Calculating Force for Punching a Hole in a Plate

In summary, to punch a 20-mm-diameter hole in a 25 mm-thick plate with a shear strength of 350 MN/m2, you need to use the formula σ = V / A and rearrange it to isolate for V. The area (A) is πr2 and when converted to meters, it is 314.15mm2. However, the shear area is not the same as the area of the punch, but rather the circumference of the punched hole multiplied by the thickness of the plate. This gives a shear area of pi x 20 x 25, resulting in a required force of 549.8 kN.
  • #1
tsukuba
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Homework Statement


What force is required to punch a 20-mm-diameter hole in a plate that is 25 mm thick? The shear strength is 350 MN/m2.

Homework Equations


σ = V / A

The Attempt at a Solution


The first thing I did was rearrange the formula to isolate for V.
I got the area which (A=πr2) gave me 314.15mm2. I change that to m and then I wne ahead and calculate the force which gave me 110.11 MN

But the answer is 549.8 kN ( they multiplied 20x25xπ to get the area)

Not sure where I am going wrong.
 
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  • #2
You have to be careful which area you use for A. When the punch punches a hole in a plate, the shear force is not applied perpendicular to the plate. It's the circular punching which shears from the rest of the plate.

If you make a sketch looking at the edge of the plate, you can see quite clearly what the shear area must be.
 
  • #3
The problem shows me a picture and yes I do see that I use include the thickness of the plate in there but how can I get the value?
The solutions says to multiply pi x 20 x25 but I don't understand where that formula comes from or I get the same value by multiplying 2 x pi x 10 x 25 but again not sure what formula that is
 
  • #4
It's the circumference of the punched hole multiplied by the thickness of the plate. ;)
 
  • #5
so multiplying circumference by height gives area as well :S ?
 
  • #6
Obviously. Look, shearing takes place when two surfaces want to slide over one another. The circumference of the piece being punched out slides over the circumference of the hole left in the plate. Both the plate and the punch out obviously have the same thickness, so the only other property you need to calculate the shear area is the circumference of the hole left in the plate.
 
  • #7
thank you for the explanation :)
 

1. What is shear stress of a plate?

Shear stress of a plate is the force per unit area that is applied parallel to the surface of a plate, causing the plate to deform or shear. It is a measure of the internal resistance of a material to shear forces.

2. How is shear stress calculated?

Shear stress can be calculated by dividing the force applied parallel to the surface of the plate by the cross-sectional area of the plate in the direction of the applied force. Mathematically, it can be represented as τ = F/A, where τ is shear stress, F is the applied force, and A is the cross-sectional area.

3. What factors affect the shear stress of a plate?

The shear stress of a plate is affected by various factors such as the material properties of the plate, the magnitude and direction of the applied force, the dimensions and shape of the plate, and the boundary conditions of the plate.

4. How does shear stress affect the deformation of a plate?

Shear stress causes a plate to deform or shear in the direction of the applied force. The amount of deformation depends on the magnitude of the shear stress and the material properties of the plate. Higher shear stress can lead to larger deformations and potentially failure of the plate.

5. What is the significance of shear stress in engineering?

Shear stress is an important concept in engineering as it helps determine the strength and stability of structures. Engineers use shear stress calculations to design and analyze various structures such as bridges, buildings, and aircraft, and ensure that they can withstand the forces applied to them without failing.

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