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Torsional Section Modulus 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{J}{R}

Z_p - Polar Modulus?J - Polar Moment of Inertia?R - Radius of Shaft?

Torsional Section Modulus Example

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Here is how the Torsional Section Modulus equation looks like with Values.

Here is how the Torsional Section Modulus equation looks like with Units.

Here is how the Torsional Section Modulus equation looks like.

0.0373 = \frac{0.0041}{110}

0.0373m³ = \frac{0.0041m⁴}{110mm}

0.0373 = \frac{0.0041}{110}

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Torsional Section Modulus Solution

Follow our step by step solution on how to calculate Torsional Section Modulus?

FIRST Step Consider the formula

Z p = \frac{J}{R}

Next Step Substitute values of Variables

∴

Z p = \frac{0.0041m⁴}{110mm}

Next Step Convert Units

∴

Z p = \frac{0.0041m⁴}{0.11m}

Next Step Prepare to Evaluate

∴

Z p = \frac{0.0041}{0.11}

Next Step Evaluate

∴

Z p = 0.0372727272727273m³

LAST Step Rounding Answer

∴

Z p = 0.0373m³

Torsional Section Modulus 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

Polar Moment of Inertia

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.

Symbol: J

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Polar Moment of Inertia

Radius of Shaft

The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.

Symbol: R

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Shaft

Other formulas in Torsion category

Go Twisting Moment given Maximum Permissible Shear Stress

T = \frac{J \cdot τ max}{R}

Go Maximum permissible shear stress

τ max = T \cdot \frac{R}{J}

Go Radius with known Maximum permissible shear stress

R = τ max \cdot \frac{J}{T}

Go Maximum permissible shear stress for given Radius and modulus of rigidity

τ max = \frac{G Torsion \cdot (θ) \cdot R}{L shaft}

How to Evaluate Torsional Section Modulus?

Torsional Section Modulus evaluator uses Polar Modulus = Polar Moment of Inertia/Radius of Shaft to evaluate 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 evaluate Torsional Section Modulus using this online evaluator? To use this online evaluator for Torsional Section Modulus, enter Polar Moment of Inertia (J) & Radius of Shaft (R) and hit the calculate button.

FAQs on Torsional Section Modulus

What is the formula to find Torsional Section Modulus?

The formula of Torsional Section Modulus is expressed as Polar Modulus = Polar Moment of Inertia/Radius of Shaft. Here is an example- 0.037273 = 0.0041/0.11.

How to calculate Torsional Section Modulus?

With Polar Moment of Inertia (J) & Radius of Shaft (R) we can find Torsional Section Modulus using the formula - Polar Modulus = Polar Moment of Inertia/Radius of Shaft.

Can the Torsional Section Modulus be negative?

No, the Torsional Section Modulus, measured in Volume cannot be negative.

Which unit is used to measure Torsional Section Modulus?

Torsional Section Modulus 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 Torsional Section Modulus can be measured.

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Torsional Section Modulus Formula

Torsional Section Modulus Example

Torsional Section Modulus Solution

Torsional Section Modulus Formula Elements

Other formulas in Torsion category

How to Evaluate Torsional Section Modulus?

FAQs on Torsional Section Modulus

Variable Name