My wife and I have a plan to shelter in place. We live in Nora in a 2nd story apt. Destroying the stairs will go a long way towards keeping the hordes away. We live a pretty spartan lifestyle to begin with and all of our back-up heating/cooking needs are done in a modern primative way anyway. If worse came to worst, we each have Bug-Out Bags and a plan to get to my grandfathers farm North of Peru. Depending on the level of disaster of course.
Destroying the stairs might just cause more problems than worrying about the hordes climbing them. If the hordes set fire to the apartment building, for example, how would you get out? In your case, bugging out early would probably be the better choice - unless you had the backing of others.