Can I add blocks to a ceiling/floor joist for mounting a pullup bar?

Question

I'm wanting to install a pull-up bar in my basement, but the 2x10 joists for the floor above would be too low when factoring in how far the pull-up bar hangs down. To increase the mounting height of the pull-up bar, I was thinking of sistering a 2x6x4 (or 2x6x6, or longer if necessary) further up on the 2x10 using structural screws, and then mounting the pull-up bar hardware to the 2x6, which would give me the proper height to hang from.

When I've sistered beams together previously, I've always used the same dimensional lumber (2x8x8 to a 2x8x8, etc.) Would sistering a 2x6 to the 2x10 cause any issues as far as structural strength? Since my kitchen floor would be above, I obviously don't want to create an issue of having too much of a dead load when I'm hanging on it, that ends up sagging the floor or weakening it.

On a related note, the ceiling is a drop ceiling with removable panels. To mount the bar, I would need to remove at least 2 of the panels. Is there any solution to have the bar mounted, but not have those 2 panels permanently open? I thought of just measuring where the mounting bars would go up through the panel, and cutting out that section. The only problem I see is that I would then never be able to remove the panels without destroying them.

Answer 1

Revision: Your comment clarified that the pullup bar will be mounted perpendicular to the joists. This eliminates my primary concern outlined below.

Yes, you can add single blocks to the sides of your joists. This will not affect the floor system in any way whatsoever. Any load from you hanging there will be roughly equivalent to you standing above.

One strategy for dealing with your ceiling tiles is to run an extra crossbar across the square, essentially through the mounting bracket. This allows you to split the tile in a visually pleasing way and hide cut edges. Use some creativity.

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I don't think one sistered* block will be wide enough since the mounting brackets would be perpendicular to the joists. You'd need several, and stacked blocks usually end up introducing movement.

I'd run 2x6 blocks on edge across the gap between two joists, with at least 3 screws through each connection. Don't install them flat as that leaves more likelihood of the blocks splitting. Be sure to pilot properly to avoid splitting.

PLAN (TOP) VIEW

         v----------- screws (3) --------------v
 ---------------------------------------------------
 ---------------------------------------------------
        | |           joist                   | |
        | |                                   | |
        | |                                   | |
        |x| <-------- blocks ---------------> |x|
        | |                                   | |
        |x|                                   |x| <-- bracket mounts
        | |                                   | |
        | |           joist                   | |
 ---------------------------------------------------
 ---------------------------------------------------
         ^----------- screws (3) --------------^

_{* This isn't really "sistering". That term implies a shared load responsibility, as in doubling a joist to remedy an inadequacy.}