A hollow aluminum shaft with an outside diameter of 80 mm and a wall thickness of 4 mm has an allowable shear stress of 80 MPa. Determine the maximum torque T that may be applied to the shaft.

Respuesta :

Answer:

The value of maximum torque applied on the shaft  [tex]T_{max}[/tex] = 2764.4 N - mm

Explanation:

Outside diameter D = 80 mm

Thickness = 4 mm

Inside diameter d = 80 -2 × 4 = 72 mm

Allowable shear stress Z = 80 M Pa

Now the value of maximum torque is given by

[tex]T_{max} = \frac{\pi}{16} Z [\frac{D^{4} - d^{4} }{D} ][/tex]

Put all the values in above formula we get

⇒ [tex]T_{max}[/tex] =  [tex]\frac{\pi}{16}[/tex] × [tex]80 [\frac{80^{4} - 72^{4} }{80} ][/tex]

[tex]T_{max}[/tex] = 2764.4 N - mm

This is the value of maximum torque applied on the shaft.