Shear Strain Calculator

✖Shear angle metal is the inclination of the shear plane with the horizontal axis at machining point.ⓘ Shear Angle Metal [ϕ]			+10% -10%
✖Rake Angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.ⓘ Rake Angle [α]			+10% -10%

✖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.ⓘ Shear Strain [𝜂]

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Formula

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Shear Strain

Formula

𝜂 = \tan (ϕ) + \cot (ϕ - α)

Example

2.338424 = \tan (46.3 °) + \cot (46.3 ° - 8.56 °)

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Shear Strain Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shear Strain = tan(Shear Angle Metal)+cot(Shear Angle Metal-Rake Angle)
𝜂 = tan(ϕ)+cot(ϕ-α)
This formula uses 2 Functions, 3 Variables

Functions Used

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., 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., cot(Angle)

Variables Used

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.
Shear Angle Metal - (Measured in Radian) - Shear angle metal is the inclination of the shear plane with the horizontal axis at machining point.
Rake Angle - (Measured in Radian) - Rake Angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.

STEP 1: Convert Input(s) to Base Unit

Shear Angle Metal: 46.3 Degree --> 0.808087443673223 Radian (Check conversion here)
Rake Angle: 8.56 Degree --> 0.149400183970687 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜂 = tan(ϕ)+cot(ϕ-α) --> tan(0.808087443673223)+cot(0.808087443673223-0.149400183970687)

Evaluating ... ...

𝜂 = 2.33842388392556

STEP 3: Convert Result to Output's Unit

2.33842388392556 --> No Conversion Required

FINAL ANSWER

2.33842388392556 ≈ 2.338424 <-- Shear Strain

(Calculation completed in 00.004 seconds)

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Shear Plane Angle

Go Shear Angle Metal = arctan((Chip Ratio*cos(Rake Angle))/(1-Chip Ratio*sin(Rake Angle)))

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Go Shear Angle Metal = atan(Width*cos(Theta)/(1-Width*sin(Theta)))

Shear Force

Go Shear Force = Centripetal Force*cos(Theta)-Tangential Force*sin(Theta)

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Go Shear Strain = tan(Shear Angle Metal)+cot(Shear Angle Metal-Rake Angle)

< Mechanical Strain Calculators

Shear Strain given Tangential Displacement and Original Length

Go Shear Strain = Tangential Displacement/Original Length

Lateral Strain

Go Lateral Strain = Change in Diameter/Original Diameter

Tensile Strain

Go Tension Strain = Change in Length/Length

Bulk Strain

Go Bulk Strain = Change in Volume/Volume

Shear Strain Formula

Shear Strain = tan(Shear Angle Metal)+cot(Shear Angle Metal-Rake Angle)
𝜂 = tan(ϕ)+cot(ϕ-α)

What is shear strain of a slide?

This shear strain or slide can be defined as the change in right angle. or The angle of deformation is then termed as the shear strain. Shear strain is measured in radians & hence is non – dimensional i.e. it has no unit.

How to Calculate Shear Strain?

Shear Strain calculator uses Shear Strain = tan(Shear Angle Metal)+cot(Shear Angle Metal-Rake Angle) to calculate the Shear Strain, Shear Strain measures how much a given deformation differs from a rigid deformation. Shear Strain is denoted by 𝜂 symbol.

How to calculate Shear Strain using this online calculator? To use this online calculator for Shear Strain, enter Shear Angle Metal (ϕ) & Rake Angle (α) and hit the calculate button. Here is how the Shear Strain calculation can be explained with given input values -> 2.338424 = tan(0.808087443673223)+cot(0.808087443673223-0.149400183970687).

FAQ

What is Shear Strain?

Shear Strain measures how much a given deformation differs from a rigid deformation and is represented as 𝜂 = tan(ϕ)+cot(ϕ-α) or Shear Strain = tan(Shear Angle Metal)+cot(Shear Angle Metal-Rake Angle). Shear angle metal is the inclination of the shear plane with the horizontal axis at machining point & Rake Angle is the angle of orientation of tool’s rake surface from the reference plane and measured on machine longitudinal plane.

How to calculate Shear Strain?

Shear Strain measures how much a given deformation differs from a rigid deformation is calculated using Shear Strain = tan(Shear Angle Metal)+cot(Shear Angle Metal-Rake Angle). To calculate Shear Strain, you need Shear Angle Metal (ϕ) & Rake Angle (α). With our tool, you need to enter the respective value for Shear Angle Metal & Rake Angle 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 Shear Strain?

In this formula, Shear Strain uses Shear Angle Metal & Rake Angle. We can use 2 other way(s) to calculate the same, which is/are as follows -

Shear Strain = Tangential Displacement/Original Length
Shear Strain = Tangential Displacement/Original Length

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