We tore down and rebuilt the chimney in 2006.
We knew that several beams had bearings in the chimney, but we were still a bit surprised when we realized that two beams for the intermediate floor had bare wood (or then charred wood) against the chimney flues, i.e., no bricks in between. So they did not have bearings in the chimney, they went straight through.
In other words, perhaps hundred-degree flue gases had passed there for many years before the house got central heating and the tiled stoves were removed.
Wooden beams are quite resistant, but we didn't feel like repeating the same construction, even if it had lasted for many years.
We solved the problem with a welded construction that lies a bit away from the chimney.
However, beware of iron beams that are laid on the chimney. A wooden beam exposed to high heat burns on the surface, which chars, then the interior is protected from the heat by the charcoal, sometimes for several hours (or for many years, if the heat is not so strong).
An iron beam exposed to high temperatures (such as a chimney fire) quickly loses its load-bearing capacity and bends or breaks.
So, lots of houses have beams laid on the chimneys, but check with a structural engineer and with the chimney sweep before you fix it, otherwise, it can become costly afterward.
/ Fredrik