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Modulus 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{τ max \cdot L shaft}{θ \cdot R}

G_Torsion - Modulus of Rigidity?τ_max - Maximum Shear Stress?L_shaft - Length of Shaft?θ - Angle of Twist?R - Radius of Shaft?

Modulus of rigidity given maximum permissible shear stress Example

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Here is how the Modulus of rigidity given maximum permissible shear stress equation looks like with Values.

Here is how the Modulus of rigidity given maximum permissible shear stress equation looks like with Units.

Here is how the Modulus of rigidity given maximum permissible shear stress equation looks like.

1.2315 = \frac{42 \cdot 4.58}{1.42 \cdot 110}

1.2315GPa = \frac{42MPa \cdot 4.58m}{1.42rad \cdot 110mm}

1.2315 = \frac{42 \cdot 4.58}{1.42 \cdot 110}

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Modulus of rigidity given maximum permissible shear stress Solution

Follow our step by step solution on how to calculate Modulus of rigidity given maximum permissible shear stress?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

G Torsion = \frac{42MPa \cdot 4.58m}{1.42rad \cdot 110mm}

Next Step Convert Units

∴

G Torsion = \frac{4.2E+7Pa \cdot 4.58m}{1.42rad \cdot 0.11m}

Next Step Prepare to Evaluate

∴

G Torsion = \frac{4.2E+7 \cdot 4.58}{1.42 \cdot 0.11}

Next Step Evaluate

∴

G Torsion = 1231498079.3854Pa

Next Step Convert to Output's Unit

∴

G Torsion = 1.2314980793854GPa

LAST Step Rounding Answer

∴

G Torsion = 1.2315GPa

Modulus of rigidity given maximum permissible shear stress 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

Maximum Shear Stress

Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.

Symbol: τ_max

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Shear Stress

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

Radius of Shaft

The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.

Symbol: R

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Shaft

Other Formulas to find Modulus of Rigidity

Go Modulus of rigidity

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

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 given maximum permissible shear stress?

Modulus of rigidity given maximum permissible shear stress evaluator uses Modulus of Rigidity = (Maximum Shear Stress*Length of Shaft)/(Angle of Twist*Radius of Shaft) to evaluate the Modulus of Rigidity, The Modulus of rigidity given maximum permissible shear stress, twist angle, and shaft length 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 given maximum permissible shear stress using this online evaluator? To use this online evaluator for Modulus of rigidity given maximum permissible shear stress, enter Maximum Shear Stress (τ_max), Length of Shaft (L_shaft), Angle of Twist (θ) & Radius of Shaft (R) and hit the calculate button.

FAQs on Modulus of rigidity given maximum permissible shear stress

What is the formula to find Modulus of rigidity given maximum permissible shear stress?

The formula of Modulus of rigidity given maximum permissible shear stress is expressed as Modulus of Rigidity = (Maximum Shear Stress*Length of Shaft)/(Angle of Twist*Radius of Shaft). Here is an example- 1.2E-9 = (42000000*4.58)/(1.42*0.11).

How to calculate Modulus of rigidity given maximum permissible shear stress?

With Maximum Shear Stress (τ_max), Length of Shaft (L_shaft), Angle of Twist (θ) & Radius of Shaft (R) we can find Modulus of rigidity given maximum permissible shear stress using the formula - Modulus of Rigidity = (Maximum Shear Stress*Length of Shaft)/(Angle of Twist*Radius of Shaft).

What are the other ways to Calculate Modulus of Rigidity?

Here are the different ways to Calculate Modulus of Rigidity-

Modulus of Rigidity=(Torque*Length of Shaft)/(Angle of Twist*Polar Moment of Inertia)

Can the Modulus of rigidity given maximum permissible shear stress be negative?

No, the Modulus of rigidity given maximum permissible shear stress, measured in Pressure cannot be negative.

Which unit is used to measure Modulus of rigidity given maximum permissible shear stress?

Modulus of rigidity given maximum permissible shear stress 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 given maximum permissible shear stress can be measured.

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Modulus of rigidity given maximum permissible shear stress Formula

​GoModulus of rigidity Formula

Modulus of rigidity given maximum permissible shear stress Example

Modulus of rigidity given maximum permissible shear stress Solution

Modulus of rigidity given maximum permissible shear stress Formula Elements

Other Formulas to find Modulus of Rigidity

Other formulas in Torsion category

How to Evaluate Modulus of rigidity given maximum permissible shear stress?

FAQs on Modulus of rigidity given maximum permissible shear stress

Variable Name

GoModulus of rigidity Formula