The invention relates to a mounted assembly for heavy machinery, inflated to its rated pressure, constituted of a rim and a tire, the tire comprising a radial carcass reinforcement anchored to two beads, surmounted by a crown reinforcement which itself is surmounted by a tread joined to the beads by sidewalls, the rim being provided with two seats extended by rim hooks and intended to receive the beads of the tire. According to the invention, at least one device external to the tire and to the rim comes to bear, applying a pressure to at least one annular part of a sidewall, said device simultaneously bearing on a rim hook, the device being of toroidal form and defining an inner cavity. The invention also proposes a tire and a process for limiting the flexion of the sidewalls of a tire.