BIZOMAT MAKEOS · Fabrication
Shearing Force for Parallel and Inclined Blades
What force does it take to shear this sheet or bar, with parallel or inclined (rake) blades?
Shearing force for straight parallel blades from the shear strength and cut area, and for straight inclined (raked) blades from tensile strength, thickness, blade angle and the relative penetration, with the handbook’s 30% machine allowance and a capacity check.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Blades | choice | Parallel blades shear the whole length at once; inclined blades cut progressively. |
| Material thickness | mm | Thickness of the material. |
| Length of cut (parallel blades) | mm | Length of the cut with parallel blades. |
| Shear strength (parallel) | MPa | Shear strength of the material. |
| Tensile strength (inclined) | MPa | Ultimate tensile strength of the material. |
| Blade inclination | ° | Angle of the upper blade to the lower. |
| Factor n (inclined) | Factor n, about 0.75–0.85 for most materials (handbook). | |
| Ratio of shear to tensile strength k (inclined) | Shear-to-tensile strength ratio, about 0.7–0.8 (handbook). | |
| Relative penetration ε (inclined) | Relative penetration of the blade at fracture (falls with thickness and hardness; from shear data). | |
| Machine capacity | kN | Rated capacity of the shear or press. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Blades
- What it is
- How the blades meet: parallel blades cut the whole length at once, inclined (raked) blades cut progressively along the length, which needs much less force.
- Units and format
- Choose one of 2 options from the list: Straight parallel; Straight inclined (raked).
- Example
- The form opens with “Straight inclined (raked)” selected as a worked example. Choose the option that matches your case.
- Get it right
- Parallel uses length of cut and shear strength; inclined uses tensile strength, rake angle, n, k and ε.
What this means: Material thickness
- What it is
- The thickness of the sheet, plate or bar being sheared.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Force rises in proportion to thickness for parallel blades and with its square for inclined blades.
- Get it right
- Use the actual thickness, including any tolerance on the high side for a capacity check.
What this means: Length of cut (parallel blades)
- What it is
- The length of the cut made in one stroke with parallel blades, the full width of the sheet being cut.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The parallel-blade force is directly proportional to the length of cut.
- Get it right
- Used only for parallel blades; inclined blades do not depend on the cut length.
What this means: Shear strength (parallel)
- What it is
- The ultimate shear strength of the material being cut, used with parallel blades. Take it from the material data sheet or supplier.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 5000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The parallel-blade force is directly proportional to it.
- Get it right
- Use the shear strength, not the yield or tensile strength.
What this means: Tensile strength (inclined)
- What it is
- The ultimate tensile strength of the material being cut, used with inclined blades together with the ratio k.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 5000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The inclined-blade force is directly proportional to it.
- Get it right
- Use the tensile strength for the actual temper or condition of the material from its data sheet.
What this means: Blade inclination
- What it is
- The rake angle of the upper blade relative to the lower blade, which spreads the cut along the length.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0.000001° to 30°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The inclined-blade force falls as the tangent of the angle rises: a steeper rake needs less force.
- Get it right
- This is the inclination along the cut, not the blade’s cutting-edge or clearance angle.
What this means: Factor n (inclined)
- What it is
- The empirical factor n in the inclined-blade formula, which allows for how the material deforms ahead of the blade. The handbook gives a typical band.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.8 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The inclined-blade force is directly proportional to n.
- Get it right
- Use the value from the handbook or your shear maker for the material; used only for inclined blades.
What this means: Ratio of shear to tensile strength k (inclined)
- What it is
- The ratio of the material’s shear strength to its tensile strength, which turns the tensile strength into a shear strength in the inclined-blade formula.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.75 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The inclined-blade force is directly proportional to k.
- Get it right
- Type it as a ratio, not a percentage; used only for inclined blades.
What this means: Relative penetration ε (inclined)
- What it is
- The relative penetration: how far the blade has entered the material, as a share of thickness, when it fractures. It falls with greater thickness and hardness.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.6 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The inclined-blade force is directly proportional to ε.
- Get it right
- Type it as a fraction of thickness, not a percentage; take it from shear data for the material.
What this means: Machine capacity
- What it is
- The rated force capacity of the shear or press that will make the cut, from its nameplate or maker’s data.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 1000000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It changes only the utilisation and verdict, not the force.
- Get it right
- It is compared with the machine force, which already includes the 1.3 allowance for clearance and wear.
Method and formulas
- Parallel blades: F = τ b T.
- Inclined blades: F = n k UTS ε T² ÷ tan α.
- Machine force = 1.3 F, allowing for blade clearance, thickness variation and edge wear.
- Example: 3 mm sheet at 2° rake needs about 48.246 kN at the machine.
Limitations
- Approximate formulas; blade clearance and sharpness change the force considerably.
- Inclined blades need a longer stroke and may twist narrow strips.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check whether a guillotine can cut a plate
- Choose a rake angle to cut the force
- Estimate shear force for a cut-off die
Who it is for
- Fabrication supervisors
- Toolmakers
- Manufacturing engineers
What you get
- Shearing force
- Machine force with allowance
- Capacity check
Interpreting the result
- A small rake angle greatly reduces force on long cuts; plate shears exploit this.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1336–1338. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Cutting force from the perimeter
In Blanking and Piercing Dies by the Numbers
What it covers: Estimating a die's cutting force from cut length, thickness and shear strength, the MP-40 die's 192.8 kN, three estimates compared, stepped punches, shear angles and a slot left out.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Shearing Force for Parallel and Inclined Blades calculator