Torsional Shear Stress Calculator

✖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.ⓘ Torque [τ]			+10% -10%
✖The Radius of Shaft is the radius of the shaft subjected under torsion.ⓘ Radius of Shaft [r_shaft]			+10% -10%
✖The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.ⓘ Polar Moment of Inertia [J]			+10% -10%

✖The Shearing Stress is a type of stress that acts coplanar with cross section of material.ⓘ Torsional Shear Stress [𝜏]

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Formula

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Torsional Shear Stress

Formula

`"𝜏" = ("τ"*"r"_{"shaft"})/"J"`

Example

`"20.51661Pa"=("556N*m"*"2000mm")/"54.2m⁴"`

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Torsional Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shearing Stress = (Torque*Radius of Shaft)/Polar Moment of Inertia
𝜏 = (τ*r_shaft)/J
This formula uses 4 Variables

Variables Used

Shearing Stress - (Measured in Pascal) - The Shearing Stress is a type of stress that acts coplanar with cross section of material.
Torque - (Measured in Newton Meter) - 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.
Radius of Shaft - (Measured in Meter) - The Radius of Shaft is the radius of the shaft subjected under torsion.
Polar Moment of Inertia - (Measured in Meter⁴) - The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.

STEP 1: Convert Input(s) to Base Unit

Torque: 556 Newton Meter --> 556 Newton Meter No Conversion Required
Radius of Shaft: 2000 Millimeter --> 2 Meter (Check conversion here)
Polar Moment of Inertia: 54.2 Meter⁴ --> 54.2 Meter⁴ No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜏 = (τ*r_shaft)/J --> (556*2)/54.2

Evaluating ... ...

𝜏 = 20.5166051660517

STEP 3: Convert Result to Output's Unit

20.5166051660517 Pascal --> No Conversion Required

FINAL ANSWER

20.5166051660517 ≈ 20.51661 Pascal <-- Shearing Stress

(Calculation completed in 00.020 seconds)

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Created by Pragati Jaju

College Of Engineering (COEP), Pune

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Osmania University (OU), Hyderabad

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< 16 Stress Calculators

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Thermal Stress in Tapered Bar

Go Thermal Stress = (4*Load*Length of Weld)/(pi*Diameter of Bigger End*Diameter of Smaller End*Bending Stress)

Beam Shear Stress

Go Shearing Stress = (Total Shear Force*First Moment of Area)/(Moment of Inertia*Thickness of Material)

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Go Shearing Stress = (Shearing Force*First Moment of Area)/(Moment of Inertia*Thickness of Material)

Shear Stress in Double Parallel Fillet Weld

Go Shearing Stress = Load on Double Parallel Fillet Weld/(0.707*Length of Weld*Leg of Weld)

Thermal Stress

Go Thermal Stress = Coefficient of Thermal Expansion*Bending Stress*Change in Temperature

Bending Stress

Go Bending Stress = Bending Moment*Distance from Neutral Axis/Moment of Inertia

Torsional Shear Stress

Go Shearing Stress = (Torque*Radius of Shaft)/Polar Moment of Inertia

Shear Stress of Circular Beam

Go Stress on Body = (4*Shearing Force)/(3*Cross sectional area)

Stress due to Gradual Loading

Go Stress due to Gradual Loading = Force/Cross sectional area

Maximum Shearing Stress

Go Stress on Body = (1.5*Shearing Force)/Cross sectional area

Shear Stress

Go Shearing Stress = Tangential Force/Cross sectional area

Bulk Stress

Go Bulk Stress = Normal Inward Force/Cross sectional area

Direct Stress

Go Direct Stress = Axial Thrust/Cross sectional area

Stress due to Sudden Loading

Go Stress on Body = 2*Force/Cross sectional area

Torsional Shear Stress Formula

Shearing Stress = (Torque*Radius of Shaft)/Polar Moment of Inertia
𝜏 = (τ*r_shaft)/J

What is Torsional Shear Stress?

Torsional shear stress or Torsional stress is the shear stress produced in the shaft due to the twisting. This twisting in the shaft is caused by the couple acting on it.Torsion occurs when two forces of similar value are applied in opposite directions, causing torque.

How to Calculate Torsional Shear Stress?

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

How to calculate Torsional Shear Stress using this online calculator? To use this online calculator for Torsional Shear Stress, enter Torque (τ), Radius of Shaft (r_shaft) & Polar Moment of Inertia (J) and hit the calculate button. Here is how the Torsional Shear Stress calculation can be explained with given input values -> 0.701107 = (556*2)/54.2.

FAQ

What is Torsional Shear Stress?

The Torsional Shear Stress or Torsional stress is defined as the shear stress produced in the shaft due to the twisting and is represented as 𝜏 = (τ*r_shaft)/J or Shearing Stress = (Torque*Radius of Shaft)/Polar Moment of Inertia. 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, The Radius of Shaft is the radius of the shaft subjected under torsion & The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.

How to calculate Torsional Shear Stress?

The Torsional Shear Stress or Torsional stress is defined as the shear stress produced in the shaft due to the twisting is calculated using Shearing Stress = (Torque*Radius of Shaft)/Polar Moment of Inertia. To calculate Torsional Shear Stress, you need Torque (τ), Radius of Shaft (r_shaft) & Polar Moment of Inertia (J). With our tool, you need to enter the respective value for Torque, Radius of Shaft & Polar Moment of Inertia 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 Shearing Stress?

In this formula, Shearing Stress uses Torque, Radius of Shaft & Polar Moment of Inertia. We can use 3 other way(s) to calculate the same, which is/are as follows -

Shearing Stress = (Total Shear Force*First Moment of Area)/(Moment of Inertia*Thickness of Material)
Shearing Stress = Tangential Force/Cross sectional area
Shearing Stress = (Shearing Force*First Moment of Area)/(Moment of Inertia*Thickness of Material)

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