Question

A solid steel shaft ABCDE turns freely in bearings at points A and E. The shaft is driven by the gear at C, which applies a torque T2 5 325 lb-ft. Gears at B and D are driven by the shaft and have resisting torques T1 5 200 lb-ft and T3 5125 lb-ft, respectively. Segments BC and CD have lengths LBC 5 20 in. and LCD 515 in. and the shear modulus G 511,600 ksi. Determine the minimum required diameter (d) of the shaft if the allowable shear stress t a 56 ksi. Also calculate the angle of twist between gears B and D.

Answer 1

Answer:

Hello your question is poorly written  below is the well written question and the diagram attached to your question is attached below as w ell

A solid steel shaft ABCDE turns freely in bearings at points A and E. The shaft is driven by the gear at C, which applies a torque T2 325 lb-ft. Gears at B and D are driven by the shaft and have resisting torques T1  200 lb-ft and T3 125 lb-ft, respectively. Segments BC and CD have lengths LBC  20 in. and LCD 15 in. and the shear modulus G 11,600 ksi. Determine the minimum required diameter (d) of the shaft if the allowable shear stress t a 56 ksi. Also calculate the angle of twist between gears B and D.

answer :

a) d ≈ 12.7 inches

b) ∅bc = 1.62 * 10^-3 rad

   ∅cd = 7.59 * 10^-4 rad

Explanation:

Given data :

G = 11600 ksi

Ta11 = 6 ksi

a)  determine the minimum  required diameter

Apply the relation below

Toc / Ip = Ta11 / R  = G*∅ / L

∴ Ip =  Tbc * R / Ta11

  π / 32 *  (d)^4 = [ ( 200 * 12 ) * ( d/2 )]  / 6

therefore : d = 12.7 inches

b) determine angle of twist between gears B and D

attached below is the detailed solution

) ∅bc = 1.62 * 10^-3 rad

   ∅cd = 7.59 * 10^-4 rad