Solving Multiple Couples in Structural Engineering Analysis

[stinlin]

I didn't know where to post this since these forums are missing the best field of engineering (Civil/Structural).

Anywho, I got to thinking about this situation - a simply supported beam (or indeterminate to the nth degree even), or even a cantilever, with multiple concentrated moments. How would one go about drawing a moment or curvature diagram for this? I drew up this hypothetical idea (see attached I guess).

You'd think on my third year of this stuff, I'd have a good idea on what to do with a situation like this, but I just seem to get very confused. I don't really know where a situation would come up like this in practice, but it's more the theory of the situation that I'm interested in.

For a concentrated moment (one), I know you can usually just say clockwise or counter-clockwise positive, but even then, drawing the moment diagram gets me. Can anyone give some insight on the best way to approach this situation?

I want to throw this in - this is NOT a homework problem, extra credit problem, etc. This is simply my own interest (and because my Structural Analysis professor is kind of mean and likes to demoralize students, so I hate asking him questions). :) Thanks!

 

[FredGarvin]

Assuming you stay within linear boundaries, simply solve three individual problems, i.e. the beam with one couple at three different locations, and superimpose the results to arrive at the final.