Torsional Section Modulus Solution

STEP 0: Pre-Calculation Summary
Formula Used
Polar Modulus = Polar Moment of Inertia/Radius of Shaft
Zp = 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
Zp = J/R --> 0.0041/0.11
Evaluating ... ...
Zp = 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)

Credits

Created by Rithik Agrawal
National Institute of Technology Karnataka (NITK), Surathkal
Rithik Agrawal has created this Calculator and 1300+ more calculators!
Verified by Mithila Muthamma PA
Coorg Institute of Technology (CIT), Coorg
Mithila Muthamma PA has verified this Calculator and 700+ more calculators!

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

Torsional Section Modulus Formula

Polar Modulus = Polar Moment of Inertia/Radius of Shaft
Zp = 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 Zp 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 Zp = 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.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!