Error? Challenge!

Even the best planning can encounter unexpected challenges - we know this from many years of experience. But what really counts is how you deal with these situations:
I have been looking at a clapperboard in my office every day for over 25 years. The fact that we made a miscalculation on one of these parts of all things is a bit of an ego crunch. But if there's one thing I realized very early on, it's that the only way to avoid making a mistake is to do nothing.
So that you don't fall into the same trap that we did, I would like to share one of our learning processes with you.

Large tanks, which are used in process engineering for a wide variety of purposes, are subject to a wide range of loads such as internal pressure, dead weight, other operating loads, earthquakes, vibrations and so on. In certain cases, e.g. when a tank is being cleaned, negative pressure can also occur in the tank.
Then, similar to the buckling of a bar that is subjected to excessive compressive force, failure is caused by unstable behavior. The container buckles!
In the case of a pole, e.g. a walking stick, on which a lightweight man weighing a graceful 140 kg is leaning, the cross-section may well be sufficient so that the stresses are still well within the permissible range of the wood. According to =F/A, the stress remains constant, no matter how long the bar is. However, if the stick exceeds a certain length while the compressive force remains constant, the thing buckles sideways and the stick no longer does what it is supposed to do (relieve the load on our graceful feet), but buckles away.
The load at which this happens is called Euler's buckling load and can be easily calculated using the relevant formulas. The ratio of the buckling load to the actual load is called the buckling factor. Multiplied by a fear factor, the so-called safety factor, this should be greater than 1.

From a mathematical point of view, a non-linear FEM calculation is carried out here, in which the internal pressure is gradually reduced further and further until this collapse occurs. The material behavior can also be described elastoplastically in the model, but this is irrelevant as the stresses are below the yield point. Imperfections can also be considered here, as a container is never manufactured exactly and uniformly. A chain always breaks at the weakest link. 
The standard, in this case the American standard ASME (American Society of Mechanical Engineers), specifies the required buckling safety for various components of a container.
However, this information was on a different page of the standard and was overlooked in the initial calculation. The proof initially appeared to have been provided, but it later transpired that the value had not been correctly taken into account.

Unfortunate when the container is already in the USA and is about to be commissioned.
We therefore reacted immediately: an additional ribbing was developed, which the customer had welded onto the container on site in the USA. Our engineers and partners worked hand in hand to provide a good solution - which could be implemented directly on site and under high time pressure. Interestingly, the cost of a dished bottom with a thicker wall was more expensive than the thinner bottom with ribbing. Good to know for next time.
It was interesting to realize that this solution was not only efficient, but also economically advantageous. The combination of our technical know-how and our determination enabled us to complete the project successfully.
We had to pay a lot of money for this lesson, but we are very sure that this mistake, which generations of calculation engineers have probably made before and which no one has noticed so far, will certainly never happen to us again.
The fact that we consider this factor to be greatly exaggerated, as the shell usually collapses beforehand (see the swimmer example) is only a small consolation.

This incident has shown us once again how important it is to see every challenge as an opportunity.

So that we can make other engineers and technicians aware of this potential pitfall, I would like to share our experience here.

In this case, I will show you where there is a pitfall:
 

The ASME VIII Div. 2 (2015) standard specifies the buckling factors:

So the critical factor 0.8 applies to the cylinder jacket.

On the next page, however, the following is written incoherently

a significantly smaller value of 0.124 for the dished end.

As this value is included as a reciprocal value in the required buckling safety, a required permissible buckling factor of 2.5 for the shell becomes a value of 16.1 for the dished end. This value is valid for a linear elastic buckling test. This is justified if the ratio between the height and diameter of the container is very small. Otherwise the shell will buckle much earlier (see Fig. 1).

To give you an idea of what an FE model and the buckling analyses can look like, here is a short study:

All calculation methods can be used for dimensioning. The safety factors are different here. The more precise the calculation, the lower the permissible buckling value can be selected.