Disclosed is a first drum half together with a second drum half forming a tire building drum of a tire building machine, and a method for operating the machine. The machine includes a first drive member and a second drive member movable in the axial direction inside the drum shaft. The first drum half includes a base movable over the drum shaft in an axial direction, a crown-up section having a plurality of crown segments and a displacement member for displacing the crown segments in a crown-up direction, wherein the first drum half further includes a first coupling member for coupling the first drive member to the base to drive the movement of the base and a second coupling member for coupling the second drive member to the displacement member to drive the displacement of the crown segments.