A hitch-mounted bicycle rack is designed to carry up to four 30-lb. bikes mounted on and strapped to two arms GH [see bike loads in the figure part (a)]. The rack is attached to the vehicle at A and is assumed to be like a cantilever beam ABCDGH [figure part (b)]. The weight of fixed segment AB is W1 = 10 lb, centered 9 in. from A [see the figure part (b)] and the rest of the rack weighs W2 = 40 lb, centered 19 in. from A. Segment ABCDG is a steel tube, 2 × 2 in., of thickness t = 1/8 in. Segment BCDGH pivots about a bolt at B of diameter dB = 0.25 in. to allow access to the rear of the vehicle without removing the hitch rack. When in use, the rack is secured in an upright position by a pin at C (diameter of pin dp = 5/16 in.) [see photo and figure part (c)]. The overturning effect of the bikes on the rack is resisted by a force couple Fh at BC.
(a) Find the support reactions at A for the fully loaded rack;
(b) Find forces in the bolt at B and the pin at C.
(c) Find average shear stresses Ï„aver in both the bolt at B and the pin at C.
(d) Find average bearing stresses σb in the bolt at B and the pin at C.
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Bike loads 4 bike loads 27 in Release pins at C& G 3 @ 4in. (api in) 6 in 16 2 in. X2 in. X in MA A 2.125 in. h-7 in Fixed support at A Ar A Bolt at B h-7 in Pin at C Pin at C 2.125 in 2 x2 x1/8 in Bolt at B (c) Section a-a