Torsional Stiffness Calculator
Calculate torsional stiffness for beams, shafts, and torsional springs using multiple methods
Calculate Torsional Stiffness
Use measured torque and angle of twist
External torque applied to the member
Angular deformation due to applied torque
Torsional Stiffness Results
Formula: k = T/φ
Method: Experimental measurement
Application: Any torsional system with measured data
Engineering Notes
Example Calculation
Experimental Method Example
Applied Torque: 80,000 N·m
Measured Angle of Twist: 0.02037 rad
Formula: k = T/φ
Calculation
k = T/φ
k = 80,000 N·m / 0.02037 rad
k = 3,927,344 N·m/rad
Calculation Methods
Experimental (k = T/φ)
Uses measured torque and twist angle
✓ Works for any torsional system
Beam Theory (k = GJ/L)
Uses material and geometric properties
✓ Design calculations for straight beams
Torsional Spring
Specialized formula for helical springs
✓ Spring design and analysis
Torsional Stiffness Tips
Higher stiffness means less angular deflection
Circular cross-sections are most efficient
Shorter lengths increase stiffness
Material properties significantly affect stiffness
Consider temperature effects on material properties
Understanding Torsional Stiffness
What is Torsional Stiffness?
Torsional stiffness is the resistance of a structural member to angular deformation when subjected to a torsional load (torque). It's analogous to the spring constant in linear systems but applies to rotational motion and twisting deformation.
Key Applications
- •Shaft design in machinery
- •Torsional spring design
- •Structural beam analysis
- •Vehicle suspension systems
Fundamental Equations
k = T/φ
General definition (experimental)
k = GJ/L
Beam theory (theoretical)
k = d⁴E/(64DNₐ)
Torsional spring formula
Units and Dimensions
- SI Units: N·m/rad
- Imperial: lbf·ft/rad, lbf·in/rad
- Dimension: [M L² T⁻²]
Method Comparison
| Method | Formula | Applications | Advantages | Limitations |
|---|---|---|---|---|
| Experimental | k = T/φ | Any torsional system | Universal applicability | Requires testing |
| Beam Theory | k = GJ/L | Straight beams, shafts | Design calculations | Linear elastic only |
| Torsional Spring | k = d⁴E/(64DNₐ) | Helical springs | Spring-specific | Helical geometry only |