A gear-and-shaft system is shown below. Shaft AB (length $L_{AB}$ = 12 in) is the input shaft and Shaft CD (length $L_{CD}$ = 15 in) has a fixed end. Both shafts are the same diameter and are made of a material with G = 5x$10^6$ psi. Gear B has radius $r_B$ = 4 in and Gear C has radius $r_C$ = 5 in. A torque T = 450 lb-in is applied at end A. If the allowable shear stress of the shafts is 7 ksi and the allowable rotation of A is $7^\circ$, what is the smallest allowable radius of the shafts? D $L_{CD}$ $r_C$ $r_B$ B C $L_{AB}$ A T
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Since gears B and C are connected, the tangential forces at the point of contact are equal. Therefore, $F_B = F_C$. $T_{AB} / r_B = T_{CD} / r_C$ $T_{CD} = T_{AB} * (r_C / r_B) = 450 * (5/4) = 562.5$ lb-in Show more…
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