Torsion of a Circular Bar

 

In a Nutshell:  Torsion of circular bars is restricted to bars with cross-sections that are

solid circular sections or annular sections. 

 

 

Calculation of the polar moment of inertia

 

Recall from calculus that the polar moment of inertia of a plane circular section is

 

     

 J  =    ∫ r2 dA    =       r2 dr    

 

                   

The two cross-sections of key interest are a circular cross-section or radius, c, and an

annular cross-section with outer radius c2 and inner radius c1.  The table below gives

the polar moment of inertia for these two cross-sections.

 

  Circular Cross-Section

   J   =  π c4 / 2

  Annular Cross-Section

   J   =  π ( c24  -  c14 ) / 2

 

The distribution of shear stress is linear for linear-elastic material response. (Figures below)

 

                                   

 

Click here to return to torsion members.

 


Return to Notes on Solid Mechanics

Copyright © 2019 Richard C. Coddington
All rights reserved.