How Do You Calculate Deflection in a Simply Supported Overhanging Beam?

[Rhysmachine]

Hey all, first post!

Looking to find a deflection equation for a simply supported overhanging beam with two supports and a point- load at the end of the canteliever. I can determine reactions at the supports but i am having trouble finding deflection between the supports.

Any help is appreciated!

the beam in question looks like (a) in the following picture but if we call L/2 a, instead.

 

[SteamKing]

This is a tricky problem. A simply supported beam with an overhanging load and no other appreciable loading is statically unstable. You have not provided any details about your calculations, so I am unable to comment on their validity. The so-called 'conjugate beam' you show reflects different end conditions from the original beam. The slope and deflection at C for the 'conjugate beam' must both vanish, whereas neither vanish at C for the given beam.

 

[Rhysmachine]

Sorry my mistake; the beam is restrained at A, vertically so I guess the triangle needs to be pointing the other way. The beam is no longer statically unstable now, right?

Ive done a number of calcs intergrating something like: P*a*x/LEI, with a number of variations to find slope then deflection, But I always seem to be ending up with an answer that would be mm^2 instead of mm. I was hoping someone might be able to go through finding the answer for me so I can find the deflection at many points along the A-B section.

Oh and the second example shouldn't be there at all. I just had to find a picture that was something like the problem I have as I couldn't upload my own pic.

 

[jhae2.718]

I'd solve the beam equation to find the displacement as a function of x or get an approximate solution using virtual work or finite elements.