Radius given Torsional Section Modulus Calculator

✖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%
✖The Polar Modulus of the shaft section is equal to the ratio of the polar moment of inertia to the radius of the shaft. It is denoted by Zp.ⓘ Polar Modulus [Z_p]			+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 Torsional Section Modulus [R]

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Formula

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Radius given Torsional Section Modulus

Formula

`"R" = "J"/"Z"_{"p"}`

Example

`"911.1111mm"="4.1e-3m⁴"/"4.5e-3m³"`

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Radius given Torsional Section Modulus Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Shaft = Polar Moment of Inertia/Polar Modulus
R = J/Z_p
This formula uses 3 Variables

Variables Used

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.
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.
Polar Modulus - (Measured in Cubic Meter) - The Polar Modulus of the shaft section is equal to the ratio of the polar moment of inertia to the radius of the shaft. It is denoted by Zp.

STEP 1: Convert Input(s) to Base Unit

Polar Moment of Inertia: 0.0041 Meter⁴ --> 0.0041 Meter⁴ No Conversion Required
Polar Modulus: 0.0045 Cubic Meter --> 0.0045 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R = J/Z_p --> 0.0041/0.0045

Evaluating ... ...

R = 0.911111111111111

STEP 3: Convert Result to Output's Unit

0.911111111111111 Meter -->911.111111111111 Millimeter (Check conversion here)

FINAL ANSWER

911.111111111111 ≈ 911.1111 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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< 18 Torsion Calculators

Shaft length for given maximum permissible shear stress and modulus of rigidity

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

Maximum permissible shear stress for given Radius and modulus of rigidity

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

Modulus of rigidity given maximum permissible shear stress

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

Twist angle given maximum permissible shear stress

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

Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle

Go Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Polar Moment of Inertia)/Torque

Twist angle given Shaft length and modulus of rigidity

Go Angle of Twist = (Torque*Length of Shaft)/(Polar Moment of Inertia*Modulus of Rigidity)

Polar moment of inertia

Go Polar Moment of Inertia = (Torque*Length of Shaft)/(Angle of Twist*Modulus of Rigidity)

Modulus of rigidity

Go Modulus of Rigidity = (Torque*Length of Shaft)/(Angle of Twist*Polar Moment of Inertia)

Twisting Moment given Polar MOI and Twist Angle

Go Torque = (Modulus of Rigidity*Angle of Twist*Polar Moment of Inertia)/Length of Shaft

Polar Moment of Inertia of Hollow Shaft

Go Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4)

Twisting Moment given Maximum Permissible Shear Stress

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

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

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

Radius given Twisting moment and Polar Moment of Inertia of shaft

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

Radius with known Maximum permissible shear stress

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

Maximum permissible shear stress

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

Radius given Torsional Section Modulus

Go Radius of Shaft = Polar Moment of Inertia/Polar Modulus

Radius of Shaft using Polar Modulus

Go Radius of Shaft = Polar Moment of Inertia/Polar Modulus

Torsional Section Modulus

Go Polar Modulus = Polar Moment of Inertia/Radius of Shaft

Radius given Torsional Section Modulus Formula

Radius of Shaft = Polar Moment of Inertia/Polar Modulus
R = J/Z_p

What is Torsion?

In 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 Torsional Section Modulus?

Radius given Torsional Section Modulus calculator uses Radius of Shaft = Polar Moment of Inertia/Polar Modulus to calculate the Radius of Shaft, The Radius given Torsional Section Modulus is defined as the radius of the cross-section of the shaft when its undergoing twisting. Radius of Shaft is denoted by R symbol.

How to calculate Radius given Torsional Section Modulus using this online calculator? To use this online calculator for Radius given Torsional Section Modulus, enter Polar Moment of Inertia (J) & Polar Modulus (Z_p) and hit the calculate button. Here is how the Radius given Torsional Section Modulus calculation can be explained with given input values -> 0.911111 = 0.0041/0.0045.

FAQ

What is Radius given Torsional Section Modulus?

The Radius given Torsional Section Modulus is defined as the radius of the cross-section of the shaft when its undergoing twisting and is represented as R = J/Z_p or Radius of Shaft = Polar Moment of Inertia/Polar Modulus. 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 & The Polar Modulus of the shaft section is equal to the ratio of the polar moment of inertia to the radius of the shaft. It is denoted by Zp.

How to calculate Radius given Torsional Section Modulus?

The Radius given Torsional Section Modulus is defined as the radius of the cross-section of the shaft when its undergoing twisting is calculated using Radius of Shaft = Polar Moment of Inertia/Polar Modulus. To calculate Radius given Torsional Section Modulus, you need Polar Moment of Inertia (J) & Polar Modulus (Z_p). With our tool, you need to enter the respective value for Polar Moment of Inertia & Polar Modulus 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 Polar Moment of Inertia & Polar Modulus. 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 = Maximum Shear Stress*Polar Moment of Inertia/Torque
Radius of Shaft = Polar Moment of Inertia/Polar Modulus

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