What happens to torque distribution in a rod or cylinder?

In a rod or cylinder subjected to torsional loading, the distribution of torque is most significant at the outer surface due to the way shear stress operates in these structures. When a cylindrical object, such as a rod, is twisted, the shear stress generated within the material is proportional to the distance from the center of the cylinder, reaching its maximum at the outer surface.

This relationship can be described by the theory of pure torsion, which dictates that the shear stress (( \tau )) in a solid cylindrical rod varies linearly with the radius (( r )). The maximum shear stress occurs at the outermost layer (the surface) of the rod or cylinder, where the radius is greatest. As one moves toward the center of the rod, the shear stress decreases to zero at the center, where no torque is transmitted through the material.

The disregard for uniform torque distribution or fluctuations arises from the basic principles of torsion mechanics. Within a homogeneous material under torsion, the stress states are designed to distribute neatly from outer surfaces to the inner core, following this linear behavior instead of exhibiting random variations. Thus, understanding that torque is greatest at the outer surface is fundamental to the analysis and design of cylindrical and rod-like structures in engineering applications.