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Shear Force on Shear Plane Formula

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Shear Force is the force which causes shear deformation to occur in the shear plane. Check FAQs

F shear = F r \cdot \cos ((ϕ + β - γ ne))

F_shear - Shear Force?F_r - Resultant Cutting Force?ϕ - Shear Angle?β - Mean Friction Angle on Tool Face?γ_ne - Working Normal Rake?

Shear Force on Shear Plane Example

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Here is how the Shear Force on Shear Plane equation looks like with Values.

Here is how the Shear Force on Shear Plane equation looks like with Units.

Here is how the Shear Force on Shear Plane equation looks like.

467.0941 = 647.55 \cdot \cos ((11.406 + 52.43 - 20))

467.0941N = 647.55N \cdot \cos ((11.406° + 52.43° - 20°))

467.0941 = 647.55 \cdot \cos ((11.406 + 52.43 - 20))

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Shear Force on Shear Plane Solution

Follow our step by step solution on how to calculate Shear Force on Shear Plane?

FIRST Step Consider the formula

F shear = F r \cdot \cos ((ϕ + β - γ ne))

Next Step Substitute values of Variables

∴

F shear = 647.55N \cdot \cos ((11.406° + 52.43° - 20°))

Next Step Convert Units

∴

F shear = 647.55N \cdot \cos ((0.1991rad + 0.9151rad - 0.3491rad))

Next Step Prepare to Evaluate

∴

F shear = 647.55 \cdot \cos ((0.1991 + 0.9151 - 0.3491))

Next Step Evaluate

∴

F shear = 467.094132790701N

LAST Step Rounding Answer

∴

F shear = 467.0941N

Shear Force on Shear Plane Formula Elements

Variables

Functions

Shear Force

Shear Force is the force which causes shear deformation to occur in the shear plane.

Symbol: F_shear

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Shear Force

Resultant Cutting Force

The Resultant Cutting Force is the total force in the direction of cutting, the same direction as the cutting speed.

Symbol: F_r

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Resultant Cutting Force

Shear Angle

Shear Angle 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

Mean Friction Angle on Tool Face

The Mean Friction Angle on Tool Face corresponds to the maximum static friction force between the tool face and workpiece.

Symbol: β

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Mean Friction Angle on Tool Face

Working Normal Rake

The Working Normal Rake angle is the angle of orientation of the tool's rake surface from the reference plane and measured on a normal plane.

Symbol: γ_ne

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Working Normal Rake

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Shear category

Go Cutting Ratio for given Shear Angle of Continuous chip

r c = \frac{\tan (ϕ)}{\cos (γ ne) + (\tan (ϕ) \cdot \sin (γ ne))}

Go Area of Shear

A s = \frac{A c}{\sin (ϕ)}

Go Shear Force on Shear Plane using Shear Strength

F s = τ \cdot \frac{A c}{\sin (ϕ)}

Go Shear Strength given Coefficient of Friction in Metal Cutting

τ = μ \cdot σ y

How to Evaluate Shear Force on Shear Plane?

Shear Force on Shear Plane evaluator uses Shear Force = Resultant Cutting Force*cos((Shear Angle+Mean Friction Angle on Tool Face-Working Normal Rake)) to evaluate the Shear Force, The Shear Force on Shear Plane formula is defined as the force that makes one surface of a substance move over another parallel surface. Shear Force is denoted by F_shear symbol.

How to evaluate Shear Force on Shear Plane using this online evaluator? To use this online evaluator for Shear Force on Shear Plane, enter Resultant Cutting Force (F_r), Shear Angle (ϕ), Mean Friction Angle on Tool Face (β) & Working Normal Rake (γ_ne) and hit the calculate button.

FAQs on Shear Force on Shear Plane

What is the formula to find Shear Force on Shear Plane?

The formula of Shear Force on Shear Plane is expressed as Shear Force = Resultant Cutting Force*cos((Shear Angle+Mean Friction Angle on Tool Face-Working Normal Rake)). Here is an example- 467.0941 = 647.55*cos((0.199072254482436+0.915076126820455-0.3490658503988)).

How to calculate Shear Force on Shear Plane?

With Resultant Cutting Force (F_r), Shear Angle (ϕ), Mean Friction Angle on Tool Face (β) & Working Normal Rake (γ_ne) we can find Shear Force on Shear Plane using the formula - Shear Force = Resultant Cutting Force*cos((Shear Angle+Mean Friction Angle on Tool Face-Working Normal Rake)). This formula also uses Cosine (cos) function(s).

Can the Shear Force on Shear Plane be negative?

No, the Shear Force on Shear Plane, measured in Force cannot be negative.

Which unit is used to measure Shear Force on Shear Plane?

Shear Force on Shear Plane is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Shear Force on Shear Plane can be measured.

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Shear Force on Shear Plane Formula

Shear Force on Shear Plane Example

Shear Force on Shear Plane Solution

Shear Force on Shear Plane Formula Elements

Other formulas in Shear category

How to Evaluate Shear Force on Shear Plane?

FAQs on Shear Force on Shear Plane

Variable Name