Question:easy
A square of side length 50 mm is to be blanked from a strip of 2 mm thickness. The sheet metal has a shear strength of 200 MPa.
To enable a single step blanking operation, the theoretical minimum blanking force required is ______ \( \times 10^3 \) N (in integer).
Note: Neglect the effect of clearances and friction.
A square of side length 50 mm is to be blanked from a strip of 2 mm thickness. The sheet metal has a shear strength of 200 MPa.
To enable a single step blanking operation, the theoretical minimum blanking force required is ______ \( \times 10^3 \) N (in integer).
Note: Neglect the effect of clearances and friction.
Show Hint
Blanking force equals shear strength times cutting perimeter times sheet thickness.
Updated On: Aug 5, 2026
Show Solution
Correct Answer: 80
Solution and Explanation
Step 1: Picture what "single step blanking" actually cuts through:
In a single stroke blanking operation, the punch shears through the sheet along the full outline of the square, all four edges at once, and nowhere is the cutting split into stages.
So the force needed depends only on the total shear area that gets separated in that one stroke.
Step 2: Build the shear area from the geometry:
Think of the cut as a thin rectangular strip running along each edge of the square, with a height equal to the sheet thickness.
Unrolling all four edges gives a total cutting length of $4 \times 50 = 200$ mm, and multiplying by the 2 mm thickness gives the shear area.
\[ A_{shear} = 200 \times 2 = 400 \text{ mm}^2 \]
Step 3: Apply the shear strength to this area:
Force equals stress times area, so multiplying the shear strength by the shear area gives the punch load needed to separate the blank in one go.
\[ F = \tau \times A_{shear} = 200 \times 400 = 80000 \text{ N} \]
Step 4: Express the answer in the requested units:
Dividing by $10^3$ converts the answer from newtons into the units the question asks for.
\[ \frac{80000}{1000} = 80 \]
Final Answer:
Whether the calculation is done edge by edge or by finding the total shear area first, the theoretical minimum blanking force comes out to 80, in units of $10^3$ N. \[ \boxed{80} \]
In a single stroke blanking operation, the punch shears through the sheet along the full outline of the square, all four edges at once, and nowhere is the cutting split into stages.
So the force needed depends only on the total shear area that gets separated in that one stroke.
Step 2: Build the shear area from the geometry:
Think of the cut as a thin rectangular strip running along each edge of the square, with a height equal to the sheet thickness.
Unrolling all four edges gives a total cutting length of $4 \times 50 = 200$ mm, and multiplying by the 2 mm thickness gives the shear area.
\[ A_{shear} = 200 \times 2 = 400 \text{ mm}^2 \]
Step 3: Apply the shear strength to this area:
Force equals stress times area, so multiplying the shear strength by the shear area gives the punch load needed to separate the blank in one go.
\[ F = \tau \times A_{shear} = 200 \times 400 = 80000 \text{ N} \]
Step 4: Express the answer in the requested units:
Dividing by $10^3$ converts the answer from newtons into the units the question asks for.
\[ \frac{80000}{1000} = 80 \]
Final Answer:
Whether the calculation is done edge by edge or by finding the total shear area first, the theoretical minimum blanking force comes out to 80, in units of $10^3$ N. \[ \boxed{80} \]
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