A tire having a section height, a maximum section width, an upper section above the maximum section width, and a lower section below the maximum section width is provided. The tire includes a circumferential tread, a pair of sidewalls, a pair of bead regions each having a bead core, and at least one carcass ply extending circumferentially about the tire from one bead region to the other. The at least one carcass ply is wound outwardly about at least one of the bead cores and extends toward the tread to form a turn-up portion that terminates at a turn-up end. The turn-up portion includes a concave segment that begins in the bead region and ends short of the turn-up end or at the turn-up end.