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# How do rotated supports work

If you rotate a support, it can only take reaction in the direction of the rotation.
So if you rotate for example a support in the Y direction (= left support in the image) over an angle of α  ↻ in the XY plane, it means that
• 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.

An example:

1. 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
2. The load Q can be split into two components QX and QY.
3. The horizontal load QX must be beared by support A, resulting in a reaction RA.X.
4. Since support A can only bear forces in this  direction, also the vertical component of the load QY must be beared by support A.
5. 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.*
6. 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 (support@buildsoft.eu)