The A-36 hollow steel shaft is 2 m long and has an outer diameter of 40 mm. When it is rotating at 77 rad/s , it transmits 32 kW of power from the engine E to the generator G. The shear modulus of elasticity for A-36 steel is 75 GPa.

Complete Question

The A-36 hollow steel shaft is 2 m long and has an outer diameter of 40 mm. When it is rotating at 77 rad/s , it transmits 32 kW of power from the engine E to the generator G. The shear modulus of elasticity for A-36 steel is 75 GPa.

Determine the smallest thickness of the shaft if the allowable shear stress is Tallow 140 MPa and the shaft is restricted not to twist more than 0.05 rad

The value is

Explanation:

From the question we are told that

    The  length is  

     The outer diameter is

     The angular speed is  

      The amount of power transmitted is  

        The shear modulus of elasticity is  

         The allowable shear stress is  

         The allowable angular displacement is  

Generally the power transmitted is mathematically represented as

Here is the amount of  torque generated by  the  hollow steel shaft

=>    

Generally the polar moment of inertia of the  hollow steel shaft is mathematically represented as

Generally the allowable displacement of the hollow steel shaft is mathematically represented as

=>  

=>  

=>  

Generally the thickness of  the shaft is mathematically represented as

=>  

=>  

magnitude and direction