Simple Static Loads Analysis

[GKatEng]

I am new to MathCAD and am doing a simple static force equilibrium analysis. My goal is to understand the best way to do this type of analysis so that I can then scale it to more complex problems. MathCAD document is attached (prepared in MathCAD Prime 3.0) and a scan of the sample problem that I’m working on is shown on the second page of the document.

I was able to get the correct result using Method-1 and Method-3 but I’m not able to get Method-2 to work. In Method-2 I’m attempting to make the resultant loads Bx and By (the variables I’m solving for) variables within a function called B. I’m then trying to call function B in the moment equilibrium equation to simplify the form of the equation. If I could get this approach (or something similar) to work it would be great because for more complex problems it would be very convenient to write equilibrium equations as a function of reaction load [B] where [B] represents Bxi + Byj + Bzk.

Also, as mentioned, Method-3 works but I don’t really understand the utility of this method if I need to manually enter the numeric coefficients into [M] and [v]. Is it possible to automatically populate the coefficients in [M] and [v] from the equilibrium equation shown in Method-1 and -2?

Another question is I’m interested in any recommendations to simplify my solution approach and / or apply best practices that others are using. For example – is it possible to do this evaluation without needing to explicitly define the unit vectors i, j, and k? Any other tips / suggestions?

[LucMeekes]

You've got three equations, solving only two variables. This means that one of the three equations is dependant (on one or both of the others). But that shouldn't hinder solving it.

Did you notice the error message for the solving of MomentSumTest(B) ->.?

In Mathcad 11 I get a similar error just for symbolically evaluating MomentSumTest(B(Bx,By))->:

If the right-hand-side of the equation you want to solve is 0, you can omit it:

Success!
Luc

[Werner_E]

See my remarks in the attached file.

As its Prime 4 I also include a pdf print of it

[GKatEng · Accepted solution]

Thanks very much, that was very helpful!!! 

[LucMeekes]

And: No, you don't have to explicitly define the unit vectors i, j and k. You can have them implicitly defined. Here is an example, with a notation that stays close to your definition of the problem:

Success!
Luc