MathCAD in Structural Engineering

For basic calculations, I guess Microsoft's Excel is to GoTo software for many (structural) engineers. About 10 years ago, a colleague of mine introduced me to MathCAD, which is a PTC software package nowadays (it was MathSoft back then). I've been hooked ever since...
 

Shear Force and Bending moment due to wind load on a building in MathCAD

My first reaction, like with most engineers I guess, was: why? Excel does what I want right? Well, yes, but when the math gets more and more complex, the sheets in Excel become less and less transparant. This increases the risk of errors in the formulas exponentially with complexity, but also when used by colleagues that are not as familiar with the structure of the sheet.
 

Shear Force and Bending moment due to wind load one a building with Microsoft Excel

That's the main advantage of a program like MathCAD. In simple terms: you type the math, and the math calculates itself! :-)

A second advantage to me: it looks so professional! Calculations from structural engineers are not for them alone, but need to be used by third parties for manufacturing, or by the authorities (here in the Netherlands) for checks of the design. Complex Excel sheets are not transparant, so the third party will have to either accept that you didn't make mistakes, or has to recalculate to validate.

Last but not least, when Excel basic functionality fails, we resort to Visual Basic. However, this makes the sheets even more prone to errors or bad use by inexperienced users. MathCAD also offers up certain programming features (like checks, loops, global parameters, etc.)

So just to share an example of the ease of use of MathCAD for sheet building... This one's in PTC MathCAD Prime 3.1, which I use next to the more powerful (but older) PTC MathCAD 15.Last week I was working on a wind calculation sheet in MathCAD, for which I already had developed a sheet in Excel, as you can see above. The idea is to expand on the functionality of the Excel sheet easily for more complex wind analysis. The sheet's based on the Eurocode with Dutch National Annex. I'll go step by step through the sheet:

(1) Initiating basic parameters:

I chose to use tables for introducing basic parameters, like wind speed depending on wind area, and terrain roughness depending on terrain category. It's an arbitrary choice, parameters like these can of course also be introduced with {if...then} statements for instance.

However, for readability, I can now clearly define project specific wind area and terrain category:

(2) Project specific parameters:

I use lookup functionality, just as in Excel, to get the parameters for this project calculation.

Fun fact! MathCAD calculates using SI units! So if I take speed squared [(m/s)^2] and multiply this with air density [kg/m^3], I automatically get a pressure unit! [Pa] Since wind pressure is usually described in [kN/m^2], I can stear the unit of the result, however, MathCAD is brutal when the unit is misdirected.

Next: wind loads over the height of a building are cut into zones, depending on the width-height ratio of the building:

Wind load vs. height, according to the Eurocode

For programming enthusiasts this screams {if...then} statement! And thus we continue :-)

(3) {if...then} and wind load over building height:

I will not go into specifics on the values presented here and why they are what they are, but it marvels me every time again that calculating and plotting can be this easy. No splitting calculation into steps. No checking line after line to see if copy paste of formulas worked. The q'p(z) formula will be demonstrated in more detail in the next step: result presentation for reporting.

(4) Presentation of project specific wind pressure:

So this specific building has a large width, small depth and relatively small height. According to the Eurocode, we have to take the wind load at the top of the building and apply it over the total height, since B (width) > H (height). It's also possible that B < H, for instance in the direction perpendicular to the one presented above.

So if we switch B and D (depth), we get the following wind pressure over height:

It'll be even more interesting when H >> B, where according to the Eurocode we have to take into account a variable wind load over the middle height zone:

And all that, captured in one {if...then} formula:

(5) Shear Force and Bending Moment:

Following the project specific wind pressure, where we calculated wind loads as a function of the height (and the wind friction at the sides and top of the building not to forget), calculating shear forces and bending moments is child's play: we only need to integrate the pressure over the height (important detail: integrate from top to bottom!) to get the results presented at the beginning of this blog:

Also, we can now easily calculate the section forces at every height of the building:

That's it for now, I hope this small exercise shows some of the power of a tool like MathCAD!