Question

A shaft is made of an aluminum alloy having an allowable shear stress of τallow = 100 MPa. If the diameter of the shaft is 100 mm, determine the maximum torque T that can be transmitted. What would be the maximum torque T′ if a 75-mm-diameter hole were bored through the shaft? Sketch the shear-stress distribution along a radial line in each case.

Answer 1

Answer:

A shaft is made of an aluminum alloy having an allowable shear stress of T_allow = 100 MPa. If the diameter of the shaft is 100 mm, determine the maximum torque T that can be transmitted.

Explanation:

Answer 2

Answer:

(a) Maximum torque is 19.63 KN.m for a diameter of 100 mm.

(b) Maximum torque is 13.42 KN.m for a hollow rod of outer diameter 100 mm  and inner diameter 75 mm.

Explanation:

The maximum torque is given by the formula:

Tmax = τmax J/c

(a)

J = (π/2)r^4 = (π/2)(0.05 m)^4

J = 9.8174 x $10^{-6}m^{4}$

T = (100 $10^{6}$ Pa)(9.8174 x $10^{-6}m^{4}$)/0.05 m

T = 19.63 KN.m

(b)

J = (π/2)(r1^4 - r2^4) = (π/2)[(0.05 m)^4 - (0.0375 m)^4

J = 6.711 x $10^{-6}m^{4}$

for maximum torque, we will take c = external radius = 0.05 m

T = (100 $10^{6}$ Pa)(6.711 x $10^{-6}m^{4}$)/0.05 m

T = 13.42 KN.m

The shear stress distribution along a radial line in each case is given in the attachement.