Supporting member gives smile (4)
I believe the answer is:
beam
I believe this is a double definition.
'supporting member' is the first definition.
'smile' is the second definition.
(to beam is to smile)
'gives' is the link.
(Other definitions for beam that I've seen before include "Smile broadly or radiate" , "Smile brightly - supporting timber" , "Ray; piece of timber" , "Supporting structure" , "Ray - large piece of wood" .)