Am I not able to prize open-ended support? (10)
I believe the answer is:
cantilever
'ended support?' is the definition.
(beam fixed at one end)
I can't explain the remainder of the clue.
(Other definitions for cantilever that I've seen before include "support at one end" , "Beam supported at only one end" , "bridge design" , "Projecting mass" , "Projecting beam fixed at one end" .)