Assembly comprising a tyre drum (1) including a turn-up mechanism (5) for use in building an unvulcanized tyre, wherein the tyre drum is provided with a central shaft (2), two bead clamps (11) and bead inner supports (13) placed around the shaft and axially spaced apart on either side of a centre plane of the tyre drum, means for radially expanding a part of the tyre components that is situated within the bead clamps, wherein the tyre drum on either side outside of the bead clamps is provided with a first and a second set of turn-up arms (5), respectively, wherein the arms at a first free end oriented towards the bead clamps are provided with a turn-up means, particularly a turn-up roller (7) or turn-up band, wherein the shaft (2) is designed hollow having a circumferential wall having an outer diameter, wherein each set of arms (5) with accompanying bead clamps (11) and bead inner supports (13) is disposed on a casing (10), of which the inner diameter corresponds with the outer diameter of the circumferential wall of the hollow shaft, wherein the assembly comprises at least two pairs of casings (10), wherein the first pair.