Does This Beam Need A Mezuzah?

When I went to this house to do a Mezuzah House Call I noticed that they had a mezuzah on this beam. Although I understood why they thought this spot needed a mezuzah, they were incorrect. Their thinking was: “Two beams, one on either side, and a beam on top, sounds like a doorway to us”. The reason it does not need a mezuzah is because these beams are not there to make a doorway, but rather to hold up the roof (לְהֲחְזָקָת תִקְרָה). Beams contribute to an obligation when they are there to create a doorway, not to hold up a roof. By the way, they mezuzah that they had here was very badly water-damaged, rendering it completely posel (invalid).