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Torsional Rigidity Formula

GoTorsional Rigidity using Torque and Length of Shaft Formula

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Torsional Rigidity is defined as how much an object of specified material resists twisting force, also known as torque. It is based on both the material of the object, as well as its shape. Check FAQs

TJ = G \cdot J

TJ - Torsional Rigidity?G - Modulus of Rigidity SOM?J - Polar Moment of Inertia?

Torsional Rigidity Example

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With units

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Here is how the Torsional Rigidity equation looks like with Values.

Here is how the Torsional Rigidity equation looks like with Units.

Here is how the Torsional Rigidity equation looks like.

90.2 = 0.022 \cdot 0.0041

90.2kN*m² = 0.022GPa \cdot 0.0041m⁴

90.2 = 0.022 \cdot 0.0041

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Torsional Rigidity Solution

Follow our step by step solution on how to calculate Torsional Rigidity?

FIRST Step Consider the formula

TJ = G \cdot J

Next Step Substitute values of Variables

∴

TJ = 0.022GPa \cdot 0.0041m⁴

Next Step Convert Units

∴

TJ = 2.2E+7Pa \cdot 0.0041m⁴

Next Step Prepare to Evaluate

∴

TJ = 2.2E+7 \cdot 0.0041

Next Step Evaluate

∴

TJ = 90200N*m²

LAST Step Convert to Output's Unit

∴

TJ = 90.2kN*m²

Torsional Rigidity Formula Elements

Variables

Torsional Rigidity

Torsional Rigidity is defined as how much an object of specified material resists twisting force, also known as torque. It is based on both the material of the object, as well as its shape.

Symbol: TJ

Measurement: Torsional RigidityUnit: kN*m²

Note: Value can be positive or negative.

Formulas to find Torsional Rigidity

Modulus of Rigidity SOM

Modulus of Rigidity SOM is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G.

Symbol: G

Measurement: PressureUnit: GPa

Note: Value can be positive or negative.

Formulas to find Modulus of Rigidity SOM

Polar Moment of Inertia

Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section.

Symbol: J

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Polar Moment of Inertia

Other Formulas to find Torsional Rigidity

Go Torsional Rigidity using Torque and Length of Shaft

TJ = \frac{T \cdot L shaft}{θ}

Other formulas in Torsional Rigidity category

Go Angle of Twist for Shaft using Torsional Rigidity

θ = \frac{T \cdot L shaft}{TJ}

Go Length of Shaft using Torsional Rigidity

L shaft = \frac{TJ \cdot θ}{T}

Go Modulus of Rigidity with Known Torsional Rigidity

G = \frac{TJ}{J}

Go Polar Moment of Inertia with Known Torsional Rigidity

J = \frac{TJ}{G}

How to Evaluate Torsional Rigidity?

Torsional Rigidity evaluator uses Torsional Rigidity = Modulus of Rigidity SOM*Polar Moment of Inertia to evaluate the Torsional Rigidity, The Torsional Rigidity formula is defined as the minimum force required to deform an object by twisting through a unit dimension. Torsional Rigidity is denoted by TJ symbol.

How to evaluate Torsional Rigidity using this online evaluator? To use this online evaluator for Torsional Rigidity, enter Modulus of Rigidity SOM (G) & Polar Moment of Inertia (J) and hit the calculate button.

FAQs on Torsional Rigidity

What is the formula to find Torsional Rigidity?

The formula of Torsional Rigidity is expressed as Torsional Rigidity = Modulus of Rigidity SOM*Polar Moment of Inertia. Here is an example- 0.0902 = 22000000*0.0041.

How to calculate Torsional Rigidity?

With Modulus of Rigidity SOM (G) & Polar Moment of Inertia (J) we can find Torsional Rigidity using the formula - Torsional Rigidity = Modulus of Rigidity SOM*Polar Moment of Inertia.

What are the other ways to Calculate Torsional Rigidity?

Here are the different ways to Calculate Torsional Rigidity-

Torsional Rigidity=(Torque*Length of Shaft)/Angle of Twist

Can the Torsional Rigidity be negative?

Yes, the Torsional Rigidity, measured in Torsional Rigidity can be negative.

Which unit is used to measure Torsional Rigidity?

Torsional Rigidity is usually measured using the Kilonewton Square Meter[kN*m²] for Torsional Rigidity. Newton Square Meter[kN*m²] are the few other units in which Torsional Rigidity can be measured.

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