- the resulting reaction forces (RX and RY) in Y and X direction are related.
RX = R * sin (α)
RY = R * cos (α)Otherwise, the resulting vector for the reaction can never have the same angle α as the support.
- the rotated Y support can not be seen as a combination of a support in the Y and X-direction (although that is what you would expect). Because in the latter case, there is no correlation between the magnitude of the reactions in Y and X direction (while that is the case in a rotated support).
- Finding equilibrium with rotated supports is not guaranteed.
- Consider a beam loaded in the middle with a point load Q. The boundary conditions are:
- In A: support in Y direction, rotated 45° ↻
- In B: support in Y direction, not rotated
- The load Q can be split into two components QX and QY.
- The horizontal load QX must be beared by support A, resulting in a reaction RA.X.
- Since support A can only bear forces in this direction, also the vertical component of the load QY must be beared by support A.
- Since RA.X = QX and RA.Y = QY, it follows that RA = Q. Translational equilibrium is met. Now let’s write a rotational equilibrium around point A: Q * 0.5* L = 0Conclusions:
- With the current boundary conditions no rotational equilibrium can be found.
- You’ll get the message in Diamonds: equilibrium issues in the following direction(s): X; Y.*
- It would be a different story when point A would be a support in the Y and X-direction. Then support A would take the horizontal force QX and support B the vertical force QY. There would be no vertical reaction in support A (RA.Y=0). The rotational equilibrium would be met.
* The message on equilibrium issues can also have other causes. If your model didn’t contain rotated supports, please send your model (*.bsf-file) to the support desk (email@example.com) ↩