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Area of Shear Formula

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Area of Shear is defined as the area of the section which is effective in resisting shear deformation. Check FAQs

A s = \frac{A c}{\sin (ϕ)}

A_s - Area of Shear?A_c - Cross Sectional Area of Uncut Chip?ϕ - Shear Angle?

Area of Shear Example

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Here is how the Area of Shear equation looks like with Values.

Here is how the Area of Shear equation looks like with Units.

Here is how the Area of Shear equation looks like.

2.2755 = \frac{0.45}{\sin (11.406)}

2.2755mm² = \frac{0.45mm²}{\sin (11.406°)}

2.2755 = \frac{0.45}{\sin (11.406)}

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Area of Shear Solution

Follow our step by step solution on how to calculate Area of Shear?

FIRST Step Consider the formula

A s = \frac{A c}{\sin (ϕ)}

Next Step Substitute values of Variables

∴

A s = \frac{0.45mm²}{\sin (11.406°)}

Next Step Convert Units

∴

A s = \frac{4.5E-7m²}{\sin (0.1991rad)}

Next Step Prepare to Evaluate

∴

A s = \frac{4.5E-7}{\sin (0.1991)}

Next Step Evaluate

∴

A s = 2.27548551683342E-06m²

Next Step Convert to Output's Unit

∴

A s = 2.27548551683342mm²

LAST Step Rounding Answer

∴

A s = 2.2755mm²

Area of Shear Formula Elements

Variables

Functions

Area of Shear

Area of Shear is defined as the area of the section which is effective in resisting shear deformation.

Symbol: A_s

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Area of Shear

Cross Sectional Area of Uncut Chip

The Cross Sectional Area of Uncut Chip is the area enclosed within the outer surface of the workpiece and the line of cut followed by the single-point cutting edge. It is calculated for one pass.

Symbol: A_c

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Cross Sectional Area of Uncut Chip

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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(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 Shear Force on Shear Plane

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

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 Area of Shear?

Area of Shear evaluator uses Area of Shear = Cross Sectional Area of Uncut Chip/sin(Shear Angle) to evaluate the Area of Shear, The Area of Shear of the member is a cross-sectional property and is defined as the area of the section which is effective in resisting shear deformation. Area of Shear is denoted by A_s symbol.

How to evaluate Area of Shear using this online evaluator? To use this online evaluator for Area of Shear, enter Cross Sectional Area of Uncut Chip (A_c) & Shear Angle (ϕ) and hit the calculate button.

FAQs on Area of Shear

What is the formula to find Area of Shear?

The formula of Area of Shear is expressed as Area of Shear = Cross Sectional Area of Uncut Chip/sin(Shear Angle). Here is an example- 2.3E+6 = 4.5E-07/sin(0.199072254482436).

How to calculate Area of Shear?

With Cross Sectional Area of Uncut Chip (A_c) & Shear Angle (ϕ) we can find Area of Shear using the formula - Area of Shear = Cross Sectional Area of Uncut Chip/sin(Shear Angle). This formula also uses Sine (sin) function(s).

Can the Area of Shear be negative?

No, the Area of Shear, measured in Area cannot be negative.

Which unit is used to measure Area of Shear?

Area of Shear is usually measured using the Square Millimeter[mm²] for Area. Square Meter[mm²], Square Kilometer[mm²], Square Centimeter[mm²] are the few other units in which Area of Shear can be measured.

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Area of Shear Formula

Area of Shear Example

Area of Shear Solution

Area of Shear Formula Elements

Other formulas in Shear category

How to Evaluate Area of Shear?

FAQs on Area of Shear

Variable Name