Torsional Stiffness Calculator

Calculate the torsional stiffness (GJ/L) of a shaft from its shear modulus, polar moment of inertia, and length. Torsional stiffness defines the torque required per unit angle of twist.

TORSIONAL STIFFNESS
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Polar Moment J
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Angle of Twist
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Max Shear Stress
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Torsional Rigidity GJ
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What Is Torsional Stiffness?

Torsional stiffness is the resistance of a structural member to twisting deformation. It is defined as the torque required to produce a unit angle of twist and is expressed in N-m per radian (or N-m per degree). It depends on the material's shear modulus, the cross-section's polar moment of inertia, and the length of the member.

High torsional stiffness is essential in drive shafts, steering columns, and aircraft propeller shafts where excessive twist could lead to vibration, misalignment, or structural failure. Engineers design these components to minimize angular deflection under operating loads.

Formula & Derivation

Torsional Stiffness kt = GJ / L
Angle of Twist φ = TL / (GJ)
Max Shear Stress τ = T × r / J

G is the shear modulus (material property), J is the polar moment of inertia (geometric property), and L is the shaft length. The maximum shear stress occurs at the outer surface of the shaft where r is the outer radius.

Material Comparison

MaterialG (GPa)Relative Stiffness
Steel801.00
Aluminum260.33
Titanium420.53
Carbon Fiber Composite5-30varies

Frequently Asked Questions

How do I increase torsional stiffness?

Increase the shaft diameter (stiffness scales with d^4), use a stiffer material (higher G), or reduce the shaft length. Using a hollow section with a larger outer diameter can achieve the same stiffness at lower weight compared to a smaller solid shaft.

What is the difference between torsional stiffness and torsional rigidity?

Torsional rigidity GJ is a property per unit length (N-m^2), while torsional stiffness GJ/L is the total resistance of a specific shaft length (N-m/rad). Rigidity is independent of length; stiffness depends on it.

Why is torsional stiffness important in vehicles?

In vehicle chassis design, torsional stiffness determines handling quality. A stiffer chassis resists body flex during cornering, allowing suspension geometry to work as designed. Modern sports cars target chassis torsional stiffness above 20,000 N-m/degree.