its location in the beam, distance from the neutral axis, and the same thing for our stress. We've done that here. It's a multi-domain function in the case of the stress distribution. I'm just using a logic block to show that because if it's above or below the yield stress, then it's going to change its relationship. That's what this does. It allows us to have a multi-domain function as a function of its position Y. Then I can set up my range variable for what I want Y to vary from. It is able to plot what that stress is. Stress in Y is a function of Y. For visibility, I added to that these horizontal lines, which show the top of the beam, the transition between the flange and the web, and the bottom of the beam down here. That is what is going on up in this section. I can collapse my section, and you see the summary calculation. You only have to look at this if it requires your attention at a given moment. We can see the elastic plastic moment and the elastic plastic curvature for the conditions that we set up. That really is a very quick snippet of a handful of features. Remember, it's not about this particular presentation. It's not about the theory that is behind it, but it's about how do we use the components of Mathcad, the capabilities of Mathcad to build the calculations that we need to do either design or some other analysis or calculation. I think with that, I'm going to hand this back to David, who's going to lead us through some Q&A. Hopefully, I didn't go too fast for it. All right. Thank you, Pat, for those Mathcad demonstrations. Thank you, Angie, for your presentation as well. Our remaining 13 minutes or so will be answering your questions. Both Pat and Angie are available. I think the number one thing that people were asking the most was about the integration of Mathcad in its document worksheet of the math, text, images. A lot of people were asking about images. They were asking, are the diagrams you were showing drawn in Mathcad? And if they're not drawn in Mathcad, how did you make them? How did you get them into Mathcad? Sure. I'm happy to answer that. These are not drawn in Mathcad. Typically, because they're fairly simple schematics, I normally choose just to draw them in PowerPoint, quite frankly, because I'm a teacher, I probably already have the diagrams available to me in PowerPoint. Now, Mathcad is capable of having an integrated object within it. You could just double-click on it, and it would go to the object in PowerPoint or something. I tend to not use that methodology because I really value the transparent background. That is not supported with the object. What I do is highlight it in PowerPoint, and I save it as a PNG file, which saves the transparent background. I import it here. Importing an image is as simple as going up to the top left and pressing the image box. You saw here, my cursor was down here. It dropped the browse for image. If I press on that, I browse to the image on my computer, and it will pop it in. That is how that is done. To be fair, I do have a YouTube video dealing specifically with the images and how to bring them in the way I lay them out. Hopefully, that answers the question. Yes. Thank you very much for that. You even answered the follow-up about the transparent figure. This question is for Angie. Please get off mute. Can we apply a conditional formatting for the flag check? Yes. Hi, David. Thank you for the question. The answer to that is that in the next version, which will be Mathcad Prime 10, we will be able to apply conditional formatting for the flag check that Dr. Heffernan walked us through. In Prime 10, we are going to have an interface that will allow us to incorporate scripting into the Mathcad worksheet. That is our plan. Through that interface, we will be able to apply the conditional formatting. If there is a failure or the flag is not okay, we could conditionally format that one color, red, perhaps. If everything is okay, if we pass the flag check, we could conditionally format that green, for example. That is coming in the next version. The anticipated timeframe for that will be, I would say, in the spring of 2024. All right. Next question also for Angie. You mentioned in your presentation about interoperability with Word, with Excel, etc. Can you speak more about the Word format? Is it rich text format? Is it a Word doc? What is up with that? Yes. The interoperability with Word is based on the rich text format, the RTF format. From Mathcad, there is an option to save the Mathcad worksheet out to the RTF format. Once you do that, you can go into Word and open the Mathcad content in Microsoft Word. All of the content will be there. Any math regions from the Mathcad worksheet will appear in the Word document as images. Any text in the Mathcad worksheet will appear in the Word document as text that can be edited. It will go into the Word document in text boxes, but those text boxes are editable. That is how you would export your Mathcad content to Word. That is one way to export your Mathcad content to Word. That is what we recommend, using the Save as RTF option to get your Mathcad worksheet into Word. Once the Mathcad worksheet is in Word, you have the full capabilities of Microsoft Word available on the Mathcad content. If you have standard headers and footers that are in a template, a Word template at your company or your organization, you can leverage those as well. Mathcad has headers and footers. If the standard is to use Word, then that's how you would do it. Okay. Thank you, Angie. For Pat, since you have the screen, can you go into a little more how to insert a combo box and how to edit the combo box? Just show folks