Practice Problem 5-1(b)

Practice Problem 5-1 (b)

Given: A solid shaft with two gears, A and B, is driven by a motor. Gears A and B apply torques to the shaft of T_A = 250 lb-in. and T_B = 300 lb-in as shown. The shaft has the following dimensions: diameter, D = 0.5 in.; L₁ = 6 in.; and L₂ = 10 in. The Shear Modulus of the shaft is G = 10 Msi.

Req'd: Determine the Angle of Twist of the shaft at Section A with respect to Section C q_AC.

Sol'n: The angle of twist of cross-section A with respect to C is the sum of the angles of twist of the two shaft segments L₁ and L₂:

q_AC = q_AB + q_BC

q_AC = (T_AB)(L_AB)/JG + (T_BC)(L_BC)/JG

q_AC = [(250 lb-in)(6 in.) + (550 lb-in.)(10 in.)]/[(0.00614 in⁴)(10 Msi)] = 0.114 rad.

q_AC =6.53°

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Updated: 05/24/09 DJD