Polar Moment of Inertia given twisting moment along with maximum permissible shear stress Calculator

✖Torque is a measure of the force that can cause an object to rotate about an axis.ⓘ Torque [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%

✖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.ⓘ Polar Moment of Inertia given twisting moment along with maximum permissible shear stress [J]

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Polar Moment of Inertia given twisting moment along with maximum permissible shear stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Polar Moment of Inertia - (Measured in Meter⁴) - 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.
Torque - (Measured in Newton Meter) - Torque is a measure of the force that can cause an object to rotate about an axis.
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 Pascal) - 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

Torque: 28 Kilonewton Meter --> 28000 Newton Meter (Check conversion here)
Radius of Shaft: 110 Millimeter --> 0.11 Meter (Check conversion here)
Maximum Shear Stress: 42 Megapascal --> 42000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = T*R/τ_max --> 28000*0.11/42000000

Evaluating ... ...

J = 7.33333333333333E-05

STEP 3: Convert Result to Output's Unit

7.33333333333333E-05 Meter⁴ --> No Conversion Required

FINAL ANSWER

7.33333333333333E-05 ≈ 7.3E-5 Meter⁴ <-- Polar Moment of Inertia

(Calculation completed in 00.004 seconds)

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Maximum permissible shear stress for given Radius and modulus of rigidity

LaTeX Go Maximum Shear Stress = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Length of Shaft

Twisting Moment given Maximum Permissible Shear Stress

LaTeX Go Torque = (Polar Moment of Inertia*Maximum Shear Stress)/Radius of Shaft

Radius with known Maximum permissible shear stress

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

Maximum permissible shear stress

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

Polar Moment of Inertia given twisting moment along with maximum permissible shear stress Formula

LaTeX Go

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

What is Torsion?

n the field of solid mechanics, torsion is the twisting of an object due to an applied torque. Torsion is expressed in either the Pascal, an SI unit for newtons per square metre, or in pounds per square inch while torque is expressed in newton metres or foot-pound force.

How to Calculate Polar Moment of Inertia given twisting moment along with maximum permissible shear stress?

Polar Moment of Inertia given twisting moment along with maximum permissible shear stress calculator uses Polar Moment of Inertia = Torque*Radius of Shaft/Maximum Shear Stress to calculate the Polar Moment of Inertia, The Polar Moment of Inertia given twisting moment along with maximum permissible shear stress is defined as the resistance towards torsion. Polar Moment of Inertia is denoted by J symbol.

How to calculate Polar Moment of Inertia given twisting moment along with maximum permissible shear stress using this online calculator? To use this online calculator for Polar Moment of Inertia given twisting moment along with maximum permissible shear stress, enter Torque (T), Radius of Shaft (R) & Maximum Shear Stress (τ_max) and hit the calculate button. Here is how the Polar Moment of Inertia given twisting moment along with maximum permissible shear stress calculation can be explained with given input values -> 7.3E-5 = 28000*0.11/42000000.

FAQ

What is Polar Moment of Inertia given twisting moment along with maximum permissible shear stress?

The Polar Moment of Inertia given twisting moment along with maximum permissible shear stress is defined as the resistance towards torsion and is represented as J = T*R/τ_max or Polar Moment of Inertia = Torque*Radius of Shaft/Maximum Shear Stress. Torque is a measure of the force that can cause an object to rotate about an axis, 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 twisting moment along with maximum permissible shear stress?

The Polar Moment of Inertia given twisting moment along with maximum permissible shear stress is defined as the resistance towards torsion is calculated using Polar Moment of Inertia = Torque*Radius of Shaft/Maximum Shear Stress. To calculate Polar Moment of Inertia given twisting moment along with maximum permissible shear stress, you need Torque (T), Radius of Shaft (R) & Maximum Shear Stress (τ_max). With our tool, you need to enter the respective value for Torque, 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.

How many ways are there to calculate Polar Moment of Inertia?

In this formula, Polar Moment of Inertia uses Torque, Radius of Shaft & Maximum Shear Stress. We can use 2 other way(s) to calculate the same, which is/are as follows -

Polar Moment of Inertia = (Torque*Length of Shaft)/(Angle of Twist*Modulus of Rigidity)
Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4)

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