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Shear Strain Formula

GoShear Strain given Tangential Displacement and Original Length Formula

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The Shear Strain is the ratio of the change in deformation to its original length perpendicular to the axes of the member due to shear stress. Check FAQs

𝜂 = \tan (ϕ) + \cot (ϕ - α)

𝜂 - Shear Strain?ϕ - Shear Angle Metal?α - Rake Angle?

Shear Strain Example

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Here is how the Shear Strain equation looks like with Values.

Here is how the Shear Strain equation looks like with Units.

Here is how the Shear Strain equation looks like.

2.3384 = \tan (46.3) + \cot (46.3 - 8.56)

2.3384 = \tan (46.3°) + \cot (46.3° - 8.56°)

2.3384 = \tan (46.3) + \cot (46.3 - 8.56)

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Shear Strain Solution

Follow our step by step solution on how to calculate Shear Strain?

FIRST Step Consider the formula

𝜂 = \tan (ϕ) + \cot (ϕ - α)

Next Step Substitute values of Variables

∴

𝜂 = \tan (46.3°) + \cot (46.3° - 8.56°)

Next Step Convert Units

∴

𝜂 = \tan (0.8081rad) + \cot (0.8081rad - 0.1494rad)

Next Step Prepare to Evaluate

∴

𝜂 = \tan (0.8081) + \cot (0.8081 - 0.1494)

Next Step Evaluate

∴

𝜂 = 2.33842388392556

LAST Step Rounding Answer

∴

𝜂 = 2.3384

Shear Strain Formula Elements

Variables

Functions

Shear Strain

The Shear Strain is the ratio of the change in deformation to its original length perpendicular to the axes of the member due to shear stress.

Symbol: 𝜂

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Shear Strain

Shear Angle Metal

Shear Angle Metal is the inclination of the shear plane with the horizontal axis at machining point.

Symbol: ϕ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Shear Angle Metal

Rake Angle

Rake Angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.

Symbol: α

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Rake Angle

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

cot

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: cot(Angle)

Other Formulas to find Shear Strain

Go Shear Strain given Tangential Displacement and Original Length

𝜂 = \frac{t}{L 0}

Other formulas in Metal Cutting category

Go Bulk Strain

ε b = \frac{∆V}{V T}

Go Tensile Strain

e tension = \frac{ΔL}{L}

Go Lateral Strain

Sd = \frac{∆d}{d}

Go Volumetric Strain

ε v = \frac{∆V}{V T}

How to Evaluate Shear Strain?

Shear Strain evaluator uses Shear Strain = tan(Shear Angle Metal)+cot(Shear Angle Metal-Rake Angle) to evaluate the Shear Strain, The Shear Strain formula is defined as the measure of how much a given deformation differs from a rigid deformation. Shear Strain is denoted by 𝜂 symbol.

How to evaluate Shear Strain using this online evaluator? To use this online evaluator for Shear Strain, enter Shear Angle Metal (ϕ) & Rake Angle (α) and hit the calculate button.

FAQs on Shear Strain

What is the formula to find Shear Strain?

The formula of Shear Strain is expressed as Shear Strain = tan(Shear Angle Metal)+cot(Shear Angle Metal-Rake Angle). Here is an example- 2.338424 = tan(0.808087443673223)+cot(0.808087443673223-0.149400183970687).

How to calculate Shear Strain?

With Shear Angle Metal (ϕ) & Rake Angle (α) we can find Shear Strain using the formula - Shear Strain = tan(Shear Angle Metal)+cot(Shear Angle Metal-Rake Angle). This formula also uses Tangent (tan), Cotangent (cot) function(s).

What are the other ways to Calculate Shear Strain?

Here are the different ways to Calculate Shear Strain-

Shear Strain=Tangential Displacement/Original Length

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