A method of assembling tire components on a tire building drum having a cylindrically-shaped forming surface extending between opposing sides (102, 104) of the drum, the drum defining axial and circumferential directions, the method comprising the steps of: laying one or more air impermeable layers onto the forming surface; positioning a pair of sidewall support inserts (108, 110) onto the one or more air impermeable layers with each sidewall support insert spaced from a respective side of the drum; placing at least one reinforcing ply over the pair of sidewall support inserts on the drum so as to suspend over the forming surface the at least one reinforcing ply between the pair of sidewall support inserts, wherein the at least one reinforcing ply comprises a plurality of perforations centrally positioned on the at least one reinforcing ply and spaced apart along a circumferential direction of the drum; stitching the at least one reinforcing ply to the pair of sidewall support inserts and to the one or more air impermeable layers at locations axially outward of each sidewall support while leaving the reinforcing ply suspended between the pair of sidewall support inserts; depositing a pair of bead fillers (122, 124) onto the at least one reinforcing ply with each bead filler spaced from a side of the drum; locating a pair of circular bead elements (118, 120) onto the drum with each bead element positioned onto the at least one reinforcing ply; turning up edges of the at least one reinforcing ply over the pair of bead fillers and the pair of bead elements; delivering a gas pressure to the surface of the forming drum so as to separate the one or more air impermeable layers from the forming surface at locations between the bead elements; moving the bead elements toward each other along the axial direction of the drum during said step of delivering a gas pressure; and using the gas pressure to push the one or more air impermeable layers away from the forming surface at locations between the bead elements and into contact with the at least one reinforcing ply. laying one or more air impermeable layers onto the forming surface; positioning a pair of sidewall support inserts (108, 110) onto the one or more air impermeable layers with each sidewall support insert spaced from a respective side of the drum; placing at least one reinforcing ply over the pair of sidewall support inserts on the drum so as to suspend over the forming surface the at least one reinforcing ply between the pair of sidewall support inserts, wherein the at least one reinforcing ply comprises a plurality of perforations centrally positioned on the at least one reinforcing ply and spaced apart along a circumferential direction of the drum; stitching the at least one reinforcing ply to the pair of sidewall support inserts and to the one or more air impermeable layers at locations axially outward of each sidewall support while leaving the reinforcing ply suspended between the pair of sidewall support inserts; depositing a pair of bead fillers (122, 124) onto the at least one reinforcing ply with each bead filler spaced from a side of the drum; locating a pair of circular bead elements (118, 120) onto the drum with each bead element positioned onto the at least one reinforcing ply; turning up edges of the at least one reinforcing ply over the pair of bead fillers and the pair of bead elements; delivering a gas pressure to the surface of the forming drum so as to separate the one or more air impermeable layers from the forming surface at locations between the bead elements; moving the bead elements toward each other along the axial direction of the drum during said step of delivering a gas pressure; and using the gas pressure to push the one or more air impermeable layers away from the forming surface at locations between the bead elements and into contact with the at least one reinforcing ply.