That depends what you mean by "...very strong." In comparison to other pressure shells it's not a hugely enormous must-add-another-inch-of-steel-plate step. Even if SL pressure is maintained in space, the max differential is only ~15 PSI ie around half of what your car tyre contains. Some Gulfstream business jets have a max differential of ~10 PSI. so the shuttle would only require another 50% gain (ignoring any other structural requirements). If the shuttle's cabin pressure was kept at half sea level pressure then the pressure differential would be ~7 or 8 PSI - less than the Gulfstream's maximum ability and in the same range as many other jets.