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**Circular bar **

As discussed, for illustration, we consider a bar with solid circular cross section of radius R, as shown in figure 9.6. From the general expression for

**Figure 9.7: Shear stresses in a bar with solid circular cross section subjected to end torsion**

torsion of a thick walled close section (9.17), we find that the shear stresses in the bar is given by,

(9.18)

where we have computed Thus, we find that the shear stress varies linearly with the radial distance, as shown in figure 9.7.

Then, the angle of twist per unit length, â„¦ is also obtained from (9.17) as,

(9.19)

Having determined the angle of twist per unit length, the entire displacement eld corresponding to an applied torque, T given by equation (9.8) is known.

The same is plotted in figure 9.8.

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