PTC Inc. (PTC) Earnings Call Transcript & Summary

Hello 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, Anji Seberino; 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. Anji 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 2 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 e-mailed 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 for Mathcad Prime, our monthly Mathcad Minute e-newsletter and a free library of civil and structural engineering Mathcad Prime example worksheets. And after the webinar, we'll have a very short survey asking for your feedback. Your feedback continues to be important to us. And if you enjoy this webinar, then PTC will have more webinars in this style in the future. And now I'm excited to give the floor to Anji Seberino. Anji, the time is now to amaze us.

Thank you, David. Hello, everyone. This is Anji Seberino, 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. So 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. So 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. So 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 our technical partners to communicate the calculation work that's been done. So 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. So 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. So 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 and natural math notation, all of it. So all math expressions, equations, formulas are represented in the document using the same notation used in technical publications and textbooks so there is no confusion around what the formula or the equation is supposed to do. So 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, and again, all of the math is live. So 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 2 engines, 2 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 takes -- 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. So 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 so 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 and 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. So data can be imported from Excel or CSV or a text file directly into Mathcad, and data can be exported from Mathcad to Excel or another destination. And we also have an API, the Application Programming Interface that enables integration with other applications as well. So of course, Mathcad does integrate out of the box with PTC Creo and PTC Windchill. But again, aside from that, we integrate with Excel, with Word and then with -- 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. So very quickly at the individual engineering level, engineers can perform calculations with transparency and precision. All of calculations in Mathcad are completed with 64 bits of floating point precision. So they're precise. Engineers can document and share their work with others, create worksheets that can be reused, at the same time, reduce the errors that unintentionally could creep into calculations and into the calculation process. And 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. So all of this enables engineering teams to ultimately produce higher-quality work, free of errors, free of calculation mistakes in shorter periods of time. So let's talk just for a moment about spreadsheets. Historically, engineers have gravitated towards using spreadsheets for engineering. And 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, and they have a very low cost of ownership at initial perception, right? So 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. So spreadsheets were initially created for business purposes, where Mathcad was initially created and designed for engineers. So 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. And so 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. So 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 19172. And on the right, we can see the equivalent Mathcad worksheet, okay? So 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. And on the right-hand side, we have visibility into the calculation for the Reynolds numbers. So 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. And the same applies for the friction factor, okay? So that's -- 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. So just to put a finer point on it. On the left here, we have 2 formulas. And on the right, we have the same 2 formulas written in spreadsheet format in this case. And so 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 a spreadsheet in order to really understand what's going on. And 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. So AEC is really a primary industry for Mathcad usage. We have a lot of customers in this industry. And 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 pipeline. So those are just some of the areas where we see heavy use of Mathcad in the AEC space. And then the types of calculations that we see that are fairly common amongst these customers include beam analysis. So that's incredibly common. We have a lot of customers using Mathcad for beam analysis, so calculating and modeling things like torsion, deflection of the 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 and then member response to wind loads, seismic loads, uniform loads. So the response that we see based on different loading conditions and loading types, maximum reliable stresses, very, very common. We see that all the time and section analysis, okay, so analyzing different sections of a bridge or a highway or a road or a beam even and then also material trade-off analysis, okay? So that's another common use case where we see Mathcad applied in the AEC space. So these are just some examples. These are just some typical calculations. There are many, many more, but 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. So Dr. Heffernan, over to you.

