Conical Tank Roofs

Just wondering - Do your calculations take into account any wind/snow/ice loading on the roof?

No, it's just for the radial stress in the roof due to internal pressure. Snow/ice reduces this stress, though obviously it adds to the problem of external pressure. That's why the purlins are added. I don't recall suppliers saying roof thickness is limited by external pressure.

This is not my area of expertise but I can see that there is complex behaviour here. It is not a statically determinate problem.

The tank wall will need a compression ring at the junction with the roof. That ring will reduce diameter under the inward pull from the roof while the roof, from side to side will get longer, the cone will change shape in ways that indicate other structural effects.

The tank side walls will stretch under internal pressure except up at the compression ring where it will shrink. This will cause bending of the tank wall and roof plates.

When you add allowances for fatigue, corrosion and local code requirements plus the availability of standard material thicknesses, then your vendors may have a more limited selection of choices than you have considered. Minimal info means that we are just guessing.

This is an area of engineering that isn't in my realm of expertise either, as I don't design steel tanks to hold gases, only water storage tanks. Natural gas????

I'm in agreement with much of passingtongreen's statements. Except, shouldn't the upper ring at the roof-to-side wall juncture be considered a "tensile ring", not a "compression ring"? It seems to me that the conical roof (with X-degree of slope) would produce a lateral outward reaction thrust, as there is a tendency for the roof to "flatten out" under gravity loading from it's original erected position. Yes, I know this counteracted by internal gas pressure, but the structural design of the tank must be analyzed under several loading cases, and combinations thereof), such as: 1. empty, 2. full of gas, 3.partially full of gas, 4. under internal vacuum, 4. all of the above cases applied in combinations with snow & ice loadings (balanced and unbalanced snow loads) and wind loadings. You get the picture, correct?

Has the OP even considered secondary actions within the roof, particularly thermal loadings and resultant stresses? P-Delta forces should be considered too.

Also, I can imagine that some degree of corrosion allowance much be considered for such a critical structure, adding to the roof plate thickness requirement. Additionally, a fair amount of wind loading occurs, both windward (pos. pressures) and leeward (neg. or suction pressures) of the entire tank, along the entire height of the tank wall & also against the sloped tank roof.

Is the roof a "floating type", allowed to rise and lower depending on the internal gas volume? Dynamic movement, and hence dynamic loadings, of the roof must be taken into account if this is the case.

LOL

I played around with the compression/tension ring, there is are conflicting effects and it could go either way, so I picked one.

I looked at some tables I have for pitched roofs with fixed ends and no columns, for a slope of 1:5, the horizontal reaction is 1.25 times the total load. We don't have a beam but it might give some idea.

LOl w/ Passingtongreen

Yeah, it's how you view things I guess and use the terminology in the end........it's either half a dozen of this or a half dozen of that.

Compression ring vs tension ring. Hmmm... that's suddenly become an extremely intriguing question. This type of calculation shouldn't fluctuate depending on perspective. But it sure seems to.

This almost approaches a conundrum status.

Very very interesting. Looking forward to someone who can shed light on this. I'm sure the answer will make total sense once it's revealed.

The upper perimeter ring can be viewed both ways: it will become a "compression ring" IMPO when the internal tank gas pressure is significant enough to push the roof upwards (if that case ever happens...We don't know the dead loading of the roof, meaning it wasn't provided to us by the OP), meaning that the internal pressure has to overcome the roof "self-weight" that is due to gravitation. Otherwise, that ring will be in tension most of the time. It depends on the loading case...singular loading or a case with combined loadings. Logic, from a Structural Engineering POV, dictates that the tank be analyzed for several loading conditions, not just a singular one.

That's the way I look at it. When there is insufficient internal gas pressure within the tank to raise it upwards, and the fact that the sloped conical roof is most likely FIXED at it's connection to the ring, there is an inherent tendency for the roof to induce outwards lateral reaction, a downward gravity reaction, and a bending moment at the roof-to-wall ring juncture.

I believe that the ring will be acting in a "tensile" mode most of the time. Really, you don't want this ring to act in a compression mode due to buckling concerns, unless you can reduce the lateral unsupported length(s) along it's perimeter path line with several roof crossing beams oriented perpendicular to the ring.....if beams (actually beam-columns subjected to combined bending about their strong axis + axial compression loading) are installed in this manner, the lateral compressive forces and end moments will cancel-out one another at the roof summit where all beams would meet.

In the event that there are no beams are installed in the roof to compensate for a compression state, then the roof steel plate shell must be analyzed and designed for combined compression loading (buckling failure mode) and bending due to the induced upward and outward loading should the internal pressure overcome the roof self-weight. that is a pretty tricky analysis sate to calculate longhand, but it can be readily modeled with ease using a state-of-the-art FEA program.

Does that make any sense to y'all?

Thanks for everybody's comments so far. I'll respond to some when I have a minute.

But just about the dead load, can take the 30 mbar as the net internal pressure (it's an arbitrary figure anyway, I'm interested in the general case). I gave roof thickness 3mm. assuming steel that's equivalent to 24mm water = 2.4mbar - almost negligible vs the 30.

I not quite following your statements Codemaster.

The steel shell thickness is derived primarily from the applied loading(s) acting on the initial shell thickness (and sectional properties....cross-sectional area and Sectional Modulus), resulting in calculated internal stresses due to those loadings.

Those stresses are then compared to Allowable Stresses for that grade of steel.....such as, max. shear stresses, max. bending stresses, and combined interaction of max. bending stresses and max. compression stresses, or the combined interaction of max. bending stresses and max. tensile stresses. If the initially assumed steel thickness doesn't fall below the Allowable stresses (any of them) or below UNITY (w/ LL adjustment duration factor included) for the combined stresses, then the shell thickness must be revised and rechecked (sometimes repeatedly) until those condition(S) result in a satisfactory answer.

Also replying to various other comments, for which - thanks.

That's right, if there are other conditions which stress the roof material e.g. bending moments, in addition to the radial tensile stress calculated in original post, this would need to be allowed for. My question is whether these other conditions occur. Circumferential tension is very low as proportional to sin(α), and is a internal force.

A further thought - if the joint between the roof and tank wall could act as a seal but not transmit forces either way, a bit like an inverted cone supported by a ring and filled with liquid, maybe the outer edge of the roof could buckle i.e. go into a wave looking on the edge of the plate. I imagine that's how the inverted cone would fail if forced through the ring. But in a tank situation that cannot happen as the roof edge is restrained by being fixed to the tank wall.

Also there is (I think) a radially inward horizontal force on the wall at the joint, but the gas pressure partially cancels that, and the wall cannot buckle (like a thin cylinder under external pressure) as the roof restrains it. Possibly a bending moment in the top few inches of the wall is caused.

you seem to be calculating based on just a nominal pressure load without allowing anything -- fabrication, transportation, installation loads have to be considered too, but then you have your environmental loads, fatigue, corrosion plus the safety allowances and local code requirements. You have said in your original post that this tank would have to take BOTH positive and negative pressure, which means that the tank has to be designed to the worst case. then in addition to all that, you have to look at available material thicknesses -- or did you want to pay for a custom production run of sheet metal?