The shaft in Fig. P4.3-7 has an outsidediameter d 0 = 55 mm and is made of a ste

Question

The shaft in Fig. P4.3-7 has an outsidediameter d0 = 55 mm and is made of a steel alloy that hasan allowable shear stressof allow = 80 MPa. The shaft is to be subjected to atorque T = 2 kN·m.

(a) Relative to the weight of asolid shaft, by what percentage could the weight of the shaftbe reduced by drilling out a core ofdiameter di ? %
(b) Repeat Part (a) if the allowable shear stressis allow = 100 MPa.
%

(a) Relative to the weight of asolid shaft, by what percentage could the weight of the shaftbe reduced by drilling out a core ofdiameter di ? %
(b) Repeat Part (a) if the allowable shear stressis allow = 100 MPa.
%

Explanation / Answer

First calculate the allowable inner diameter: = Tc/J where c is the outer radius and J is/(2(c-outer^4-c-inner^4)) This will give you the inner diameter. Then all you have to do is subtract (c-outer^2 -c-inner^2)/(c-outer^2) from 1 and multiply by 100 to get thepercent.

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