Figure P12.59 shows a symmetrically matched pair of steel torsion springs in a conventional arrangement for supporting the weight of a domestic overhead garage door. The 25-mm shaft is supported to the fixed structure by bearings (not shown) at each end and in the center. A cable wrapped around each of the pulleys supports the weight of the door. (The 110-mm diameter is measured to the axis of the wrapped cable.) Each spring has D = 45 mm, d = 6 mm, and 120 turns. The total extension of the cables from spring-unloaded to door-closed positions is 2.1 m.
(a) Calculate the nominal bending stress in the springs in the door-closed position.
(b) List important factors that would tend to make the actual maximum stress different from the nominal value.
(c) What supporting force is provided by each cable in the door-closed position?