The spool consists of a uniform cylinder 6 in diameter betwe

The spool consists of a uniform cylinder, 6 in diameter, between two cylindrical disks, 18 in diameter. The spool weights 16 lbs. A spring having k = 24 lb/ft is attached to cords wrapped around the disks. A second cord is wrapped around the center of the spool, passes over a small pulley and is attached to a 30 lb crate A. If the crate has a speed of 4 ft/s downward when the spring is stretched 4 in and the spool rolls without slipping, determine: The maximum distance that the crate will drop. The speed of v_c and the speed v_A of the crate when the stretch in the spring is zero. The radius of gyration about axel going through the center of gravity is 4.743 in.

Solution

select the lightest W-shape (using A992 Grade 50 material) that will provide

a factor of safety against tensile yielding equal to 1.67,

a factor of safety against shear yielding equal to 1.50, and

a maximum transverse deflection that does not exceed L/480.