I have a cat tree that the plastic portion that holds a column upright broke. The original plastic was thin and failed from an 8lb cat's use. The column slides over the support, and the support is held to the platform by a captured nut. The column inside diameter is 60mm, the support will fit, but for me it was very snug so I ended up sanding the outside of the support to allow a little more room.

This was one of my first adventures with OpenSCAD so I probably went a bit overboard on the thicknesses but it is very sturdy.

The nut cavity is 15.6mm at its widest, not sure what size nut that makes it, but it seems very standard for the cat trees I have assembled.

To install drop the nut into the supports nut cavity, and slide over the bolt until they connect. Next twist the support so that the threads are captured by the nut until the support is snug against the base. Finally slide the column over the support.