A steel tyre of a thickness of 10 mm, a width of 80 mm and an inside diameter of 1,500 mm is heated and shrunk on to a steel wheel of a diameter of 1,501 mm. If the coefficient of static friction between the tyre and the wheel is 0.3, what twisting moment is required to twist the tyre relative to the wheel? Neglect the deformation of the wheel. E = 200 GPa.
Width of tyre, b = 80 mm
Thickness of tyre, t = 10 mm
Tyre diameter, D = 1,500 mm
Wheel diameter, D′ = 1,501 mm
Change in the inner diameter of tyre = 1,501 − 1,500 = 1 mm
where p is junction pressure between the tyre and the wheel
