Flat Plate Stress from Internal Pressure 2

[Garrett Green]

Hello, I am hoping someone on here can double check my calc. I design hydraulic cylinders and my machinists are asking for me to change a design to increase tool life. Essentially I will be taking the thickness of the endcap to 0.175" which is a little bit thinner than my tube wall which concerned me. I tried finding the proper calculations in ASME Section VIII for boilers and pressure vessels but could not find any section referring to calculation stress on a flat plate.

The problem setup is as follows:

the part is 1.5" long and 3.375" in diameter.
It is made from 12L14 Steel
a flat bottom drill is boring a hole to a depth of 1.325" leaving a flat "plate" 1.5" in diameter with a thickness of .175"

I found a video online using Roark's formulas for stress and strain to find a solution to this but seeing as I do not actually own this book I wanted to ask for confirmation from others who might. In the video he states he is using Table 11.2 and following along with Case 10a.

I have attached my calc to show my work. If anyone here is willing to help and sees anything wrong let me know.

Thank you!![URL unfurl="true"]https://res.cloudinary.com/engineering-com/image/upload/v1708353738/tips/Xerox_Scan_02192024092041_uqai9w.pdf[/url]

 

[DriveMeNuts]

The equations in your calc don't match Case 10a, and you are not using that case anyway.
Case 10a is simply supported. Your application is fixed support, which matches Case 10b.
Which is Y[sub]c[/sub] = (-P x r[sup]4)[/sup]/(64D), M[sub]centre[/sub] = (q x r[sup]2[/sup])(1+v)/16, M[sub]edge[/sub] = (-q x r[sup]2[/sup])/8
This obviously doesn't consider fatigue failure, and other modes of failure. I hope that there is a generous radius around the inner edge of the flat base.

 

[Garrett Green]

Thank you for the help! I will update my calc accordingly and I have already found Roark's online to purchase because it seems like a great resource.

I was thinking of fatigue strength as well and with my stress value at 1/3 of my yield I did not expect to see a fatigue failure. I have also worked with 12L14 enough to know it handles these repeated loads well in our cylinders. However, with the updated formulas you gave me I am looking at 2/3 the yield strength using the Moment on the edges. With this in mind I am going to review fatigue failure theory and see what I can find. Luckily we also have the capability to test this in house and can put more cycles than the cylinder will ever see in its lifetime in just a couple of days. I can also test shock loading which isn't something it will see during normal operation but it can happen.

There is a decent radius on the corners depending on what I find with # of cycles to failure I will either have to take a look at this radius or just reject the redesign.

Thank you again!

 

[DriveMeNuts]

Section 5.5.2.3 of ASME VIII Div 2 states that if a integral pressure component operates at less than 20% of maximum design pressure, then a fatigue assessment is not required.
But even at 33% of design pressure, millions of cycles will be possible. Just include radiused corners.

 

[GD2]

OP,
You are correct. The end plate has to be thicker than the cylindrical wall due to higher bending stress.
That’s why blind flange thickness is always higher than normal flange or cylindrical wall thickness.
Sec viii Div 1 provides equation for blank.

GDD
Canada

 

[Garrett Green]

GD2, Can you be more specific where that equation is in Sec viii Div 1? I have that and have looked through it for quite some time looking for anything related to stresses on a flat plate or blind flange and I must just keep overlooking the section!

Thank you

 

[Geoff13]

Have you reviewed UG-34 for flat heads? Looks like you'd be similar to Figure UG-34 detail (b-2), but you'd need to provide the specified radius.

 

[Garrett Green]

Thank you Geoff!! While none of these are perfectly exact to what I am doing, I believe Figure UG-34 (b-2) is very close to what I have. I will need to work through it now but this is very helpful!

Thank you again!