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Polar Modulus using Maximum Twisting Moment Formula

GoPolar Modulus Formula

GoPolar Modulus of Hollow Shaft Formula

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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. Check FAQs

Z p = (\frac{T}{τ max})

Z_p - Polar Modulus?T - Torque?τ_max - Maximum Shear Stress?

Polar Modulus using Maximum Twisting Moment Example

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Here is how the Polar Modulus using Maximum Twisting Moment equation looks like with Values.

Here is how the Polar Modulus using Maximum Twisting Moment equation looks like with Units.

Here is how the Polar Modulus using Maximum Twisting Moment equation looks like.

0.0007 = (\frac{28}{42})

0.0007m³ = (\frac{28kN*m}{42MPa})

0.0007 = (\frac{28}{42})

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Polar Modulus using Maximum Twisting Moment Solution

Follow our step by step solution on how to calculate Polar Modulus using Maximum Twisting Moment?

FIRST Step Consider the formula

Z p = (\frac{T}{τ max})

Next Step Substitute values of Variables

∴

Z p = (\frac{28kN*m}{42MPa})

Next Step Convert Units

∴

Z p = (\frac{28000N*m}{4.2E+7Pa})

Next Step Prepare to Evaluate

∴

Z p = (\frac{28000}{4.2E+7})

Next Step Evaluate

∴

Z p = 0.000666666666666667m³

LAST Step Rounding Answer

∴

Z p = 0.0007m³

Polar Modulus using Maximum Twisting Moment Formula Elements

Variables

Polar Modulus

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.

Symbol: Z_p

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Polar Modulus

Torque

Torque is a measure of the force that can cause an object to rotate about an axis.

Symbol: T

Measurement: TorqueUnit: kN*m

Note: Value can be positive or negative.

Formulas to find Torque

Maximum Shear Stress

Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.

Symbol: τ_max

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Shear Stress

Other Formulas to find Polar Modulus

Go Polar Modulus

Z p = \frac{J}{R}

Go Polar Modulus of Hollow Shaft

Z p = \frac{π \cdot (({d o}^{4}) - ({d i}^{4}))}{16 \cdot d o}

Go Polar Modulus of Solid Shaft

Z p = \frac{π \cdot d^{3}}{16}

Other formulas in Polar Modulus category

Go Diameter of Solid Shaft with known Polar Modulus

d = {(\frac{16 \cdot Z p}{π})}^{\frac{1}{3}}

Go Inner diameter of Hollow Shaft using Polar Modulus

d i = {(({d o}^{4}) - (\frac{Z p \cdot 16 \cdot d o}{π}))}^{\frac{1}{4}}

Go Polar Moment of Inertia using Polar Modulus

J = R \cdot Z p

Go Polar Moment of Inertia of Solid Shaft

J = \frac{π \cdot d^{4}}{32}

How to Evaluate Polar Modulus using Maximum Twisting Moment?

Polar Modulus using Maximum Twisting Moment evaluator uses Polar Modulus = (Torque/Maximum Shear Stress) to evaluate 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 evaluate Polar Modulus using Maximum Twisting Moment using this online evaluator? To use this online evaluator for Polar Modulus using Maximum Twisting Moment, enter Torque (T) & Maximum Shear Stress (τ_max) and hit the calculate button.

FAQs on Polar Modulus using Maximum Twisting Moment

What is the formula to find Polar Modulus using Maximum Twisting Moment?

The formula of Polar Modulus using Maximum Twisting Moment is expressed as Polar Modulus = (Torque/Maximum Shear Stress). Here is an example- 0.000667 = (28000/42000000).

How to calculate Polar Modulus using Maximum Twisting Moment?

With Torque (T) & Maximum Shear Stress (τ_max) we can find Polar Modulus using Maximum Twisting Moment using the formula - Polar Modulus = (Torque/Maximum Shear Stress).

What are the other ways to Calculate Polar Modulus?

Here are the different ways to Calculate Polar Modulus-

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

Can the Polar Modulus using Maximum Twisting Moment be negative?

No, the Polar Modulus using Maximum Twisting Moment, measured in Volume cannot be negative.

Which unit is used to measure Polar Modulus using Maximum Twisting Moment?

Polar Modulus using Maximum Twisting Moment is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Polar Modulus using Maximum Twisting Moment can be measured.

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