this is the span chart for loading dimensional lumber.

[https://irp-cdn.multiscreensite.com/57e36f82/files/uploaded/SPF%20Span%20Chart.pdf]

I have to design floors for new construction and a 2x10 can support a decent load. BUT, that depends on the Grade of the wood.

this chart can help but if it is an unknown grade then I would stick to the #2 grade chart. I doubt anyone would use a #3 for a floor.

https://www.hunker.com/13400811/how-to-calculate-floor-load-capacity

when the building code calls for a floor load of 40# per square foot (PSF) live load that means people, furniture and temporary loads. A 10# PSF dead load is the fixtures like cabinets or flooring like a heavy tile type. These are the typical loading for homes.

what you are doing is adding a point load to that already figured loading.

your climbing wall is going to be resting on the floor and only attached to the ceiling for support. that means all the load is going to go down and the joist is holding only the angled load. So, when you tie the top of wall to 5 joists that means you (I will assume a 200lb guy) will have that weight spread across 5 points. 200/5=40lb at each point. then because it is only the angle load it will be significantly less.

the hanging things will be the full load at the attached points. if you see flex or bouncing of your floor you can Sister 3/4in OSB to the side of the joists and That will stiffen each joist tremendously. I highly recommend this just for a more solid feeling floor above especially if you are playing hard and having the dynamic load of a guy moving and swinging.

to Sister the osb to the joist..

Cut strips the same depth of the joist. then construction adhesive the osb with 2 lines about 1/3rd up and 1/3 down and screws every foot 2 inches from top and 2-3in up from bottom. Screw with a size that won't protrude the other side of the joist but just close enough. a 2 inch wood screw is what I would use. that joist will not move.

PS.. the angled wall is actually going to be a net support for the floor and not a net detriment. Taking a 12 ft span and making it smaller. Any floor load above is going to go straight to the bottom of the climbing wall to the benefit of the structure.