## Torsion on a Circular Rod

Consider a circular shaft subjected to only torsion. Is the shear stress constant throughout the shaft? If not, where is the max shear stress?

Hint
Torsion is the act of twisting an object via an applied torque.
Hint 2
For shafts with a uniform cross-section, the torsion formula is:
$$T=\frac{J\tau }{r}$$$where $$T$$ is the applied torque or moment of torsion, $$\tau$$ is the max shear stress at the outer surface, $$r$$ is the perpendicular distance between the rotational axis and the farthest point in the section (at the outer surface), and $$J$$ is the torsion constant for the section. Torsion is the act of twisting an object via an applied torque. For shafts with a uniform cross-section, the torsion formula is: $$T=\frac{J\tau }{r}$$$
where $$T$$ is the applied torque or moment of torsion, $$\tau$$ is the max shear stress at the outer surface, $$r$$ is the perpendicular distance between the rotational axis and the farthest point in the section (at the outer surface), and $$J$$ is the torsion constant for the section.
Rearranging the equation to express shear stress:
$$\tau=\frac{Tr }{J}$$\$
From the expression, the max shear stress occurs at the outermost fibers in the circular shaft, where “r” is greatest.
The max shear stress occurs at the outermost fibers in the circular shaft.