Thanks, Anji. So yes, we're going to get right into it. So I have 2 worksheets that I'm going to present today. The first one, I thought it was really important was to start off with the design worksheet because it is so core to what we do as civil engineers. So I'll start there, and then I'll go on and look at a bit of a section analysis with the second worksheet. So right off the bat, you're seeing my worksheet, my design worksheet. So this looks at doubly reinforced rectangular concrete beam. And it does -- it figures out what the moment resistance is for that concrete beam. But hopefully, what you're seeing is something that would look very similar to what you would do if you're doing this by hand. And that's 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. So 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. And so if you see my cursor, I'm hanging around the geometric properties here to the right of the image, above the image in from PowerPoint and saved it as a PNG because I like the transparent background, so a very flexible choice of presentation. So I have my 2 variables defined. So I have the width and the height defined as B and H. And you notice that there's a colon equal sign. And so that defines B as 250 millimeters. It defines H as 500 millimeters. Well, I can now use those because they've been defined, I go just below it. And if I wanted to know the area, and I can define the area as the times age. Now 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. Now I know there was a question about units. So it's choosing the base unit, meters squared. If I wanted that as millimeter squared, I could choose millimeter squared, and it will recalculate it. And 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. So that's 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. So 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 doesn't recognize B anymore because it's below it. So it has to be top to bottom, left to right formatting. So let's get rid of that, and let's get into this a little bit. So I'm a structural engineer, this is about civil engineering. So it's bigger than just structural engineers. But I hope you can look at the 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. So I've laid out my sheet. I think the communication aspects that Anji 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. And I tried to lay out my worksheets to do the best of that. So 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. And 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. And then 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 component -- or the part of the worksheet that interest you the most. So I'm just going to pop it open here by pressing the plus sign, scroll up so you can see where we came from. And now you see this collapsible area opened up in front of us. And in this collapsible area, we're going to select the reinforcing bars for the beam and compute the effect of depth. Now as you will see in all of my sheets, I always put my references to the right. So you see the code reference here. Now I'm using the Canadian code. So CSA 23.3. If you're using ACI code or Euro code, it really doesn't matter. There is -- one, they're fairly similar. But 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. So a couple of features that I want to point out. So the first one is a drop-down combo box. And so where I'm using it here so I have a variable, so EXP is a variable for the exposure. And on the dropdown box, I'm assigning it to 1 of 3 conditions, which the code allows for and changes the amount of cover that we need depending on whether it's exposed or not exposed. And so having done that, the next feature is this logic box, right? So 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. Now I finish that off, I go down right to the bottom here. And 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 1.5x the maximum dimension of our aggregates. And so we're able to take into account those types of multiple code requirements by using either a logic box itself or these in-line functions where I can say maximum of cover or 1.5x the area max. And then that returns the value based on this logic, and we get a cover value. So it works out really quite nice to be able to compactly build the fundamental requirements of the code in one spot. So I'm going to keep scrolling down. So I use another combo box, and I use it multiple times. And so here, I'm using a combo box to assign the reinforcing bars. Now this list basically gives us all of the metric standard reinforcing bars that we use. And if you're working in empirical units, then you would just have a different -- build yourself a different combo box. Now I want to go into the edit mode just to show you what's behind the scenes. So if I go into edit, this is the data table that I put in to be incorporated into this combo box. And so we select the bar, that's what's in the first row. And 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 first -- or the number from the first row -- or first column, pardon me. And it's going to be the area in millimeter squared. Now I've -- 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. But this is 500 millimeters square. So it's picking that up if you were to choose 25 m. And then in the second element of the array, it's picking up the diameter, which is 25.2 millimeters. So if I pop back out, you can see if I change this, it's going to come up with different numbers. And 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. And so it makes it a really nice, easy way to select from a data table. So I had alluded, and I meant to mention it earlier, I'm going to scroll back up to the top. So up to the top here, grade control. So the first one is the origin. So 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 0, and then you can find that up in the calculation tab if you like. I prefer to work with the first element having an index of 1. And so I reset the origin of my arrays to have that. And I'd like to put it here directly on the sheets itself so anybody looking at it can see that I have reset the origin to 1. And the second one was is I assigned a custom unit, MMS, to be the same as millimeter squared. And that allowed me to draw that out from the combo box. So that kind of what that was about. And so this is all now going through the calculations. And 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. So we get a lot of use out of this combo box because the same one is being used in 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. So bar prime in one case, bar in the second case and stir up in the third case. And I finish off this set of calculations really, again, by using one of these in-line equations that chooses the maximum of 1.4x the bar diameter or 1.4x the maximum aggregate size or 30 millimeters, so whichever is greater, and we get a different number. So 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. So in 1B, we're checking the minimum tensions deal, right, which is a code requirement. And so we have ASME being calculated here. So what I wanted to point out here, obviously, you can see the equation, like Anji was pointing out earlier, but in this case, it's an empirical formula. And so 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. So we have 1 pressure unit, so megapascal is being the square root, and it's being divided by another megapascal below it. And so we're going to end up with a unit inconsistency here. So what I'm doing and what you have to do in those cases basically strip units out on the way and make sure that the units coming back to you at the end of the formula are what you would expect. And so 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. But I wanted to point out that you do have to manage those units, particularly with empirical formula that we get in the codes. So you'll see this in a lot of my sheets. I use flags all the time. So 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. And so 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." And so I do that just by setting up these flags using a very simple boolean if statement behind it. So we'll keep going down. Again, I love the logic. I think Anji 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. And so hopefully, that's coming across. And I put in a fair bit of effort into combining images and text to go with the calculation so that the logic flow of the calculation is completely obvious. And hopefully then when you hand it off to your checker after validation that they'll be able to find any errors that you might have let creep into it. And 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. So -- and 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 reinforce 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. And we go down, we have a couple more flags. Our compression steel does yield, which was an assumption up here. So 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, well -- sorry, 275. When I click out of it, you'll see the calculation start to scroll through it, and I can go down. I can check my flags and check the amount. And without getting into too much automation, I can use this to optimize my design as I like. So I'm going to stop there on this one and pop over to the next sheet. And it's going to allow me to show just a couple of different features of