Problem 8.25

Since we are told that 80 kW of power are transmitted to shaft AB, the torque can be computed:

Therefore, the forces are:

at gear C ==>

at gear D ==>

The forces have been moved to the centerline of the shaft, with T representing the torque that shows up as a result of that translation. Assuming that gear E rotates clockwise,

Only the reactions at one end are necessary. Taking moments about an axis coincident with B_y, and using the forces found above,

Taking moments about an axis coincident with B_z,

The bending moment M_y at C is 120A_z = 1.3369 x 10⁶ N-mm, or 1336.9 N-m. The plot is below:

Since the bending moment varies linearly, I can use a proportion to get the value of M_y at D:

The bending moment M_z at D is 280A_y = 1782.5 N-m. The plot follows:

Since the bending moment varies linearly, I can use a proportion to get the value of M_z at C:

The equation for the shearing stress is

Thus, I need to determine the first two terms of the radicand at C and at D to determine which is larger:

Therefore, the calculation of the radius must be done at D: