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 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%

✖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.ⓘ Torsional Section Modulus [Z_p]

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Torsional Section Modulus Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Polar Moment of Inertia: 0.0041 Meter⁴ --> 0.0041 Meter⁴ No Conversion Required
Radius of Shaft: 110 Millimeter --> 0.11 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z_p = J/R --> 0.0041/0.11

Evaluating ... ...

Z_p = 0.0372727272727273

STEP 3: Convert Result to Output's Unit

0.0372727272727273 Cubic Meter --> No Conversion Required

FINAL ANSWER

0.0372727272727273 ≈ 0.037273 Cubic Meter <-- Polar Modulus

(Calculation completed in 00.004 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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Coorg Institute of Technology (CIT), Coorg

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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

Torsional Section Modulus Formula

LaTeX Go

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

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 Torsional Section Modulus?

Torsional Section Modulus calculator uses Polar Modulus = Polar Moment of Inertia/Radius of Shaft to calculate the Polar Modulus, The Torsional Section Modulus formula is defined as the ratio of the polar moment of inertia to the radius of the shaft. It is also called as the polar modulus. Polar Modulus is denoted by Z_p symbol.

How to calculate Torsional Section Modulus using this online calculator? To use this online calculator for Torsional Section Modulus, enter Polar Moment of Inertia (J) & Radius of Shaft (R) and hit the calculate button. Here is how the Torsional Section Modulus calculation can be explained with given input values -> 0.037273 = 0.0041/0.11.

FAQ

What is Torsional Section Modulus?

The Torsional Section Modulus formula is defined as the ratio of the polar moment of inertia to the radius of the shaft. It is also called as the polar modulus and is represented as Z_p = J/R or Polar Modulus = Polar Moment of Inertia/Radius of Shaft. 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 Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.

How to calculate Torsional Section Modulus?

The Torsional Section Modulus formula is defined as the ratio of the polar moment of inertia to the radius of the shaft. It is also called as the polar modulus is calculated using Polar Modulus = Polar Moment of Inertia/Radius of Shaft. To calculate Torsional Section Modulus, you need Polar Moment of Inertia (J) & Radius of Shaft (R). With our tool, you need to enter the respective value for Polar Moment of Inertia & Radius of Shaft 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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