What evidence do you have that a model with a Linear mesh will run as a Quadratic element?
Is it because you see an extra node in the mesh Statistics as shown below?
That doesn't imply the element runs as quadratic. After this model solves, I can look in the Solution output and see that one linear element BEAM188 was used.
If I change to a Quadratic mesh...
then I get one Quadratic BEAM189 element in the Solution output.
You might ask, "Why is there an extra node?" I expect it is used to orient the beam cross-section.
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