the combo box again. Yeah. I'm just going to switch over to the other sheet. The combo box, I did notice in a couple of the questions, they were asking if it was bringing up a separate database or file, and they aren't. You can access Excel files, but not the way the combo box is set up. Let me drop this down, and we'll look at this combo box. Basically, the combo box, if I go to edit, is effectively a table. We set up in the top, we just set up, I can highlight this and I can type it. I could change this from bar to, I do not know, steel. You set up what you want it to be. You set up the columns and you apply their units to it here in the brackets. Then you have to fill the table with the data that you want it to draw on. It is going to assign, as I say, in the format of an array, with the first element being the first column, the second element being the second column, it is going to assign it to whatever variable you want. I always have to do this. I have to go looking for where is my combo box? I cannot remember. You build these and you don't have to go back and do them all the time. Input, output. That's what I thought. That's where I started. Combo box here. If we put in an empty combo box, you see it comes with that configuration. All you have to do is add rows and columns to your table and fill it out. Then it's going to work. Hopefully that is what you're looking for. Yes. I think next question, can you show us any text formatting/printing features/improvements? I'm also interested in how the hidden boxes look when printed. Maybe this is an Angie question, but Pat also has the screen. Yeah. I'm happy to have a go and let Angie just add to it because she knows it better than me. With the last format, if I go up to text formatting, if you're familiar with styles in Microsoft Word, we now saw the introduction of styles. You can get a lot of consistency across your worksheet by applying styles. For example, if I wanted to change that to heading two or heading three or what I use for references, you get that level of control. It does not have auto numbering, paranumbering in that yet, as best I understand, but you can do that. We do not have subscripts and superscripts yet for the text boxes. I understand that may be coming at some point in time in the future. You can see all of the things that you can adjust within your text formatting, whether it is bold, italic, underline, color, background color, increase the size. You can have numbered lists and bulleted lists within that section. Did I cover everything you mentioned, David? I'm saying that as I'm trying to think. Yeah, you're looking at the next question. You expect me to remember the old one. I know. I'll just jump in and add to that that we did also add in the last release the ability to add internal links within the document, which will help incredibly with navigation. We have the ability to link externally to external sources, but now we also have the ability to link internally. We could create, for example, a—I use the term table of contents with some hesitation because it does not have all of the features of a fully featured table of contents like you might have in Word. We could create a page one with a table of contents per se where you have links to multiple different sections or destinations in the document. You can link forward, you can link backwards. That was added in the last release as well. I think the last part of that question was about the appearance of the area when printing or creating a PDF. Oh, and whether they're open or closed when you print them. If you're creating a PDF or printing them, the collapsed area will show or not show depending on whether you have it open at the time of printing. If it's collapsed, this is what you're going to print. If it's open, this is what you're going to print. I think that's probably my cue to ask another question. Yeah. Let's ask the one that just came in. Maybe it'll be our last question. You mentioned repeated variables have warnings and the clear function negates that. I have not seen that feature in Mathcad Prime. It seems like you can repeat variables without warnings. It depends on the options you have chosen. If I go down here, for example, and I go rows and I set it equal to five, it's right below the one above it. You see the green box pops up. That green box, the way my that's the default. What it's telling me is that n rows is being redefined. It was already defined. You see it above it, n rows equals two. Now it's being redefined. If I do not want that to happen, if I were to clear the variable and go n rows and step out, that warning is going to disappear because it is not being redefined because it was cleared before I went to it. That is what that was all about. Redefinition warnings were added starting in Mathcad Prime 8. Is that right, Angie? That is correct. Yes. Yes. You need to upgrade your version of Mathcad Prime to 8 or 9 if you do not see redefinition warnings yet. With that, that is all the time we have because we are rapidly approaching a 60-minute point. Thank you again to everyone who participated. Thank you especially to Angie and Pat for your time today. There will be a survey that should appear on your screen shortly. Hopefully, we'll see you in our next webinar coming later this summer, the Mathcad Virtual Conference 2023. Enjoy the rest of your day. The replay will be available on mathcad.com, hopefully later this week, as well as Pat's first worksheet for download. If we did not answer your question today, you can press the connect with a Mathcad expert button on your console and hopefully get your question answered later. Thank you. Goodbye.