#305 The shaft is hollow from A to B and solid

The shaft is hollow from A to B and solid - Mechanical Engineering

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Free Chegg Question

The shaft is hollow from A to B and solid from B to C. Determine the maximum shear stress developed in the shaft. The shaft has an outer diameter of 80 mm, and the thickness of the wall of the hollow segment is 10 mm .

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Free Chegg Answer

 

shear stress = T*r/J

J is the polar moment of inertia equal to pi*d^4/32

to find maximum shear stress we check shear stress in the beam AB and BC

net torque on beam AB = 4 +2  = 6KNm

and J of AB is  =  pi*.08^4/32  = 4.02*10^-6

shear stress (in AB)  = 6*10^3*.04/4.02*10^-6  

                                       = 59.6 MPa

for BC(hollow shaft) J is = pi*.08^4/32 - pi*.01^4/32   = 4.02025*10^-6

torque  = 2 KNm

shear stress (in BC)  = 2*10^3*.04/4.02*10^-6  

                                       = 19.89 MPa

thus max shear stress is 59.6 MPa in shaft AB