Abstract: A tire comprises at least a left tread portion, a right tread portion, wherein the left tread portion and the right tread portion are axially separated by a longitudinally oriented groove. A tread reinforcement comprises a plurality of tread reinforcing layers wherein the reinforcement elements are formed of parallel reinforcements arranged in opposing layers, and each of the opposing layers has a bias angle relative to the circumferential direction. The bias angles of the reinforcement elements in each of the tread reinforcing layers corresponds to a plurality of equilibrium membrane shapes determined from membrane equilibrium equations that are joined together to create a continuous, complex shape.