Question

The solid shaft with a 20 mm radius is used to transmit the torques applied to the gears. Determine the maximum torsional shear stress developed in in the shaft.

Answer 1

Answer:

τ = (7.96 x 10⁴ m⁻³)T

This is the expression for maximum allowable shear stress in terms of the maximum torque applied in Nm.

Explanation:

The maximum allowable shear stress on the solid shaft can be given by the torsional formula as follows:

τ = Tc/J

where,

τ = Maximum Allowable Shear Stress = ?

T = Maximum Torque Applied to the Shaft

c = maximum distance from center to edge = radius in this case = 20 mm = 0.02 m

J = Polar Moment of inertia = πr⁴/2 = π(0.02 m)⁴/2 = 2.51 x 10⁻⁷ m⁴

Therefore,

τ = T(0.02 m)/(2.51 x 10⁻⁷ m⁴)

τ = (7.96 x 10⁴ m⁻³)T

This is the expression for maximum allowable shear stress in terms of the maximum torque applied in Nm.