Mathcad and how they might be usable to you. So on this sheet, I put it together, it's basically going to look at the plastic analysis of a T-beam. So looking at the section of properties. Now most of us will draw that in for standard sections. Most of us will draw that information from tables in a steel design manual or somewhere else. But if you're using a nonstandard section, you're going to have to do these calculations yourself. And so that's what this sheet does. It basically assumes that you're using a nonstandard section. You put in the geometry in terms of the flange and the web, heights and widths, the material properties. And we're going to go through now, and we're going to calculate the moment of inertia of the section in the centroid. You need those to go on to the rest. We're going to calculate the elastic moment capacity in curvature of the section, and then we're going to do the same thing for the plastic moment capacity. Again, you see how I'm using the collapsable sections and the summary outputs to be able to decide where I want to go look at my worksheet without getting overwhelmed, and I build right into it. So you see 3A and 3B down here when we're looking at the plastic moment capacity in curvature, typical of a lot of the stuff we do, you have to start with an assumption. So 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. And then I put that into a flag. So the flag is telling me, yes, indeed, the neutral axis does occur in the web in this instance. And so that assumption was correct, and 3A is going to control the calculations, whereas 3B is what we would do if that assumption was incorrect. And we assume that the plastic neutral axis now occurs in the flange, but we see that, that assumption is false. So for all intents and purposes, I can ignore 3B in this case. And I don't even have to open it up. So let's see what we have under some of these. So let me open the first one. So here, we're going to calculate the centroid of the cross section as well as the moment of inertia for this section. And we're going to do that using the normal mechanics that we would have learned in school. So we're going to break it up into 2 standard sections, the web and the flange. And 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 to a little bit it came from a different worksheet that I already had done up because calculating this information for T-beam or an I-beam is pretty common. And so I was able to just copy and paste that and put it in here and then make sure that my variables match up. So in this case, I'm using arrays to do it. So 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 have -- 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, so 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 plan. And so I went to the effort of building it up in arrays so that I can have this clarity of communication in the calculation of not just the 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 the textbook. I'm just going to switch over to draft mode here because pagination is blocking our visibility of that formula. So now you're not seeing the pages that laid out, you're just seeing a whole flat sheet. And so 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. So let me close that. The -- so 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. So of course, this uses a strain compatibility model, and then we look at the conditions. So 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. So 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. And again, we're using a series of arrays to go through and to calculate the forces for the different components. And this is where the force equilibrium is being established, and we're checking for equilibrium. So I have a flag. This is going to tell me whether equilibrium has been met. And we carry on to calculate the elastic moment capacity as well as the curvature of the beam. And 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, and we're ready to go on and look at the plastic moment capacity. So we know 3A is governing. So I can open that up. You see the conditions shown in the diagram for the plastic, fully plastic. So our plastic hinge has just established itself in our strain and stress diagrams. And we're going to go through this similar calculation using the similar logic and determine what the plastic section modulus is here and plastic moment and the plastic curvature. And that goes down here. So the logic is the same. It's just using the same components so I don't have to spend a lot of time on that. But what I wanted to do is to show a couple of other features. So I started to create a section which is to calculate the moment capacity in curvature at the moment when the entire flange becomes plastic. So it's an elastic plastic condition. But I haven't completed that yet. And I didn't want anybody to be using it until I was completing it. So Mathcad does allow you to protect the areas. So I've locked that area. It won't open unless I unprotect it. And 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 calculation, stop people from breaking a validated worksheet by messing with things inside it, there's similar features that you would use in Excel if you were walking down different sections. But what I wanted to do is to go down and look at Section 5. So I created this condition so that I could show you some of the -- I don't want to do that, undo, Control Z. It allows me to show you some of the numerical capabilities that Mathcad has. And 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. And we're going to establish that and set it and then 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. So let me open that up. So it looks really complicated. It really is just little bits carrying on. And 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, so I use these clear statements so that I cannot -- so I can reset a bunch of variables, so I don't get a bunch of warnings that I'm redefining variables. So I use that where appropriate. That's why the clear flag is there. So 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. So it's plastic at the top, plastic at the bottom, elastic in the middle. And 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. So where does it get different from what we've done before? So 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. So 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 as -- or as functions of Y bar, which is the height of the neutral axis. And so all of these heights that we have in here are now being set up as a function of Y bar. So we can't get a numerical solution for them, but we are setting up their definition. And if we were to -- 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. So 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. So this is where the magic happens. So what we've done is we've incorporated the solve block, and I know in Anji's presentation, she showed you a solve block in the PowerPoint. Here, we see working. So 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 millimeters. And then I am going to set up the constraints that the solve block needs to satisfy. And in this case, that is force equilibrium, where all of the compressor forces have to be equal to the tensile forces. So we're using another different equal sign here. We're using that comparison equal sign. And so this sets up the condition that the solve block needs to satisfy. And we go -- then go down and we say, okay, now what we want you to do is to find the value for Y bar such that this constraint is met. And it is able to iterate numerically to find the value of 104.5 and change millimeters, which sets the height of the neutral axis. And with the contract that I have chosen here, that is then assigning it to the variable Y bar. So 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. And same thing with all of the dimensions, all the heights of those various stress block components. And again, I'm using a flag to make sure that my assumption at the start was actually realized. So the last thing I did, and this was more out of interest's sake, I'm just going to roll down, this is the calculation of the elastic-plastic moment capacity in curvature. But what I wanted to do is to plot the height or the stress distribution over the height of the beam for this condition. And so 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. And so 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. And so that's what this does, it allows us to have a multi-domain function as a function of its position Y. And then I can set up my range variable for what I want Y to vary from. And it's able to plot what that stress is, so stress and Y as a function of Y. Now I just add -- 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. And that's what's going on up in this section. And again, I can collapse my section, and you see the summary calculation. So you only have to look at this if it's -- requires your attention at a given moment. And we can see the elastic-plastic moment and the elastic-plastic curvature for the conditions that we set up. And 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's 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 cancellation. So I think with that, I'm going to hand this back to David, who's going to lead us through some Q&A. And hopefully, I didn't go too fast.

