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Design a circular steel section to lift a structure 3

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Something like that would generally be set in sections and field-welded. Depending on the circumstances, it may be welded from one side only due to access.
Fabricating full length, transporting, and raising from a horizontal position to vertical may be problematic as well.
If not specifically designed for it, the liner may not support its own weight when lifted at each end only.
It is also not uncommon to use two trunnions on an assembly shaped like this.

I really don't understand your sketch there, so not sure exactly what you're looking at.
If your lifting assembly is a torus with square cross-section, you can check overall bending and shear due to vertical load by cutting a cross section at a diameter and summing loads and moments on either side.
You can check torsion by taking a smaller section as free-body. Note that torsion and shear will be zero at certain points due to symmetry so choose cross sections carefully to take advantage.
Due to curvature, bending stresses will actually be a little higher on the inside, but this can oftentimes be neglected.
If there is radial loading on the assembly, Roark has equations for a circular hoop loaded by N equally spaced radial loads that will be helpful.
Refer to ASME BTH for allowable stresses, etc., if the US- may vary elsewhere.

On a small lift, you do all your homework, call in a rental crane with operator, and they set it for you.
If you're honestly in a biggest-crane-in-the-world situation, the people that own and operate those machines would generally have a lot of engineering expertise available as well.
The choice of how much of that liner to set at a time would generally be an economic decision, factoring in crane cost as well.
FYI, I find the Liebherr LR 13000 described as the biggest crawler crane in the world, has a maximum hook height of 236m or so.
 
Can you lift it in 3 or 4 segments? with temporary bolts to be field welded in place?

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

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