Crushing Stress in Pin Design - What is Projected Area?

[jayanth nivas]

Hi all,
I today learned that for pin design there is a parameter called,crushing stress,where the pulling force of the fork is divided over projected area,I learned that projected area was d*t where d was the diameter of the pin and t was the contact length between pin and the fork being pulled.Can anyone explain me how the area was derived,it seems i cannot understand why curved surface area of the cylinder cannot be taken for it.Or the difference between CSA and projected area of cylinder.

Sorry if I have misstated something and thanks in advance

 

[256bits]

Hello jayanth
Crushing stress or bearing stress uses projected area.
You have a round pin in a same size round hole. The force pulling the fork(yoke) and rod apart acts in one direction. The projected area is what the hole and pin 'see' of each other in holding the force. Definitely one obtains a nominal stress acting over the profected area, whereas in fact the first contact may be between the pin and hole some where in line with the direction of force.

If it was a square pin in a square hole does that make it easier to grasp.

It definitely is not the CSA minus the projected area.

 

[jayanth nivas]

Hello jayanth
It definitely is not the CSA minus the projected area.

I did not mean the algebric difference between CSA and projected area,I wanted to know why conceptual difference between both.If Projected area is d*t and there is clearance between the hole in the fork and pin (Which there should be),the contact will take place only over some arc length.My question is instead of considering the arc length,why do we consider the entire diameter of pin.

Also can someone provide mathematical proof for projected area ?

I'm sorry to ask the same question again and again.I cannot find any material on internet for this.So,if anyone could point me some source I would be much obliged.

Thanks in advance...

 

[256bits]

The bearing stress is a assumed to be the nominal or average stress and as such uniform where the pin/hole mating surfaces. If you want to determine the actual compressive stress progression for an extremely critical part then perhaps go to an FE analysis, but for simplicity the bearing stress equation as given is used. The actual compressive stress will be something resembling an ellipse that moves farther along the surfaces as the force increases up to a maximun to the point where your part fails. Taking an average of that ellipse gives you a handy acceptable way to design a part against failure with a safety facture included.

Here is a discussion on PF rearding holes of pin/hole of different diameter,
https://www.physicsforums.com/showthread.php?t=379576