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Polar Moment of Inertia given Torsional Shear Stress Formula

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The Polar Moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape. Check FAQs

J = \frac{T \cdot R}{τ max}

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

Polar Moment of Inertia given Torsional Shear Stress Example

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Here is how the Polar Moment of Inertia given Torsional Shear Stress equation looks like with Values.

Here is how the Polar Moment of Inertia given Torsional Shear Stress equation looks like with Units.

Here is how the Polar Moment of Inertia given Torsional Shear Stress equation looks like.

2.2262 = \frac{0.85 \cdot 110}{42}

2.2262mm⁴ = \frac{0.85kN*m \cdot 110mm}{42MPa}

2.2262 = \frac{0.85 \cdot 110}{42}

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Polar Moment of Inertia given Torsional Shear Stress Solution

Follow our step by step solution on how to calculate Polar Moment of Inertia given Torsional Shear Stress?

FIRST Step Consider the formula

J = \frac{T \cdot R}{τ max}

Next Step Substitute values of Variables

∴

J = \frac{0.85kN*m \cdot 110mm}{42MPa}

Next Step Convert Units

∴

J = \frac{850N*m \cdot 0.11m}{42MPa}

Next Step Prepare to Evaluate

∴

J = \frac{850 \cdot 0.11}{42}

Next Step Evaluate

∴

J = 2.22619047619048E-12m⁴

Next Step Convert to Output's Unit

∴

J = 2.22619047619048mm⁴

LAST Step Rounding Answer

∴

J = 2.2262mm⁴

Polar Moment of Inertia given Torsional Shear Stress Formula Elements

Variables

Polar Moment of Inertia

The Polar Moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.

Symbol: J

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Polar Moment of Inertia

Torsional Moment

Torsional Moment is the torque applied to generate a torsion (twist) within the object.

Symbol: T

Measurement: TorqueUnit: kN*m

Note: Value can be positive or negative.

Formulas to find Torsional Moment

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 in I Beam category

Go Longitudinal Shear Stress in Flange at Lower Depth of I beam

τ = (\frac{V}{8 \cdot I}) \cdot (D^{2} - {d w}^{2})

Go Transverse Shear given Longitudinal Shear Stress in Flange for I beam

V = \frac{8 \cdot I \cdot τ}{D^{2} - {d w}^{2}}

Go Moment of Inertia given Longitudinal Shear Stress at lower edge in Flange of I beam

I = (\frac{V}{8 \cdot τ}) \cdot (D^{2} - {d w}^{2})

Go Moment of Inertia given Longitudinal Shear Stress in Web for I beam

I = (\frac{b f \cdot V}{8 \cdot τ \cdot b w}) \cdot (D^{2} - {d w}^{2})

How to Evaluate Polar Moment of Inertia given Torsional Shear Stress?

Polar Moment of Inertia given Torsional Shear Stress evaluator uses Polar Moment of Inertia = (Torsional Moment*Radius of Shaft)/(Maximum Shear Stress) to evaluate the Polar Moment of Inertia, The Polar Moment of Inertia given Torsional Shear Stress is defined as a shaft or beam's resistance to being distorted by torsion, as a function of its shape. The greater the magnitude of the polar moment of inertia, the greater the torsional resistance of the object. Polar Moment of Inertia is denoted by J symbol.

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

FAQs on Polar Moment of Inertia given Torsional Shear Stress

What is the formula to find Polar Moment of Inertia given Torsional Shear Stress?

The formula of Polar Moment of Inertia given Torsional Shear Stress is expressed as Polar Moment of Inertia = (Torsional Moment*Radius of Shaft)/(Maximum Shear Stress). Here is an example- 2.2E+12 = (850*0.11)/(42000000).

How to calculate Polar Moment of Inertia given Torsional Shear Stress?

With Torsional Moment (T), Radius of Shaft (R) & Maximum Shear Stress (τ_max) we can find Polar Moment of Inertia given Torsional Shear Stress using the formula - Polar Moment of Inertia = (Torsional Moment*Radius of Shaft)/(Maximum Shear Stress).

Can the Polar Moment of Inertia given Torsional Shear Stress be negative?

No, the Polar Moment of Inertia given Torsional Shear Stress, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Polar Moment of Inertia given Torsional Shear Stress?

Polar Moment of Inertia given Torsional Shear Stress is usually measured using the Millimeter⁴[mm⁴] for Second Moment of Area. Meter⁴[mm⁴], Centimeter⁴[mm⁴] are the few other units in which Polar Moment of Inertia given Torsional Shear Stress can be measured.

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Polar Moment of Inertia given Torsional Shear Stress Formula

Polar Moment of Inertia given Torsional Shear Stress Example

Polar Moment of Inertia given Torsional Shear Stress Solution

Polar Moment of Inertia given Torsional Shear Stress Formula Elements

Other formulas in I Beam category

How to Evaluate Polar Moment of Inertia given Torsional Shear Stress?

FAQs on Polar Moment of Inertia given Torsional Shear Stress

Variable Name