Silo/ Tank Shell Question 2

[dmitriy555]

I have a 106' tall by 32.5' diameter tank. It has a hopper that starts at 50' elevation and goes down 23' and has a 7' diameter opening. The tank has 22 W-shape columns that extend only up to the elevation of 80'. the thickness of the tank plate is 3/16" from top to about 80' and than it becomes 1/4" and goes all the way to the ground elevation. My question is:
Does the tank need the shell plate around the columns below the top of the hopper and if so what purpose does it serve? What loads does it experience? As it seems to me it is a non-structural skin. I need to know this in order to design an opening in the bottom portion of this shell.
I can provide a sketch.

 

[dmitriy555]

This interesting discussion prompted me to look for more references, and I found "Pressure Vessel Design Handbook". It categorize the lower portion of the shell as "Support Skirt" and gives formulas for stresses, however it ignores the column load capacity which seems too conservative. See attached PDF

P.S. The columns do extend into the tank on the inside. Confirmed by a site visit.

 

[ishvaaag]

Anyway, Chrisalope, I think you can extoll more vertical load carrying capacity of the shell. It seems by your calcs the Saturn rocket wouldn't be able to stand. I mean, you need to consider the real system, with any stiffening action present, in this case by the W shapes, and the cylindrical shape itself; some kind of slender pipe, rigidized. Not now, but I may produce some evaluation of the carrying capacity later.

 

[dhengr]

Chrislaope:
I’ll have to chew on your two pages of calcs. for a while to determine what I really think of them and your 40 to 80 kip bracing forces. I believe I will still end up thinking you are mixing apples and oranges in your thinking and approach to this problem. I’m not sure that a plastic section modulus would be the first thing I looked at in a bracing and buckling problem in a shell structure. AISC is a fine reference for steel design in general, but I think they generally steer clear of plate and shell structures, which are animals slightly different than regular structural steel structures, such as for buildings and bridges, etc.

BA’s equation 11-9, pg 465, (Timoshenko & Gere, “Theory of Elastic Stability”) is the critical buckling stress for a cylinder with a 32.5' dia., radius a=195", and a shell plate thickness h=.25", a cylinder or shell of revolution. In the particular mode of buckling Timoshenko was considering, the critical buckling stress is independent of the cylinder length, and dependent on the ratio of the shell dia. and plate thickness. This Timoshenko equation and sever others come into play in tank and shell design, but the design of steel stacks, tanks, silos, storage bunkers, shells of revolution, and the like, have a much more prescriptive flavor in the codes and standards by which they are designed, very much based on history and experience. Finally, with the advent of computers, we can do a more rigorous analysis of these structure, but I still would not stray to far from the standards and history.

Dmitriy:
You still haven’t answered my questions about where are you doing this and what codes/stds. govern this type of design, or are guiding your design. You have gotten some good general suggestions here, but you really need a design std. to hang your hat on. Your pressure vessel handbook find is certainly of interest, and I’ve just glanced at it so far. But, I suspect you’ll find that’s a different animal too. Internal pressures and much different D (tank dia.) and t (shell plate thickness), or D/t ratios, make their’s a much different world and design problem than the one you are dealing with. Steel stack, silo and tank people talk in terms of thin shell structures and thick shell structures, when they are really talking about the D/t or t/D ratios depending on which code/std. you look at. And, the difference in design approach has to do with how the mode of buckling occurs as a function of D/t rations, thus BA’s formula. Also, the two approaches take a different tack on shell plate stiffening and bracing.

 

[paddingtongreen]

@ishvaaag, the rocket won't stand unless it is full of fuel. the outward pressure prevents buckling.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[dmitriy555]

dhengr

the part from "Pressure Vessel Design Handbook" is all I found as a reference. Not sure what codes are applicable to the tank, silo design - as we deal more with the design of platforms for industrial applications. The reason for which I need to know what purpose "Support Skirt" serves and stresses it experience is to design an opening in it. as well as to broaden my engineering understanding of steel tanks.

 

[chrislaope]

dhengr and ishvaaag:

1st of all, I agree my calcs in estimating the cylinder shell axial load capacity is a little bit too conservative. There should be some more accurate theory and method to calculate the cylinder shell axial load capacity. However before we find another reliable method to estimate the cylinder shell axial load capacity, my calcs provides a safe, time saving and therefore a more economic option. By this way you can sleep solidly in the night because it's safe.

BAretired and dhengr:

Currently I do not have Timoshenko & Gere' book at my hand, but based on my educated guess, I think Equation 11-9 on p. 465 of that reference deals with the buckling condition with load applied on circumference of the cylinder shell as shown in Fig. 1 of the attached document. I guess there should also be some Equation which will deal with the buckling mode with load axially applied on the cylinder shell as shown in Fig. 2 of the attached document.

 

[ishvaaag]

paddinton, I know that inner pressure in stabilizes against local buckling, yet I think to remember the wall was also rigidized. At some point the tanks are not full nor pressurized and have still to stand meaningful weight. Also, at the big diameter of Saturn V maybe transmitting the pressure to the outer walls was not so practical, would have to look if such was the case, or it was a circular array of tanks etc. N1, the failed russian rocket competitor had spherical tanks, and trussed skirts so for N1 the shell was surely a more heavy partner in vertical or axial loads.

Anyway, the mere use as a silo (in practice) proves that the carrying capacity must be higher than what proposed bt chrisalope, and that was my point; of course in silos the outward pressure also stabilizes against (inwards) local buckling. Anyway, we aren't going to repeat here any standard to build silos or tanks, I think.

Yet without any inner pressure square tubes of orthotropic walls are made as columns and beamcolumns; and circular ones are also feasible in akin layout; anyone can read about these things in Galambos' IV or V editions.

I find interesting cases like this because it brings the issue of overall buckling of the structures, relative bracing etc. Everything must be considered together.

 

[BAretired]

chrislaope,

The critical buckling stress I gave earlier is theoretical. It does not depend on length because the shell does not buckle over the 50' length. If you don't believe that, try crushing a coke can. A cylindrical shell subject to axial load buckles in small waves.

In actual tests, however, failure occured at a much lower stress than theory predicted. An empirical formula was developed which is given at the top of p. 471 of Timoshenko and Gere and I will not bother to repeat here.

In the present case, we are dealing with a cylindrical shell stiffened by columns, so the issue is considerably more complex and may need to be checked out.

BA