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

GoShaft length for given maximum permissible shear stress and modulus of rigidity 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 J}{T}

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

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

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Here is how the Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle equation looks like with Values.

Here is how the Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle equation looks like with Units.

Here is how the Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle equation looks like.

8317.1429 = \frac{40 \cdot (1.42) \cdot 0.0041}{28}

8317.1429m = \frac{40GPa \cdot (1.42rad) \cdot 0.0041m⁴}{28kN*m}

8317.1429 = \frac{40 \cdot (1.42) \cdot 0.0041}{28}

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Strength of Materials » fx Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle

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

Follow our step by step solution on how to calculate Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L shaft = \frac{40GPa \cdot (1.42rad) \cdot 0.0041m⁴}{28kN*m}

Next Step Convert Units

∴

L shaft = \frac{4E+10Pa \cdot (1.42rad) \cdot 0.0041m⁴}{28000N*m}

Next Step Prepare to Evaluate

∴

L shaft = \frac{4E+10 \cdot (1.42) \cdot 0.0041}{28000}

Next Step Evaluate

∴

L shaft = 8317.14285714286m

LAST Step Rounding Answer

∴

L shaft = 8317.1429m

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

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

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

Other Formulas to find Length of Shaft

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

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

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 Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle?

Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle evaluator uses Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Polar Moment of Inertia)/Torque to evaluate the Length of Shaft, The Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle formula 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 Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle using this online evaluator? To use this online evaluator for Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle, enter Modulus of Rigidity (G_Torsion), Angle of Twist (θ), Polar Moment of Inertia (J) & Torque (T) and hit the calculate button.

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

What is the formula to find Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle?

The formula of Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle is expressed as Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Polar Moment of Inertia)/Torque. Here is an example- 8317.143 = (40000000000*(1.42)*0.0041)/28000.

How to calculate Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle?

With Modulus of Rigidity (G_Torsion), Angle of Twist (θ), Polar Moment of Inertia (J) & Torque (T) we can find Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle using the formula - Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Polar Moment of Inertia)/Torque.

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)*Radius of Shaft)/Maximum Shear Stress

Can the Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle be negative?

No, the Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle, measured in Length cannot be negative.

Which unit is used to measure Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle?

Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle 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 Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle can be measured.

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

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

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

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

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

Other Formulas to find Length of Shaft

Other formulas in Torsion category

How to Evaluate Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle?

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

Variable Name

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