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Shaft length for given maximum permissible shear stress and modulus of rigidity Formula

GoShaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle Formula

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

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

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

Shaft length for given maximum permissible shear stress and modulus of rigidity Example

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Here is how the Shaft length for given maximum permissible shear stress and modulus of rigidity equation looks like with Values.

Here is how the Shaft length for given maximum permissible shear stress and modulus of rigidity equation looks like with Units.

Here is how the Shaft length for given maximum permissible shear stress and modulus of rigidity equation looks like.

148.7619 = \frac{40 \cdot (1.42) \cdot 110}{42}

148.7619m = \frac{40GPa \cdot (1.42rad) \cdot 110mm}{42MPa}

148.7619 = \frac{40 \cdot (1.42) \cdot 110}{42}

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Shaft length for given maximum permissible shear stress and modulus of rigidity Solution

Follow our step by step solution on how to calculate Shaft length for given maximum permissible shear stress and modulus of rigidity?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L shaft = \frac{40GPa \cdot (1.42rad) \cdot 110mm}{42MPa}

Next Step Convert Units

∴

L shaft = \frac{4E+10Pa \cdot (1.42rad) \cdot 0.11m}{4.2E+7Pa}

Next Step Prepare to Evaluate

∴

L shaft = \frac{4E+10 \cdot (1.42) \cdot 0.11}{4.2E+7}

Next Step Evaluate

∴

L shaft = 148.761904761905m

LAST Step Rounding Answer

∴

L shaft = 148.7619m

Shaft length for given maximum permissible shear stress and modulus of rigidity Formula Elements

Variables

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

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

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

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

Other Formulas to find Length of Shaft

Go Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle

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

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 Shaft length for given maximum permissible shear stress and modulus of rigidity?

Shaft length for given maximum permissible shear stress and modulus of rigidity evaluator uses Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Maximum Shear Stress to evaluate the Length of Shaft, The Shaft length for given maximum permissible shear stress and modulus of rigidity along with twist angle is defined as the length of the shaft that is undergoing torsion. Length of Shaft is denoted by L_shaft symbol.

How to evaluate Shaft length for given maximum permissible shear stress and modulus of rigidity using this online evaluator? To use this online evaluator for Shaft length for given maximum permissible shear stress and modulus of rigidity, enter Modulus of Rigidity (G_Torsion), Angle of Twist (θ), Radius of Shaft (R) & Maximum Shear Stress (τ_max) and hit the calculate button.

FAQs on Shaft length for given maximum permissible shear stress and modulus of rigidity

What is the formula to find Shaft length for given maximum permissible shear stress and modulus of rigidity?

The formula of Shaft length for given maximum permissible shear stress and modulus of rigidity is expressed as Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Maximum Shear Stress. Here is an example- 148.7619 = (40000000000*(1.42)*0.11)/42000000.

How to calculate Shaft length for given maximum permissible shear stress and modulus of rigidity?

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

What are the other ways to Calculate Length of Shaft?

Here are the different ways to Calculate Length of Shaft-

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

Can the Shaft length for given maximum permissible shear stress and modulus of rigidity be negative?

No, the Shaft length for given maximum permissible shear stress and modulus of rigidity, measured in Length cannot be negative.

Which unit is used to measure Shaft length for given maximum permissible shear stress and modulus of rigidity?

Shaft length for given maximum permissible shear stress and modulus of rigidity is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Shaft length for given maximum permissible shear stress and modulus of rigidity can be measured.

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Shaft length for given maximum permissible shear stress and modulus of rigidity Formula

​GoShaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle Formula

Shaft length for given maximum permissible shear stress and modulus of rigidity Example

Shaft length for given maximum permissible shear stress and modulus of rigidity Solution

Shaft length for given maximum permissible shear stress and modulus of rigidity Formula Elements

Other Formulas to find Length of Shaft

Other formulas in Torsion category

How to Evaluate Shaft length for given maximum permissible shear stress and modulus of rigidity?

FAQs on Shaft length for given maximum permissible shear stress and modulus of rigidity

Variable Name

GoShaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle Formula