The setter shows contentment in supporting structure (1-4)
I believe the answer is:
i-beam
'supporting structure' is the definition.
(I-beam is an example)
'the setter shows contentment' is the wordplay.
'the setter' becomes 'I' (the person that set the crossword).
'shows contentment' becomes 'beam' (I am not sure about this - if you are sure you should believe this answer much more).
'i'+'beam'='I-BEAM'
'in' is the link.
(Other definitions for i-beam that I've seen before include "Structural girder" , "Common type of metal girder" , "Rigid metal girder" , "Metal girder I-shaped in cross-section" .)