Safety Factors for threaded pressure vessel?? 1

[mikepl]

Hi there, I have spent three days trying to solve this problem. Any help will be GREATLY appreciated.

Ok, I have this threaded vessel. Its a hollow cylinder which is capped on both ends with nuts that enage on the threaded portions. It is packed with mixture which is compressed with a pressure of 25,000 psi, axially. The thread is a #10-32. Now all I want to do is solve for the factor of safety for the tensile and shear stresses working on the external threads of the columns.


Part 1: Tensile SF

Know I know SF = yield strength of my material /
tensile stress in part

So I know my yield stress and solve for tensile stress.

According to Roarks's formula:
stress = ((Q)*(b^2)) / (a^2 - b^2)
q = stress = 25,000 psi (known)
b= hole radius = known
a = OD radius
BUT because its threaded a is not immediately know I assume
so I went to ASME B.1.1-1989, p141
and found that the tensile stress area is equal to As

As = .7855 * (D- (.9743/(1/P))^2
I plugged everything in and solved for As

This was for a SOLID thread though, not hollow

I then worked my way backwards and solved for the radius, knowing the area and solved for "a"

Question 1: IS this the correct way of trying to find the tensile SF??


PArt 2 - Shear Stress

Same problem shear SF is unknown,

So SF = Shear strength of material (known) /
shear stress

Now how do I solve for shear strength of the external threads? My pressure of 25,000 is axial..

I can know it has to do with the Length of engagement, which is known. That beasically what I am trying to do, si come up with an adequate Length of engagement for a SF.

I do know that thread shear area= ASs (ASME-1989 B.1.1)
= [ (PI) * (1/P) * (LE) * (D1max)] *
[ (1/ 2(1/P)) + .57735 (d2min - D1max) ]

I can solve for ASs and obtain a value but I don't know what to do next..

I have ASs, a material shear strength, and an axial pressure known inside the vessel, so whats the relationship.

Does this shear strength even take into account the hole of the vessel even though I am just concerned with the shearing fo the external threads?

I have searched the internet for days with no success.

Thanks in advance!

MIke

 

[CoryPad]

Answer for Part 1: Yes, that would be an appropriate way to calculate a safety factor. Be careful with your As formula - it is based on diameter, so you need to remove pi (which changes the 0.7854 factor) is you use the Roark equation, which is based on radius.

Answer for Part 2: You need to calculate the thread stripping strength for both the screw and the nut. Threads shear near their roots, so you needn't consider the hole unless you don't have fully formed threads. If you know the applied force (F = &[ignore]pi[/ignore]; q b²), and you calculate the screw and nut shear areas AS_s and AS_n, then you divide F by AS_s and compare this to SS_s (the screw shear strength) and you divide F by AS_n and compare this to SS_n (the nut shear strength).

 

[mikepl]

Thanks for the help!

I am a little confused on your euqation for
the applied force, is that F = (?) * q * b^2,

I am assuming q is still the pressure of 25,000 psi

What is the first character in that equation?

 

[CoryPad]

That character is pi, 3.141 592 654 (looks like an n, doesn't it?). The other variables are from your first post: q = 25 000 psi and b = hole radius.