All right. Thank you, Pat, for those Mathcad demonstrations, and thank you, Anji, for your presentation as well. Our remaining 13 minutes or so, we'll be answering your questions. And both Pat and Anji are available. And I think the #1 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 are asking about images. So 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 can -- happy to answer that. So these are not drawn in Mathcad. So 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. And so you could just double click on it, and it would go to the object in PowerPoint or something. I intend to not use that methodology because I really value the transparent background, and that isn't supported with the object. So what I do is that I highlight it in PowerPoint, and I save it as a PNG file, which saves the transparent background. And then I import it here. And importing an image is simple as you go up to the top left, and you press the image box. And you saw it here, it dropped -- my cursor was down here. It dropped the browse for image if I press on, I browse to the image on my computer, and it will pop it in. So that's how that is done. And 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. So hopefully, that answers the question.

Yes. Thank you very much for that. You even answered the follow-up about transparent figure. This question is for Anji. So please get off mute. Can we apply a conditional formatting for the flag check?

Yes. David, so 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. So in Prime 10, we're going to have an interface that will allow us to incorporate scripting into the Mathcad worksheet. That's our plan. And through that interface, we will be able to apply the conditional formatting. So if the -- if there's a failure or the flag is not okay, we could conditionally format that one color, red perhaps. And if everything is okay, if we pass the flag check, we could conditionally format that green, for example. So that's coming in the next version. And the anticipated time frame for that will be in, I would say, in the spring of 2024.

All right. Next question also for Anji. You mentioned in your presentation about interoperability with Word, with Excel, et cetera. Can you speak more about the Word format? Is it rich text format? Is it a Word doc? What's up with that?

