Wednesday, 15 April 2020

EXAMPLE 3.1.2. HOLLOW SHAFT

1. Determine the torque T that causes a maximum shearing stress of 50 MPa in the hollow cylindrical steel shaft shown.

2. Determine the maximum shearing stress caused by the same torque T in a solid cylindrical shaft of the same cross-sectional area.




Problem 1: 



The general formula relating shearing stress with torque is:

                                         where shearing stress is already given as 50 MPa


The value of c to be considered will be the radius which can give the maximum shearing stress, thus, consider the outermost radius.

                             c= 45mm

The polar moment of inertia is computed as:

                                      

                               
                                      

Thus:


                     

                                      

Problem 2: 


With the computed valued of T=5.74 kN-m (5,743,225.07N-mm) and a cross-sectional area of 45mm radius, we are asked to determine the shearing stress.

Before solving the shearing stress, we need to consider another value for the polar moment of inertia, J, since it is transformed to a solid shaft.



                          

Then, we can solve for the shearing stress:


                         

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