The tire (70) of the invention incorporates a carcass ply cord material (93) with variable modulus of elasticity to provide an active sidewall structure (82a, 82b). The variable modulus cord material is incorporated in the axially outwardmost ply (90) of a carcass (80) having two plies (88, 90) separated by elastomeric inserts (89a, 89b) in the sidewalls (82a, 82b). The outer ply cord material (93) provides an increased modulus of elasticity with an increase in elongation. The inner ply cords (91) have a modulus that substantially exceeds that of the outer ply cords (93) under normal loads in the inflated mode. Thus, the inner ply (88) dominates the structural response of the sidewalls (82a, 82b) at normal loads in the inflated mode. Under severe sidewall deflection, such as when the tire is uninflated, the outer ply cord (93) is elongated, increasing its modulus of elasticity and thus, shifting the load from the axially inwardmost ply (88) to the axially outwardmost ply (90).