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Q8) A winding drum is driven through 85% efficient 1:1 gearing by a solid square section shaft with a length of side x. The shaft rotates at 150 rpm whilst lifting a 20-tonne mass at a constant velocity of 0.25m/s and the angle of twist within the shaft is 1^o for its overall length of 30x.

Calculate the minimum dimension for length of side x. (16)

Note:

Modulus of rigidity for the shaft material = 80 GN/m²

Polar 2nd moment of area for solid square cross section = x^4/6