What is the best shape for carrying a torque efficiently?

The hollow circular shape is the best choice for carrying torque efficiently due to its geometry, which maximizes the distribution of material away from the center of rotation. In a circular cross-section, the material is uniformly spaced from the axis, which allows for even stress distribution when torques are applied. This helps to optimize the moment of inertia, thereby enhancing strength and reducing the likelihood of failure under shear and bending stresses.

The circular shape also minimizes the torsional shear stress for a given applied torque, making it particularly effective in applications such as shafts, where torque is commonly encountered. The hollow section further reduces weight, allowing for material savings without compromising strength.

Other shapes, like square, triangular, and solid rectangular, do not provide the same level of efficiency in torque transmission. They tend to have higher stress concentrations or less effective distribution of material relative to the axis of rotation, making them less effective for applications requiring the efficient transfer of torque.