Yes. So the interoperability with Word is based on the rich text format, the RTF format. So from Mathcad, there is an option to save the Mathcad worksheet out to the RTF format. Once you do that, then you can go into Word and open the Mathcad content in Microsoft Word. And all of the content will be there. So the math, any math regions from the Mathcad worksheet will appear in the Word document as images. And any text in the Mathcad worksheet will appear in the Word document as text that can be edited. So it will go into the Word document in text boxes, but those text boxes are editable. And so that is how you would export your Mathcad content to Word. That's 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, then you have the full capabilities of Microsoft Word available on the Mathcad content. So 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. But if the standard is to use Word, then that's how you would do it.

Okay. Thank you, Anji. 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?

Yes. I'm just going to switch over to the other sheet. So the combo box, I did notice in a couple of questions. They were asking if it was bringing up a separate database or file like -- and they aren't. You can access Excel files, but not the way the combo box is set up. So let me drop this down, and we'll look at this combo box. And basically, the combo box, if I go to edit, is effectively a table. And so we set up in the top, we just set up, I can highlight this, and I can type it like I could change this from bar to, I don't know, steel. You set up what you want it to be. So you set up the columns, and you apply their units to it here in the brackets. And then you have to fill the table with the data that you wanted to draw on. And then it's 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's going to assign it to whatever variable you want. So if I'm just -- it's -- we're -- I always have to do this. I have to go looking for where is my combo box? I can't 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 why I started -- we're just -- we're all -- combo box, here. So if we put in an empty combo box, you see it comes with that configuration. And all you have to do is add rows and columns to your table and fill it out, and then it's going to work. So I -- hopefully, that is what you're looking for?

Yes. I think the 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 Anji question, but Pat also has the screen.

Yes. I'm happy to have a go, and let Anji just add to it because she knows it better than me. So with the last format, so if I go up to text formatting, if you're familiar with styles in Microsoft Word, we now saw the introduction of styles. And so you can get a lot of consistency across your worksheet by applying styles. And so for example, if I wanted to change that to heading 2 or heading 3 or what I use for references, and you get that level of control. Now it doesn't have auto number and par number in that yet as best I understand, but you can do that. So we don't have subscripts and superscripts yet for the text boxes. I understand that may be coming at some point in time in the future. But you can see all of the things that you can adjust within your text formatting whether it's bold, italic, underline, color, background color, increase the size. You can have numbered lists and bulleted list within that section. So that's -- did I cover everything you mentioned, David?

I'm saying that as I'm trying...

Yes, you're looking at the next question. You're expecting to remember the old one.

I know.

I would -- 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. So we have the ability to link externally to external sources, but now we also have the ability to link internally. So we could create, for example, a -- I use the word -- I use the term table of contents with some hesitation because it doesn't have all of the features of a fully featured table of contents like you might have in Word. But we could create a Page 1 with a table of contents per se, where you have links to multiple different sections or destinations in the document. So you can link forward, you can link backwards. So that was added in the last release as well. And then I think the last part of that question was about the appearance of the area when printing or creating...

Whether they're open or closed when you print them. So 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. So if it's collapsed, this is what you're going to print. If it's open, this is what you're going to print.

Okay. I think that's probably my cue to ask another question.

Yes.

There's a -- let's ask the one that just came in. Maybe it will be our last question. You mentioned repeated variables have warnings and the clear function to gate set. I have not seen that feature in Mathcad Prime. It seems like you can repeat variables without warnings.

Well, it depends on the options you have chosen. But if I go down here, for example, and I go rows, and I set it equal to 5. It's right below the one above it. And you see the green box pops up. So that's -- green box the way my -- that's the default. And what it's telling me is that N rows is being redefined. It was already defined. You see it above it N rows equals 2. Now it's being redefined. So if I don't 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's not being redefined because it was cleared before I went to it. So that's what that was all about.

And redefinition warnings were added starting in Mathcad Prime 8. Is that right, Anji?

That is correct. Yes.

Yes. So you need to upgrade your version of Mathcad Prime to 8 or 9 if you do not see redefinition warnings yet. And with that, that's all the time we have because we're rapidly approaching the 60-minute point. Thank you again to everyone who participated. Thank you especially to Anji and Pat for your time today. There will be a survey that should appear on your screen shortly. And hopefully, we'll see you in our next webinar coming later this summer, the Mathcad Virtual Conference 2023. Enjoy the rest of your day. And the replay will be available on mathcad.com hopefully later this week as well as Pat's first worksheet for download. And 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, and goodbye.