Polar Modulus using Maximum Twisting Moment Calculator

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

✖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 using Maximum Twisting Moment [Z_p]

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Formula

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Polar Modulus using Maximum Twisting Moment

Formula

`"Z"_{"p"} = ("T"/"τ"_{"max"})`

Example

`"0.000667m³"=("28kN*m"/"42MPa")`

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Download Torsional Rigidity and Polar Modulus Formulas PDF

Polar Modulus using Maximum Twisting Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Modulus = (Torque/Maximum Shear Stress)
Z_p = (T/τ_max)
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.
Torque - (Measured in Newton Meter) - Torque is a measure of the force that can cause an object to rotate about an axis.
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)
Maximum Shear Stress: 42 Megapascal --> 42000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z_p = (T/τ_max) --> (28000/42000000)

Evaluating ... ...

Z_p = 0.000666666666666667

STEP 3: Convert Result to Output's Unit

0.000666666666666667 Cubic Meter --> No Conversion Required

FINAL ANSWER

0.000666666666666667 ≈ 0.000667 Cubic Meter <-- Polar Modulus

(Calculation completed in 00.004 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal

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< 9 Polar Modulus Calculators

Inner diameter of Hollow Shaft using Polar Modulus

Go Inner Dia of Shaft = ((Outer Diameter of Shaft^4)-((Polar Modulus*16*Outer Diameter of Shaft)/pi))^(1/4)

Polar Modulus of Hollow Shaft

Go Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft)

Polar Moment of Inertia given Torsional Section Modulus

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

Polar Moment of Inertia using Polar Modulus

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

Polar Modulus

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

Polar Moment of Inertia of Solid Shaft

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

Diameter of Solid Shaft with known Polar Modulus

Go Dia of Shaft = ((16*Polar Modulus)/pi)^(1/3)

Polar Modulus using Maximum Twisting Moment

Go Polar Modulus = (Torque/Maximum Shear Stress)

Polar Modulus of Solid Shaft

Go Polar Modulus = (pi*Dia of Shaft^3)/16

Polar Modulus using Maximum Twisting Moment Formula

Polar Modulus = (Torque/Maximum Shear Stress)
Z_p = (T/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 Modulus using Maximum Twisting Moment?

Polar Modulus using Maximum Twisting Moment calculator uses Polar Modulus = (Torque/Maximum Shear Stress) to calculate the Polar Modulus, The Polar Modulus using Maximum Twisting Moment formula is defined as the ratio of the polar moment of inertia (J) to the radius of the shaft. Polar Modulus is denoted by Z_p symbol.

How to calculate Polar Modulus using Maximum Twisting Moment using this online calculator? To use this online calculator for Polar Modulus using Maximum Twisting Moment, enter Torque (T) & Maximum Shear Stress (τ_max) and hit the calculate button. Here is how the Polar Modulus using Maximum Twisting Moment calculation can be explained with given input values -> 0.000667 = (28000/42000000).

FAQ

What is Polar Modulus using Maximum Twisting Moment?

The Polar Modulus using Maximum Twisting Moment formula is defined as the ratio of the polar moment of inertia (J) to the radius of the shaft and is represented as Z_p = (T/τ_max) or Polar Modulus = (Torque/Maximum Shear Stress). Torque is a measure of the force that can cause an object to rotate about an axis & Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.

How to calculate Polar Modulus using Maximum Twisting Moment?

The Polar Modulus using Maximum Twisting Moment formula is defined as the ratio of the polar moment of inertia (J) to the radius of the shaft is calculated using Polar Modulus = (Torque/Maximum Shear Stress). To calculate Polar Modulus using Maximum Twisting Moment, you need Torque (T) & Maximum Shear Stress (τ_max). With our tool, you need to enter the respective value for Torque & 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 Modulus?

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

Polar Modulus = Polar Moment of Inertia/Radius of Shaft
Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft)
Polar Modulus = (pi*Dia of Shaft^3)/16

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