Area of Shear Calculator

✖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.ⓘ Cross-sectional Area of Uncut Chip [A_c]			+10% -10%
✖Shear angle is the inclination of the shear plane with the horizontal axis at machining point.ⓘ Shear angle [ϕ]			+10% -10%

✖Area of Shear is defined as the area of the section which is effective in resisting shear deformation.ⓘ Area of Shear [A_s]

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Formula

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Area of Shear

Formula

`"A"_{"s"} = "A"_{"c"}/sin("ϕ")`

Example

`"2.275486mm²"="0.45mm²"/sin("11.406°")`

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Area of Shear Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Shear = Cross-sectional Area of Uncut Chip/sin(Shear angle)
A_s = A_c/sin(ϕ)
This formula uses 1 Functions, 3 Variables

Functions Used

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., sin(Angle)

Variables Used

Area of Shear - (Measured in Square Meter) - Area of Shear is defined as the area of the section which is effective in resisting shear deformation.
Cross-sectional Area of Uncut Chip - (Measured in Square Meter) - 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.
Shear angle - (Measured in Radian) - Shear angle is the inclination of the shear plane with the horizontal axis at machining point.

STEP 1: Convert Input(s) to Base Unit

Cross-sectional Area of Uncut Chip: 0.45 Square Millimeter --> 4.5E-07 Square Meter (Check conversion here)
Shear angle: 11.406 Degree --> 0.199072254482436 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_s = A_c/sin(ϕ) --> 4.5E-07/sin(0.199072254482436)

Evaluating ... ...

A_s = 2.27548551683342E-06

STEP 3: Convert Result to Output's Unit

2.27548551683342E-06 Square Meter -->2.27548551683342 Square Millimeter (Check conversion here)

FINAL ANSWER

2.27548551683342 ≈ 2.275486 Square Millimeter <-- Area of Shear

(Calculation completed in 00.004 seconds)

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Created by Parul Keshav

National Institute of Technology (NIT), Srinagar

Parul Keshav has created this Calculator and 300+ more calculators!

Verified by Kethavath Srinath

Osmania University (OU), Hyderabad

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< 9 Shear Calculators

Cutting Ratio for given Shear Angle of Continuous chip

Go Cutting Ratio = tan(Shear angle)/(cos(Working Normal Rake)+(tan(Shear angle)*sin(Working Normal Rake)))

Shear Angle of Continuous Chip Formation

Go Shear angle = atan((Cutting Ratio*cos(Working Normal Rake))/(1-(Cutting Ratio*sin(Working Normal Rake))))

Total Shear force by tool

Go Total Shear Force by Tool = (Cutting Force*cos(Shear angle))+(Thrust force*sin(Shear angle))

Shear Force on Shear Plane

Go Shear Force = Resultant Cutting Force*cos((Shear angle+Mean Friction Angle on Tool Face-Working Normal Rake))

Shear Force on Shear Plane using Shear Strength

Go Total Shear Force by Tool = Shear Strength of Material*Cross-sectional Area of Uncut Chip/sin(Shear angle)

Area of Shear

Go Area of Shear = Cross-sectional Area of Uncut Chip/sin(Shear angle)

Shear Strength given Coefficient of Friction in Metal Cutting

Go Shear Strength of Material = Coefficient of Friction*Yield Pressure of Softer Material

Shear Strength of Material given Total Frictional force in metal cutting

Go Shear Strength of Material = Total Frictional Force by Tool/Area of Contact

Shear Strength of Material on Shear Plane

Go Shear Strength of Material = Total Shear Force by Tool/Area of Shear

Area of Shear Formula

Area of Shear = Cross-sectional Area of Uncut Chip/sin(Shear angle)
A_s = A_c/sin(ϕ)

What is the significance shear angle?

The shear angle is of fundamental importance in chip formation. The smaller the shear angle the larger the strain, the machining forces, and the power requirements. There is nothing in the geometry of the tool that dictates what the shear angle should be.

How to Calculate Area of Shear?

Area of Shear calculator uses Area of Shear = Cross-sectional Area of Uncut Chip/sin(Shear angle) to calculate 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 calculate Area of Shear using this online calculator? To use this online calculator for Area of Shear, enter Cross-sectional Area of Uncut Chip (A_c) & Shear angle (ϕ) and hit the calculate button. Here is how the Area of Shear calculation can be explained with given input values -> 2.3E+6 = 4.5E-07/sin(0.199072254482436).

FAQ

What is 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 and is represented as A_s = A_c/sin(ϕ) or Area of Shear = Cross-sectional Area of Uncut Chip/sin(Shear angle). 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 & Shear angle is the inclination of the shear plane with the horizontal axis at machining point.

How to calculate 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 is calculated using Area of Shear = Cross-sectional Area of Uncut Chip/sin(Shear angle). To calculate Area of Shear, you need Cross-sectional Area of Uncut Chip (A_c) & Shear angle (ϕ). With our tool, you need to enter the respective value for Cross-sectional Area of Uncut Chip & Shear angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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