ASME Sec VIII Pt2 Stress

[chris456s]

In BPVC Sec VIII pt 2 paragraph 4.3.10.2,
the middle term for stress sigma_sm for spherical shells has a sin squared phi in the denominator.
Phi is listed as a spherical location in the Nomenclature section.
So for infinitesimal values of phi, the stress on externally loaded spherical shell would be infinitely large.
There is always such a location.
This makes no sense.
Am I interpreting phi incorrectly?
How can this stress be used to validate a design when (no matter the geometry, so long as F is not equal 0 ) I can find a location (phi) such that the stress is too large?

 

[Geoff13]

Not sure what your F force is, but as phi approaches zero the force F will also go to zero. It is only be the portion of F that is within the area defined by phi that will create stress at the location being evaluated.

(For future reference, it's Div 2, not Pt 2.)

 

[DriveMeNuts]

Your theoretical prediction is correct. However, the word "infinitesimal" can only be used in the theoretical world.
Perhaps you a making the error by using this word to attempt to make a real-world prediction?
If you are thinking "infinitesimally", then you are likely deviating from the intention of the PBVC code.
Also, paragraph 4.3.10.2 applies to "applied net section" loads. What you describe is a small attachment. Any load will therefore be considered as "local". Other methods such as WRC 537 handle calculating stresses local to small attachments.

To achieve this infinite stress that you propose, the sphere needs an infinitesimally small attachment.
I'm trying to imagine the expression on the fabricator's face when they read the fabrication drawing which requests that they fabricate an infinitesimally small attachment.

Geoff13, F is a force. It remains constant irrespective of the value of phi.

 

[chris456s]

I dont think you understand what I am saying
I am not describing a small attachment
phi is a location according to the Nomenclature section.
So even a huge attachment can have location on it ranging from phi = 0 to phi = 360 deg
So if I choose a very small phi...like 0.00001 degrees from what ever axis phi is measured from, that term with F in it becomes very big.
I has nothing to do with a tiny attachment. But a location.
Is phi not a location?

furthermore, F is a net load and the equation is related to a shell. So attachments have nothing to do with it.
Maybe the shell is a sphere with no attachments and load F is from accelerations due to being on a ship that is bouncing with waves.
My question is simply.... notice that for small phi the stress is huge, and phi is a location (unless im wrong)...so there is always a location small phi for which the stress is unacceptable. How can this be?

My interpretation of phi must be wrong. but the Nomeclature section says phi is the "angle to locate a circumferential section in a spherical shell." So for the section located by phi = 0.000000000001 the stress is huge??????

 

[TGS4]

Remember the validity limits (including the inequalities) detailed in subparagraph (b):

(b) For spherical shells for 0 deg < ϕ < 180 deg:

Indeed for values of 0° < ϕ < 1°, the longitudinal stress and shear stress can approach infinity, theoretically.

Thankfully we live in the real world.

If you have a problem with the equation(s), please submit an inquiry to the ASME Code Committee.

 

[chris456s]

Thanks for that
But how is this not related to the real world?
A location related to tiny phi exists on all items.
So how can anyone use this equation?
Ignoring small values of phi is like selectively reporting on only locations that have passing values

 

[DriveMeNuts]

They are able to use this equation because they have the experience and expertise to have the engineering judgment to know its limits of use. Computerised people can't yet design pressure vessels. Judgement is required.

Phi is not a location. Phi is the size of the hole in the sphere.
When phi is small, it is more accurately described as a small hole or nozzle (A small attachment isn't a good description).
ASME VIII div 2 has separate rules for nozzles. WRC 537 also handles loading and stresses around nozzles.

The code committee could add a clause directing a young inexperienced engineer to use the nozzle reinforcement rules for small phi (i.e. small openings), however an experienced engineer familiar with pressure vessels and the code has the experience and judgement to know to do this anyway.

E-mail a two sentence inquiry to the ASME Code Committee and see what happens.

 

[chris456s]

thanks for your help.
I found my problem.
My 2015 version of the code was missing phi in a graphic
Like I thought, I was completely misinterpreting what phi was.
I looked in a older version and phi was defined in the graphic.
It is all so clear now.