A Banks Orbital requires some form of unobtainium, with tensile strength much greater than any known substance. I'm trying to figure out how that substance would stand up to impacts and explosions.
To be specific, say the material in question is, to coin a word, paraneutronium, basically 'as strong as neutronium would be if it were a solid instead of liquid, and stable at zero ambient pressure'. Or, like a single layer of graphene, except with neutrons in place of carbon atoms.
The nuclear force is a close-range force (it is strongly attractive at a distance of 1.0 fm and becomes extremely small beyond a distance of 2.5fm)
Assuming the neutrons are spaced 1.0 fm apart (and effectively assuming a square grid, ignoring the possibility of a hexagonal lattice like graphene; it doesn't matter for current purposes of order of magnitude estimation).
The measured binding energy of the deuteron is 2.2 MeV. Not the same thing, but a plausible proxy; say that's the bond energy we are looking at here. That's 3.5e-13 J.
Force = energy/distance = 3.5e-13/1e-15 = 350 N. That seems plausible; the above Wikipedia page gives the repulsive force between a pair of protons close to each other as 40 N, and the strong nuclear force must overcome the electromagnetic repulsion in nuclei containing tens of protons.
A square meter of paraneutronium contains 1e30 neutrons, has a thickness of ~1e-15 m, and a mass of 1675 kg.
A meter-wide strip of paraneutronium has a tensile strength of 3.5e17 N.
The maximum length of paraneutronium that could support itself in 1 g = 3.5e17 / (1675 * 9.8) = 2.13e13 m = 2.13e10 km, twenty billion kilometers. That compares favorably with the radius of a Banks Orbital = 1.8 million kilometers; we have a little over ten thousand times the minimum necessary tensile strength.
That means a single layer of paraneutronium could support, say 1 km thickness of rock ~= 3000 tons/m^2, and still have a severalfold safety margin.
All well and good when nothing goes wrong, but in a science fiction story, something always goes wrong or there wouldn't be a story. So what happens when the load-bearing shell suffers an unexpected impact?
What happens if it gets hit by a 1-meter rock at 100 km/s?
Or a 100-km asteroid at that speed?
Or a 1-megaton nuclear warhead?