I'm wondering if the pressurization of the cabin has a part to play in the structural integrity of the fuselage, the same way an unopened soda bottle is stiffer compared to one that's open.
There is no aircraft limitation on the 737 that requires pressurization to fly. Realistically, even on O2 the whole time, going very high could be unpleasant. I think the Air Force limit was FL 250 for routine unpressurized flight (recalling the T-37); when we depressurized the C-130 for high altitude air drops, we had some amount of pre-breathing that we did, and I never dropped anything near, at, or above FL 250.
But all of those are policy limitations, based on the human physiology involved, not the aircraft itself.
In airline life, I've done a maintenance ferry flight at 10,000' unpressurized, which is the highest we can have the cabin without needing to put on O2 masks. There are probably ways to ferry higher than that if you really had to (crossing the Rockies, for example), but it wouldn't be preferable. Again, though, that's looking at the human element rather than the jet.
I suspect that the reason that there aren't any limitations as postulated in the OP is that the aircraft itself is sufficiently strong that the extra rigidity of pressurization doesn't add anything necessary. After all, the aircraft structure has to be able to withstand a sudden depressurization at cruise altitude, along with the ensuing emergency descent down to 14,000'. When the structure is strong enough to handle all of that, I expect that what's gained by pressurization is just icing on the cake.
Yes airliners can fly unpressurised, because pressurisation is not part of the critical load calculations.
The aeroplane fuselage is dimensioned using the critical G-loads from gusts. The largest gust impacts are at:
- low altitude (higher air density, ground effect)
- low airspeed (gust load is introduced more rapidly into the structure)
Both conditions are at take-off and landing, where the pressure differential is much lower than in cruise.
Any airliner, or any other airplane for that matter, that falls apart if made to fly unpressurized, does not pass certification. The 'Soda Bottle Effect' does add to the structural rigidity of the fuselage, but this is in no way considered part of the required structural integrity of the airframe. On the contrary, if considered at all, it is to see if it jeopardizes it. Don't beat me up over what specific rule, section or paragraph says so, but I recall the use of pressurized gas as a component of structural integrity in aviation is for obvious reasons categorically prohibited. It would be widely in use if that wasn't so.
This actually did happen with a Boeing 737 on Helios Airways 522. Due to a bad switch setting and lack of communication between ground and flight crew, the pressurization was disabled. The plane sounded an alarm, but it used the same sound as an alarm that meant something completely different on the ground. The flight crew mistook that alarm for the one that couldn't happen in flight, and therefore ignored it. The plane never pressurized so the internal and external pressures were equal for the whole flight. The flight crew became incapacitated, the passenger oxygen masks dropped, and the plane flew its entire flight plan unpressurized on autopilot, up to entering a holding pattern over its destination. One interesting thing that did happen is that the alarm light for avionics cooling came on. The avionics are air-cooled, and without pressurization there might not be enough air to cool them. Even with the alarm, the avionics including autopilot continued to function.
Unfortunately the crew never woke up and never landed the plane. It eventually ran out of fuel and crashed, killing all aboard, but the plane itself functioned perfectly until it ran out of fuel.
Because of the cost of flying an empty plane, commercial flights are sometimes undertaken unpressurised, according to a British Airways maintenance engineer I knew (so it’s an unverified third-party claim). They stay below 10,000ft - normal pressure altitude in an airliner is 8000ft based on my own measurements.