Torsion in Shafts Calculator | Torque, Shear Stress & Angle

Torsion in shafts Tool Formula:

Shear Stress (τ)

\[ T = \frac{T \times r}{J} \]

(where τ = shear stress, T = applied torque, r = radius, J = polar moment of inertia)

Polar Moment of Inertia for Solid Circular Shaft (J):

\[ J = \frac{\pi \times d^{4}}{32} \]

(where d = diameter of the shaft)

Angle of Twist (θ):

\[ \theta = \frac{T \times L}{J \times G} \]

(where θ = angle of twist, T = applied torque, L = length of shaft, J = polar moment of inertia, G = modulus of rigidity)

Torsion in Shafts Calculator is an engineering, student, and educational tool used to analyze circular shafts when it is subjected to torsional loads. Torsion causes shear stress in the material used in that shaft, and it creates an angle of twist in the length of the shaft that is vital in rotating machines, power transmission shafts, and drive systems.

There is the ability of the user to input torque (T), the shaft length (L), the shaft diameter (d), and material properties (shear modulus G). The calculator takes solid and hollow shafts, calculating the highest shear stress (τ = T × r / J), the angle of twist (θ = T × L / G × J), and the polar moment of inertia (J). The calculation is step-by-step to demonstrate the formulae and intermediate values, hence easy to understand the torsional behavior.

SI units are acceptable: N·m, mm, m, Pa/MPa. The tool is suitable for mechanical engineers, structural engineers, students, and educators in the analysis of the shaft strength, torsional deformation, and rotational design both academically and professionally.