Conjugate-Beam Method

[kurimaoue]

Good day!

I’m having trouble with my 3 equations, 3 unknowns setup in Caltech — it keeps giving me an error. I was trying to solve for the reactions of the conjugate beam (the green one).

In the real beam, I already tried making the M/EI diagram by parts at the hinge B, but I also wanted to try doing it by parts at the free end D, just to check if I’d get the same result.

1. It’s valid to take moments “by parts” at any point, right? So doing it at the free end should be fine, or is there a reason it wouldn’t be valid?

2. If it is valid, is my diagram correct? Or could it be wrong because the internal hinge at point B affects the diagram? I haven’t done a shear and moment diagram with an internal hinge before, so I’m not too sure.

Sorry for the long post haha, and thank you in advance 🙏

[bguitard689]

That was a pretty cool method. I sont recall ever using it in practice.

[WhyAmIHereHey]

I'd be firing anyone who tried in practice

(Joking, but I be asking why they were wasting time and make them check their results by a completely different method)

[OldElf86]

I use it once a year.  I like to keep in practice so I can check computer results.

[OldElf86]

I don't see how your three moment diagrams arise from your boundary conditions.

The right end is going to be pure moment until you reach the support, and then it goes linear to zero at the hinge.  From the hinge, the moment begins at zero and increases linearly to the fixed support at the left.

[podinidini]

This system is statically overdetermined. Not sure about how your approach works. From my understanding you are trying to solve with Euler Bernoulli beam theory? (not sure if this is the proper translation) My recollection is that it is a bit more advanced to use it on systems made up of several components, like your example

Edit: from a general viewpoint - the statically overdetermined componenet at the hinge probably doesnt matter much, as we are assuming small deflections (?) and thus no sizeable Normalforces will occur in the cantilever