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## 20 thoughts on “HOMEWORK H28.A”

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Would the cross sectional area be the area perpendicular to the force needed to cut the hole out?

Yes I believe so. It would be the circumference times the thickness of the cut out.

I believe it would be the area parallel to the force being applied. So in this case it would be the thickness of the sheet times by the circumference of the future hole.

I think all of you are referring to the same and the correct area. Doesn't matter if you call it "perpendicular" or "parallel" to the force.

It is the circumference times the thickness of the sheet.

Sorry, not clear which area they are talking about?

I believe they are discussing the area of the sheet that is to be punched out.

I think the area they were referring to was the sides of the piece to be punched out.

The way I like to look at it is just the perimeter of the hole being cut times the thickness of the sheet.

I apologize @ Yifan Zhu, this is how I should have worded my response . In hindsight I realize my answer probably caused more confusion than clarification.

I know when there is a pin we multiply A by 2. But in this case I am a bit confused do we multiply A by the circumference?

I referenced the first example for this section when starting this problem and basically the area is the circumference multiplied by the thickness

@Zaid, you do that for a double-shear pin, which is a totally different scenario to this one.

Here, you just need to use the area being sheared, which is the circumference of the hole times the thickness of the sheet

Just to re-iterate as there seems to be a lot of confusion about which area to take. You need to take the area of the inside surface of the hole (it is difficult to convey this without a diagram), which is basically the circumference of the hole times the thickness of the sheet.

Is it alright if we find the circumference of the metal sheet and just multiply it with the thickness of it?

Circumference of the hole *

Yes, that's correct

Why is the area sometimes be considered as an area of a circle while sometimes it is considered as the surface area of a cylinder?

So again, this is slightly difficult to explain with just text. But the idea is that you can image the shear force on an object to be applied by a knife. And you take the area that will be in contact with the knife to calculate the shear stress.

So once you find the shear area you can mulitple it by the tres and you have your punching force?

Yes, after finding the equation for the sum of the forces in the y-direction, and solving it for P, I was left with what you stated above to find the punching force