Question on the buckling of spherical caps/cylindrical shells 2

[WARose]

Even though I’m a structural guy: I decided to post this question here since I figured pressure vessel designers probably face this problem on a day to day basis. (The tank I am mounting to actually has dimensions similar to most pressure vessels I’ve seen.)

I’ve got a situation where a client wants to put a pipe support on a (unpressurized) water tank’s shallow, spherical cap (actually, according to the client: the tank has been unused for sometime). The loads aren’t excessive and I have confidence in the stresses I’ve worked up (both locally and as a whole)……however: with the spherical cap I was wondering about buckling from the vertical load near the apex. (Sort of a snap-through type buckling.) One reference I have (i.e. ‘Pressure Vessel Design Handbook’, by: Henry Bednar) figures the stress from such a local load and suggests superimposing it on the other stresses (from overturning and so forth) and comparing that to an overall allowable. Some years back, I remember looking in the ASME code and most of the allowables I saw were due to overall buckling (not local).

One paper I bought over at ASME (i.e. ‘Interaction of Critical Pressures and Critical Concentrated Loads Acting on Shallow Spherical Shells’, by: Evan-Iwanowski & Loo, 1966) suggested (based on my calculations from their results) that collapse loads from such a load at the apex would be so tremendous that there would be problems with the yielding of the material and displacement long before such a buckling mode was initiated.

So I guess my overall question is this: For such localized loads on a spherical cap, is this type of buckling check not done….and if so, is it because it’s not going to control the design? And while I’m thinking on it: does the same thing apply to cylindrical shells?

Thanks in advance.

 

[fegenbush]

I have had to perform these types of checks before. Spherical structures are quite stable until they are not. I have had success in being conservative and spreading point loads over an extended area.

Some references that may help in your future work for this situation:

Roark's Formulas for Stress and Strain (spherical plate formula)
WRC 107 (WRC 537 has replaced it, but many use the old charts)
Theory of Plates and Shells by Timoshenko
Design of Welded Structures by Blodgett

 

[TGS4]

I was going o mention some of the references that fegenbush provided, but stopped. Most of those are used to calculate the local stresses in the spherical head, which, unfortunately, doesn't really have any bearing on whether or not the head buckles.

I say unfortunately, because buckling is related to the stiffness of a structure, and not the current state of stress.

In general, I would say that the types of local buckling checks that you are referring to aren't done. That's not to say that they shouldn't be done, mind you. Here's a paper that discusses a similar issue:

http://pressurevesseltech.asmedigitalcollection.asme.org/article.aspx?articleid=1485031

 

[WARose]

Thanks for the suggestion fegenbush, I have Roark’s (6th edition) and wasn’t aware of that particular equation (will have to hunt it down). I have Blodgett’s book (just about every structural engineer does). In fact I used it to verify some of my stress calcs. I’ve thought about getting WRC 107, but just about every place I find it, they want an arm and a leg for it.

TGS4, thanks for the info, that’s the kind of feedback I was looking for.

 

[chicopee]

About showing a sketch of the tank position and the proposed pipe support. Standard practice if it were a vertical tank is to have the tank support at or near the discontinuity between the head and vertical wall of the tank unless I am reading you OP in an entirely different manner.

 

[WARose]

Standard practice if it were a vertical tank is to have the tank support at or near the discontinuity between the head and vertical wall of the tank....

That's what I asked for.....but the (pipe) routing forced this situation. (I finally gave up on arguing about it. )