Angle of Twist Calculator
Calculate the angle of twist in circular shafts subjected to torsional loading
Calculate Angle of Twist
Calculation Results
Formula used: φ = TL/(JG)
Max shear stress: 0.00 MPa
Twist per unit length: 0.000000 rad/m
Engineering Analysis
Example Calculation
Aluminum Shaft Example
Material: Aluminum 6061-T6 (G = 26 GPa)
Shaft diameter: 100 mm (solid circular)
Shaft length: 3 m
Applied torque: 10 kN·m
Solution Steps
1. Polar moment: J = πD⁴/32 = π(0.1)⁴/32 = 9.82 × 10⁻⁶ m⁴
2. Angle of twist: φ = TL/(JG) = (10,000 × 3)/(9.82 × 10⁻⁶ × 26 × 10⁹)
3. Result: φ = 0.117 rad = 6.73°
Material Properties
Key Formulas
Angle of Twist
φ = TL/(JG)
Solid Circular
J = πD⁴/32
Hollow Circular
J = π(D⁴-d⁴)/32
Max Shear Stress
τ = Tr/J
Understanding Angle of Twist
What is Angle of Twist?
The angle of twist is the relative rotation between two cross-sections of a shaft when subjected to torsional loading. It represents how much one end of the shaft rotates relative to the other end due to applied torque.
Key Parameters
- •Torque (T): Applied twisting moment
- •Length (L): Distance between cross-sections
- •Polar Moment (J): Geometric property of cross-section
- •Shear Modulus (G): Material property resisting shear deformation
Mathematical Foundation
φ = TL/(JG)
Basic torsion formula
τ = Gγ = Tr/J
Shear stress-strain relationship
Assumptions:
- • Circular cross-section
- • Uniform material properties
- • Linear elastic behavior
- • Constant torque along length
- • Plane sections remain plane
Engineering Applications
Power Transmission
- • Drive shafts
- • Propeller shafts
- • Motor shafts
- • Turbine shafts
Structural Design
- • Building columns
- • Bridge members
- • Tower structures
- • Framework elements
Mechanical Systems
- • Gear systems
- • Coupling design
- • Spring systems
- • Tool design