Strength of Materials

6.5 TORSION OF HOLLOW CIRCULAR SHAFT

Let a hollow circular shaft subjected to a torque T be considered (Figure 6.3). An elemental ring of area dA is considered. Then

 

dA = 2πrdr      (6.16)

 

 

Fig. 6.3 Hollow circular shaft.

 

Let R_e and R_i be the external and internal radius and D_e and D_i be the external and internal diameter of the hollow shaft, respectively.

From Equation (6.7), the shear stress at the radius r is

 

 

Shear force dF as the elemental ring

 

 

Now the torque, dT, due to this shear force as the elemental ring