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# Wall thickness calculation based on contact pressure

## Wall thickness calculation based on contact pressure

(OP)
Hello,

I'm working on a force transmission calculation where a 22mm diameter pin is assembled into a 24mm diameter hole. If you visualize a 22mm circle within a 24mm hole, the pin is pushed radially by a certain force so it pushes against the wall of the hole. Can anyone please help me calculate the required wall thickness around the 24mm dia hole to withstand this force? I can calculate the contact pressure at the interface, but how do I use that to arrive at the wall thickness needed? Or will a simple calculation of equating the allowable stress to the force divided by the load bearing area (determined by multiplying the depth of the hole by the wall thickness) suffice?Thanks for any help you can provide.

### RE: Wall thickness calculation based on contact pressure

Refer Table 14.1 case No 2 of Roark.

In addition to the pressure force, D_1, D_2 and length of cylinder L are the parameters.
But you need to check the tearing of plate (with hole) under tensile load also to check with the member failure stress.

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### RE: Wall thickness calculation based on contact pressure

(OP)
Yes, I realize I'll need to check for the tearing of the plate. My question is, how? Do I take the calculated contact pressure and put it into thick/thin (depending on wall thickness) cylinder equations to estimate the hoop stress? Will that suffice? And lastly, will the thick/thin cylinder theory hold good for this kind of loading?

Thank you,
Abhi

### RE: Wall thickness calculation based on contact pressure

You should consult some textbook or handbook for bolted joint design for clarification on concepts.. Depending on joint configuration various possible failures are to be considered like edge tearing of member (plate), shear of bolt, tensile yielding of member, bearing stress on bolts, bearing stress on holes etc. Before actual design you should refer some structural or mechanical code.

Engineers, think what we have done to the environment !https://www.linkedin.com/in/goutam-das-59743b30/

### RE: Wall thickness calculation based on contact pressure

Lifting codes often have calculations for pinned connections (for shackles and lifting lugs).

ASME BTH-1 has formulas/ criteria for pinned connections that you could use.

### RE: Wall thickness calculation based on contact pressure

(OP)
An update on this.

I had my assembly set up and analyzed by FE. The stress at the contact turned out to be 513 MPa (74000 psi). The stress using the thick walled cylinder calculation was 414 MPa (60000 psi). Simple pin joint & the ASME BTH-1 calculations give stresses almost 10 times lower than the FE value. That's probably because they assume half the surface area of the pin is in contact with the wall (which is not the case here). While the 414 MPa too is not very accurate, it's the closest theoretical estimate to FE I have right now.

Thank you.

### RE: Wall thickness calculation based on contact pressure

What are the yield strengths of your materials?

### RE: Wall thickness calculation based on contact pressure

(OP)
The pin is hardened alloy steel (AISI 52100) and the plate with the hole is 65-45-12 ductile iron. They yield at 295 ksi and 45 ksi respectively.

This is my exact setup:
The force pushing a pin of 0.625" diameter against a hole of 0.651" diameter is 610.1 lbf with a 0.375" length of contact. The resulting Hertzian contact pressure is 30,916 psi and the contact half width is 0.034". The principal stresses in the x, y and z directions are -9387, -5858 and -24,423 psi. The max. sub-surface shear is 9283 psi at a depth of 0.026 in. While the contact shear seems to be within the yield (shear yield of 65-45-12 is ~25.6 ksi), I wasn't sure if the wall thickness around the hole (0.24") would be able to resist tearing. My question is, do I just use the force 610.1 lbf to calculate the wall strength, or do I use the Hertzian contact pressure? Logically, the stresses should be the same either way, but the hoop stress resulting from using the contact pressure in thick walled cylinder calculations is very high (~60000 psi).

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