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

 

[pmacias]

Hello,

Thank you for sharing your question. The projected area in pin design is an important factor in determining the crushing stress, which is the maximum stress a pin can withstand before it fails under a pulling force. The projected area is calculated by multiplying the diameter of the pin by the contact length between the pin and the fork. This area represents the cross-sectional area of the pin that is in contact with the fork.

The reason why the curved surface area (CSA) of the cylinder cannot be used for this calculation is because it does not accurately represent the area of contact between the pin and the fork. The CSA only takes into account the surface area of the curved sides of the cylinder, but in pin design, it is the ends of the pin that are in contact with the fork and experiencing the pulling force. Therefore, the projected area is a more accurate representation of the area of contact and is used to calculate the crushing stress.

It is also important to note that the projected area is different from the total surface area of the cylinder. The total surface area takes into account the curved surface area as well as the ends of the cylinder. However, in pin design, we are only concerned with the area of contact between the pin and the fork, which is why we use the projected area.

I hope this helps to clarify the concept of projected area and its importance in pin design. If you have any further questions, please feel free to ask. Best of luck with your studies!