A run-flat support assembly for a wheel rim of a pneumatic tired wheel and method for use of the same are disclosed. In one embodiment, a tubular support structure is positioned in a tire cavity of the pneumatic tired wheel and coupled to the wheel rim to turn concurrently with an axis of rotation of the wheel rim. A skeletal structure is disposed within the tubular support structure. Circumferentially spaced linkages are displaceably secured to respective mounting races of a body of the skeletal structure. Each of the circumferentially spaced linkages is adapted to plastically fail at a pre-determined moment load in a run-flat condition, thereby pivoting relative to the respective mounting race.