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Torsional Shear Stress Formula

GoShear Stress Formula

GoShearing Stress Formula

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The Shearing Stress is a type of stress that acts coplanar with cross section of material. Check FAQs

𝜏 = \frac{τ \cdot r shaft}{J}

𝜏 - Shearing Stress?τ - Torque?r_shaft - Radius of Shaft?J - Polar Moment of Inertia?

Torsional Shear Stress Example

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Here is how the Torsional Shear Stress equation looks like with Values.

Here is how the Torsional Shear Stress equation looks like with Units.

Here is how the Torsional Shear Stress equation looks like.

20.5166 = \frac{556 \cdot 2000}{54.2}

20.5166Pa = \frac{556N*m \cdot 2000mm}{54.2m⁴}

20.5166 = \frac{556 \cdot 2000}{54.2}

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Torsional Shear Stress Solution

Follow our step by step solution on how to calculate Torsional Shear Stress?

FIRST Step Consider the formula

𝜏 = \frac{τ \cdot r shaft}{J}

Next Step Substitute values of Variables

∴

𝜏 = \frac{556N*m \cdot 2000mm}{54.2m⁴}

Next Step Convert Units

∴

𝜏 = \frac{556N*m \cdot 2m}{54.2m⁴}

Next Step Prepare to Evaluate

∴

𝜏 = \frac{556 \cdot 2}{54.2}

Next Step Evaluate

∴

𝜏 = 20.5166051660517Pa

LAST Step Rounding Answer

∴

𝜏 = 20.5166Pa

Torsional Shear Stress Formula Elements

Variables

Shearing Stress

The Shearing Stress is a type of stress that acts coplanar with cross section of material.

Symbol: 𝜏

Measurement: StressUnit: Pa

Note: Value should be greater than 0.

Formulas to find Shearing Stress

Torque

Torque is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.

Symbol: τ

Measurement: TorqueUnit: N*m

Note: Value should be greater than 0.

Formulas to find Torque

Radius of Shaft

The Radius of Shaft is the radius of the shaft subjected under torsion.

Symbol: r_shaft

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Radius of Shaft

Polar Moment of Inertia

The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.

Symbol: J

Measurement: Second Moment of AreaUnit: m⁴

Note: Value can be positive or negative.

Formulas to find Polar Moment of Inertia

Other Formulas to find Shearing Stress

Go Shear Stress

𝜏 = \frac{F t}{A cs}

Go Shearing Stress

𝜏 = \frac{V \cdot Ay}{I \cdot t}

Other formulas in Stress category

Go Beam Shear Stress

ζ b = \frac{ΣS \cdot Ay}{I \cdot t}

Go Bending Stress

σ b = M b \cdot \frac{y}{I}

Go Bulk Stress

B stress = \frac{N.F}{A cs}

Go Direct Stress

σ = \frac{P axial}{A cs}

How to Evaluate Torsional Shear Stress?

Torsional Shear Stress evaluator uses Shearing Stress = (Torque*Radius of Shaft)/Polar Moment of Inertia to evaluate the Shearing Stress, The Torsional Shear Stress formula is defined as the shear stress produced in the shaft due to the twisting. Shearing Stress is denoted by 𝜏 symbol.

How to evaluate Torsional Shear Stress using this online evaluator? To use this online evaluator for Torsional Shear Stress, enter Torque (τ), Radius of Shaft (r_shaft) & Polar Moment of Inertia (J) and hit the calculate button.

FAQs on Torsional Shear Stress

What is the formula to find Torsional Shear Stress?

The formula of Torsional Shear Stress is expressed as Shearing Stress = (Torque*Radius of Shaft)/Polar Moment of Inertia. Here is an example- 20.51661 = (556*2)/54.2.

How to calculate Torsional Shear Stress?

With Torque (τ), Radius of Shaft (r_shaft) & Polar Moment of Inertia (J) we can find Torsional Shear Stress using the formula - Shearing Stress = (Torque*Radius of Shaft)/Polar Moment of Inertia.

What are the other ways to Calculate Shearing Stress?

Here are the different ways to Calculate Shearing Stress-

Shearing Stress=Tangential Force/Cross Sectional Area
Shearing Stress=(Shearing Force*First Moment of Area)/(Moment of Inertia*Thickness of Material)

Can the Torsional Shear Stress be negative?

No, the Torsional Shear Stress, measured in Stress cannot be negative.

Which unit is used to measure Torsional Shear Stress?

Torsional Shear Stress is usually measured using the Pascal[Pa] for Stress. Newton per Square Meter[Pa], Newton per Square Millimeter[Pa], Kilonewton per Square Meter[Pa] are the few other units in which Torsional Shear Stress can be measured.

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