03 August 2018
- Last edited 03 August 2018
The paper is actually right. Just think about the equilibrium of the beam alone, without the other components (column and joint).
As static equilibrium equations must be fullfiled, the moment in the support of a cantiliver beam subjected to a concentrated force P in the end, no matter whether it is a fully or partially rigid support, will always be PL. This 'dissipated' moment that you are thinking of is actually an increase in rotation, not a reduction in moment, you see?
In your model, you have a beam that is supported by two columns which have rigid ends and, therefore, your model is statically indeterminate and the solution is not as simple as calculating PL, but you can retrieve reactions from ansys after the solution and get the full static determination of the structural frame and then perform the same procedure.
Also, you mentioned that you are getting rotation from just dividing the vertical displacement in midspan by the half-length of the beam. This is actually imprecise. Remember both the beam and the column will deform and the actual joint rotation will be the difference between the final angle between them (alpha in the attached figure, which is a little larger than 90º ) and the initial one (90º in your case). Also remember that both the beam and the column rotations must be taken locally at the joint and not in the end of the beam as the rotation decreases towards the center of the beam or the support of the column that you are studying.