Polar Moment of Inertia given Torsional Shear Stress Calculator

✖Torsional Moment is the torque applied to generate a torsion (twist) within the object.ⓘ Torsional Moment [T]			+10% -10%
✖The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.ⓘ Radius of Shaft [R]			+10% -10%
✖Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.ⓘ Maximum Shear Stress [τ_max]			+10% -10%

✖The Polar Moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.ⓘ Polar Moment of Inertia given Torsional Shear Stress [J]

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Polar Moment of Inertia given Torsional Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Moment of Inertia = (Torsional Moment*Radius of Shaft)/(Maximum Shear Stress)
J = (T*R)/(τ_max)
This formula uses 4 Variables

Variables Used

Polar Moment of Inertia - (Measured in Millimeter⁴) - The Polar Moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.
Torsional Moment - (Measured in Newton Meter) - Torsional Moment is the torque applied to generate a torsion (twist) within the object.
Radius of Shaft - (Measured in Meter) - The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.
Maximum Shear Stress - (Measured in Megapascal) - Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.

STEP 1: Convert Input(s) to Base Unit

Torsional Moment: 0.85 Kilonewton Meter --> 850 Newton Meter (Check conversion here)
Radius of Shaft: 110 Millimeter --> 0.11 Meter (Check conversion here)
Maximum Shear Stress: 42 Megapascal --> 42 Megapascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = (T*R)/(τ_max) --> (850*0.11)/(42)

Evaluating ... ...

J = 2.22619047619048

STEP 3: Convert Result to Output's Unit

2.22619047619048E-12 Meter⁴ -->2.22619047619048 Millimeter⁴ (Check conversion here)

FINAL ANSWER

2.22619047619048 ≈ 2.22619 Millimeter⁴ <-- Polar Moment of Inertia

(Calculation completed in 00.020 seconds)

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Polar Moment of Inertia given Torsional Shear Stress Formula

LaTeX Go

Polar Moment of Inertia = (Torsional Moment*Radius of Shaft)/(Maximum Shear Stress)
J = (T*R)/(τ_max)

What is Polar Moment of Inertia?

The Polar Moment of Inertia basically describes the cylindrical object's (including its segments) resistance to torsional deformation when torque is applied in a plane that is parallel to the cross-section area or in a plane that is perpendicular to the object's central axis.

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

Polar Moment of Inertia given Torsional Shear Stress calculator uses Polar Moment of Inertia = (Torsional Moment*Radius of Shaft)/(Maximum Shear Stress) to calculate 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 calculate Polar Moment of Inertia given Torsional Shear Stress using this online calculator? To use this online calculator 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. Here is how the Polar Moment of Inertia given Torsional Shear Stress calculation can be explained with given input values -> 2.2E+12 = (850*0.11)/(42000000).

FAQ

What is Polar Moment of Inertia given Torsional Shear Stress?

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 and is represented as J = (T*R)/(τ_max) or Polar Moment of Inertia = (Torsional Moment*Radius of Shaft)/(Maximum Shear Stress). Torsional Moment is the torque applied to generate a torsion (twist) within the object, The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface & Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.

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

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 is calculated using Polar Moment of Inertia = (Torsional Moment*Radius of Shaft)/(Maximum Shear Stress). To calculate Polar Moment of Inertia given Torsional Shear Stress, you need Torsional Moment (T), Radius of Shaft (R) & Maximum Shear Stress (τ_max). With our tool, you need to enter the respective value for Torsional Moment, Radius of Shaft & Maximum Shear Stress and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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