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

✖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 [J]			+10% -10%
✖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 given Twisting moment and Polar Moment of Inertia of shaft [R]

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

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Radius of Shaft - (Measured in Millimeter) - 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.
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.

STEP 1: Convert Input(s) to Base Unit

Maximum Shear Stress: 42 Megapascal --> 42000000 Pascal (Check conversion here)
Polar Moment of Inertia: 0.0041 Meter⁴ --> 0.0041 Meter⁴ No Conversion Required
Torque: 28 Kilonewton Meter --> 28000 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R = τ_max*J/T --> 42000000*0.0041/28000

Evaluating ... ...

R = 6.15

STEP 3: Convert Result to Output's Unit

0.00615 Meter -->6.15 Millimeter (Check conversion here)

FINAL ANSWER

6.15 Millimeter <-- Radius of Shaft

(Calculation completed in 00.004 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal

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< Torsion Calculators

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

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

LaTeX Go

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

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

Radius given Twisting moment and Polar Moment of Inertia of shaft calculator uses Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque to calculate 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 calculate Radius given Twisting moment and Polar Moment of Inertia of shaft using this online calculator? To use this online calculator 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. Here is how the Radius given Twisting moment and Polar Moment of Inertia of shaft calculation can be explained with given input values -> 6.15 = 42000000*0.0041/28000.

FAQ

What is Radius given Twisting moment and Polar Moment of Inertia of shaft?

The Radius given Twisting moment and Polar Moment of Inertia of shaft is defined as the radius of the shaft cross-section and is represented as R = τ_max*J/T or Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque. Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area, 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 is a measure of the force that can cause an object to rotate about an axis.

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

The Radius given Twisting moment and Polar Moment of Inertia of shaft is defined as the radius of the shaft cross-section is calculated using Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque. To calculate Radius given Twisting moment and Polar Moment of Inertia of shaft, you need Maximum Shear Stress (τ_max), Polar Moment of Inertia (J) & Torque (T). With our tool, you need to enter the respective value for Maximum Shear Stress, Polar Moment of Inertia & Torque 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 Radius of Shaft?

In this formula, Radius of Shaft uses Maximum Shear Stress, Polar Moment of Inertia & Torque. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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