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Modulus of rigidity Formula

GoModulus of rigidity given maximum permissible shear stress Formula

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Modulus of Rigidity 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. Check FAQs

G Torsion = \frac{T \cdot L shaft}{θ \cdot J}

G_Torsion - Modulus of Rigidity?T - Torque?L_shaft - Length of Shaft?θ - Angle of Twist?J - Polar Moment of Inertia?

Modulus of rigidity Example

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Here is how the Modulus of rigidity equation looks like with Values.

Here is how the Modulus of rigidity equation looks like with Units.

Here is how the Modulus of rigidity equation looks like.

0.022 = \frac{28 \cdot 4.58}{1.42 \cdot 0.0041}

0.022GPa = \frac{28kN*m \cdot 4.58m}{1.42rad \cdot 0.0041m⁴}

0.022 = \frac{28 \cdot 4.58}{1.42 \cdot 0.0041}

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Modulus of rigidity Solution

Follow our step by step solution on how to calculate Modulus of rigidity?

FIRST Step Consider the formula

G Torsion = \frac{T \cdot L shaft}{θ \cdot J}

Next Step Substitute values of Variables

∴

G Torsion = \frac{28kN*m \cdot 4.58m}{1.42rad \cdot 0.0041m⁴}

Next Step Convert Units

∴

G Torsion = \frac{28000N*m \cdot 4.58m}{1.42rad \cdot 0.0041m⁴}

Next Step Prepare to Evaluate

∴

G Torsion = \frac{28000 \cdot 4.58}{1.42 \cdot 0.0041}

Next Step Evaluate

∴

G Torsion = 22026794.9158365Pa

Next Step Convert to Output's Unit

∴

G Torsion = 0.0220267949158365GPa

LAST Step Rounding Answer

∴

G Torsion = 0.022GPa

Modulus of rigidity Formula Elements

Variables

Modulus of Rigidity

Modulus of Rigidity 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_Torsion

Measurement: PressureUnit: GPa

Note: Value should be greater than 0.

Formulas to find Modulus of Rigidity

Torque

Torque is a measure of the force that can cause an object to rotate about an axis.

Symbol: T

Measurement: TorqueUnit: kN*m

Note: Value can be positive or negative.

Formulas to find Torque

Length of Shaft

Length of Shaft is the distance between two ends of shaft.

Symbol: L_shaft

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Angle of Twist

Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.

Symbol: θ

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Angle of Twist

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 Modulus of Rigidity

Go Modulus of rigidity given maximum permissible shear stress

G Torsion = \frac{τ max \cdot L shaft}{θ \cdot R}

Other formulas in Torsion category

Go Twisting Moment given Maximum Permissible Shear Stress

T = \frac{J \cdot τ max}{R}

Go Maximum permissible shear stress

τ max = T \cdot \frac{R}{J}

Go Radius with known Maximum permissible shear stress

R = τ max \cdot \frac{J}{T}

Go Maximum permissible shear stress for given Radius and modulus of rigidity

τ max = \frac{G Torsion \cdot (θ) \cdot R}{L shaft}

How to Evaluate Modulus of rigidity?

Modulus of rigidity evaluator uses Modulus of Rigidity = (Torque*Length of Shaft)/(Angle of Twist*Polar Moment of Inertia) to evaluate the Modulus of Rigidity, The Modulus of rigidity when Shaft length, Polar MOI, Twisting Moment, and Twist angle is defined as the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Modulus of Rigidity is denoted by G_Torsion symbol.

How to evaluate Modulus of rigidity using this online evaluator? To use this online evaluator for Modulus of rigidity, enter Torque (T), Length of Shaft (L_shaft), Angle of Twist (θ) & Polar Moment of Inertia (J) and hit the calculate button.

FAQs on Modulus of rigidity

What is the formula to find Modulus of rigidity?

The formula of Modulus of rigidity is expressed as Modulus of Rigidity = (Torque*Length of Shaft)/(Angle of Twist*Polar Moment of Inertia). Here is an example- 2.2E-11 = (28000*4.58)/(1.42*0.0041).

How to calculate Modulus of rigidity?

With Torque (T), Length of Shaft (L_shaft), Angle of Twist (θ) & Polar Moment of Inertia (J) we can find Modulus of rigidity using the formula - Modulus of Rigidity = (Torque*Length of Shaft)/(Angle of Twist*Polar Moment of Inertia).

What are the other ways to Calculate Modulus of Rigidity?

Here are the different ways to Calculate Modulus of Rigidity-

Modulus of Rigidity=(Maximum Shear Stress*Length of Shaft)/(Angle of Twist*Radius of Shaft)

Can the Modulus of rigidity be negative?

No, the Modulus of rigidity, measured in Pressure cannot be negative.

Which unit is used to measure Modulus of rigidity?

Modulus of rigidity is usually measured using the Gigapascal[GPa] for Pressure. Pascal[GPa], Kilopascal[GPa], Bar[GPa] are the few other units in which Modulus of rigidity can be measured.

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Modulus of rigidity Formula

​GoModulus of rigidity given maximum permissible shear stress Formula

Modulus of rigidity Example

Modulus of rigidity Solution

Modulus of rigidity Formula Elements

Other Formulas to find Modulus of Rigidity

Other formulas in Torsion category

How to Evaluate Modulus of rigidity?

FAQs on Modulus of rigidity

Variable Name

GoModulus of rigidity given maximum permissible shear stress Formula