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Radius given Twisting moment and Polar Moment of Inertia of shaft Formula

GoRadius with known Maximum permissible shear stress Formula

GoRadius given Torsional Section Modulus Formula

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

R = τ max \cdot \frac{J}{T}

R - Radius of Shaft?τ_max - Maximum Shear Stress?J - Polar Moment of Inertia?T - Torque?

Radius given Twisting moment and Polar Moment of Inertia of shaft Example

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Here is how the Radius given Twisting moment and Polar Moment of Inertia of shaft equation looks like with Values.

Here is how the Radius given Twisting moment and Polar Moment of Inertia of shaft equation looks like with Units.

Here is how the Radius given Twisting moment and Polar Moment of Inertia of shaft equation looks like.

6.15 = 42 \cdot \frac{0.0041}{28}

6.15mm = 42MPa \cdot \frac{0.0041m⁴}{28kN*m}

6.15 = 42 \cdot \frac{0.0041}{28}

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Radius given Twisting moment and Polar Moment of Inertia of shaft Solution

Follow our step by step solution on how to calculate Radius given Twisting moment and Polar Moment of Inertia of shaft?

FIRST Step Consider the formula

R = τ max \cdot \frac{J}{T}

Next Step Substitute values of Variables

∴

R = 42MPa \cdot \frac{0.0041m⁴}{28kN*m}

Next Step Convert Units

∴

R = 4.2E+7Pa \cdot \frac{0.0041m⁴}{28000N*m}

Next Step Prepare to Evaluate

∴

R = 4.2E+7 \cdot \frac{0.0041}{28000}

Next Step Evaluate

∴

R = 0.00615m

LAST Step Convert to Output's Unit

∴

R = 6.15mm

Radius given Twisting moment and Polar Moment of Inertia of shaft Formula Elements

Variables

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

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 Radius of Shaft

Go Radius with known Maximum permissible shear stress

R = τ max \cdot \frac{J}{T}

Go Radius given Torsional Section Modulus

R = \frac{J}{Z p}

Go Radius of Shaft using Polar Modulus

R = \frac{J}{Z p}

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 Maximum permissible shear stress for given Radius and modulus of rigidity

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

Go Modulus of rigidity given maximum permissible shear stress

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

How to Evaluate Radius given Twisting moment and Polar Moment of Inertia of shaft?

Radius given Twisting moment and Polar Moment of Inertia of shaft evaluator uses Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque to evaluate the Radius of Shaft, The Radius given Twisting moment and Polar Moment of Inertia of shaft is defined as the radius of the shaft cross-section. Radius of Shaft is denoted by R symbol.

How to evaluate Radius given Twisting moment and Polar Moment of Inertia of shaft using this online evaluator? To use this online evaluator for Radius given Twisting moment and Polar Moment of Inertia of shaft, enter Maximum Shear Stress (τ_max), Polar Moment of Inertia (J) & Torque (T) and hit the calculate button.

FAQs on Radius given Twisting moment and Polar Moment of Inertia of shaft

What is the formula to find Radius given Twisting moment and Polar Moment of Inertia of shaft?

The formula of Radius given Twisting moment and Polar Moment of Inertia of shaft is expressed as Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque. Here is an example- 6.15 = 42000000*0.0041/28000.

How to calculate Radius given Twisting moment and Polar Moment of Inertia of shaft?

With Maximum Shear Stress (τ_max), Polar Moment of Inertia (J) & Torque (T) we can find Radius given Twisting moment and Polar Moment of Inertia of shaft using the formula - Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque.

What are the other ways to Calculate Radius of Shaft?

Here are the different ways to Calculate Radius of Shaft-

Radius of Shaft=Maximum Shear Stress*Polar Moment of Inertia/Torque
Radius of Shaft=Polar Moment of Inertia/Polar Modulus
Radius of Shaft=Polar Moment of Inertia/Polar Modulus

Can the Radius given Twisting moment and Polar Moment of Inertia of shaft be negative?

No, the Radius given Twisting moment and Polar Moment of Inertia of shaft, measured in Length cannot be negative.

Which unit is used to measure Radius given Twisting moment and Polar Moment of Inertia of shaft?

Radius given Twisting moment and Polar Moment of Inertia of shaft is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Radius given Twisting moment and Polar Moment of Inertia of shaft can be measured.

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Radius given Twisting moment and Polar Moment of Inertia of shaft Formula

​GoRadius with known Maximum permissible shear stress Formula

​GoRadius given Torsional Section Modulus Formula

Radius given Twisting moment and Polar Moment of Inertia of shaft Example

Radius given Twisting moment and Polar Moment of Inertia of shaft Solution

Radius given Twisting moment and Polar Moment of Inertia of shaft Formula Elements

Other Formulas to find Radius of Shaft

Other formulas in Torsion category

How to Evaluate Radius given Twisting moment and Polar Moment of Inertia of shaft?

FAQs on Radius given Twisting moment and Polar Moment of Inertia of shaft

Variable Name

GoRadius with known Maximum permissible shear stress Formula

GoRadius given Torsional Section Modulus Formula