Statically indeterminate torsion refers to a situation in structural mechanics where a component or structure is subjected to torsional loads (twisting forces) and the resulting internal forces cannot be determined solely by applying equilibrium equations.

Where:

• $\Delta \theta$ is the angle of twist,
• $T$ is the applied torque,
• $L$ is the length of the shaft,
• $G$ is the shear modulus of elasticity of the material,
• $J$ is the polar moment of inertia of the cross-sectional area of the shaft.