Abstract: A hopper bottom for supporting a cylindrical side wall of a grain bin thereon comprises an outer wall arranged to be supported on a support surface and an inclined inner wall supported in spaced relation vertically above the outer wall, which has an inverted cone shape. A manifold or ducting is provided between the outer and inner walls for guiding air received from a blower between the outer and inner walls. Ventilation openings are provided across a full radius of the inner wall so that the air from the manifold is released upwardly to ventilate material received vertically above the hopper bottom. The manifold or ducting also is in fluidic communication with a discharge chute formed between openings in the inner and outer walls, through which the material passes on exit from the hopper bottom, to emit the air in an inward and downward direction to assist the gravity discharge.