Just use a repair hammer and look at pieces of your building, it will tell you how much stability it has.
In general stuff will have lower stability the further away from support it is (walls, pillars doorways etc), and it's starting stability will depend on the piece it is placed on top of. Once stability is 0 it means you either can not place the piece, or if it concerns an already placed piece that got it's stability lowered because you tore down something somewhere below it, it will actually collapse.
So you maintain strength upwards by for example placing walls straight on top of walls of the floor below it. And by not making spaces too wide open. In general, a building with narrow hallways and relatively small rooms can be turned in a much higher building then something with wide open spaces, central stairways with lots of open space etc. So your bottom floor is basically a school example of a type of floor that does not allow for a lot of floors above it. It has heaps of open space, and a big hole in the middle.
Strengthening with pillars helps, but it helps (a lot) more, to have pillars straight underthe pillars of the next floor, etc
a building constructed like this:
[___[___[___[
[___[___[___[
will maintain a lot more strength upwards, then a building constructed like this:
[__[____[____[
[____[____[__[
Hope that makes any sense
In the main building I made on the previous server, I spent a lot of attention to having pillars and walls straight above eachother.