For statically indeterminate torsion problems—where equilibrium equations alone are insufficient to determine internal resisting twisting moments because there are more unknown reactive torques than independent equilibrium equations—the solution requires supplementing equilibrium with a compatibility equation expressing that the net angular rotation at a fixed support (or between coupled elements) must equal zero, combined with the torque-rotation (torque-displacement) relationship. This theory also covers the normal (tensile) stress generated on a 45° helical plane by pure torsional shear stress, which explains why brittle materials subjected to torsion fail along that inclined plane rather than the plane of maximum shear.
For statically indeterminate torsion problems—where equilibrium equations alone are insufficient to determine internal resisting twisting moments because there are more unknown reactive torques than …