I haven't taken off the facia to have a proper look at the timbers but I bent the facia outwards a bit and from underneath I saw a piece of timber running parallel to the fascia and I assumed it had joists meeting it at a 90 degree angle (so running backwards from the doors)Ah, you don’t have rafters, it’s a flat roof….hardly any load at all.
don’t the joists go side to side?