1. Those joists should be able to hold the weight of the wall with no problem. I recommend using 3/4 inch plywood tho instead of 1/2 inch. Will feel more sturdy.
2. As long as you are going directly into those joists you shouldn’t have any issue mounting monkey bars or other hanging things.

I do not do construction personally, but I did build a home rock wall for the kids and have a 30 degree incline that I can climb and feel secure on

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It is also crucially important for point (2) that we know exactly what type of play equipment and regimens you intend to put in place.

Something like this would be ideal: https://dealsformomsblog.com/2021/05/16/ninja-warrior-basement/

Okay, so at least one swing?

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I used to move heavy tools for a living- we routinely drilled a 1/2” hole 2” from the top of a 2x10 exposed ceiling joist in basements with a 12 foot span and hoisted 1100 pound lathes onto their floor stands from one point.

For eyed lags or hooks, pre drill perfectly in the middle of joists to just under root diameter and add a dab of PL premium to the hole, but wax the fastener if you ever want to get it out- this consolidates the deformed fibres the screw threads form and adds pullout resistance. Four GRK structural fasteners to a bracket spanning two joists is much better than one big lag if you have that option.

Good luck. I made a rock climbing wall in my basement years ago and my elbows and wrists still hurt from drilling the holes for the t nuts. Make sure you use at least 2 screws to pin the t nuts to the plywood. They will back out and fall out if you don't secure it.

I know nothing about nothing but, I'd say to be on the safe side you need to not only calculate the weight of the equipment but also find an average body-weight and calculate for every piece of equipment being used to max capacity at the same time. just to be on the safe side. it's not just about if it'll hold it, but consider the possibility of sagging over time.

...unless you happen to have a grand piano in the room upstairs.

Kids swing or grand piano OP, can’t have both.

How much weight is on the floor above this area?

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Agreed. Anytime my kid goes in the vicinity of my grand piano, they both fall through the floor to their deaths.

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Note that if you have exposed joists, you can attach the climbing wall studs directly instead of bothering with stringers running crossways.

If going perpendicular to the joists, you can pick an appropriate joist, cut the studs to lean right against it.

If parallel to the joists, just run each stud up one side of the joist and screw. Then your wall will have the same spacing as the ceiling. Will use less material and be simpler and stronger.

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.

Also, something that swings will exert more force on the supports than something static.

That sounds awful, how many pianos have you had to replace? That must be expensive.

I think you need some new drill bits if your joints hurt from drilling holes.

Don't matter how sharp my bit is, drilling literally 1000's of holes and hammering in 1000's of T-nuts, and shooting 1000's of screws will hurt.

So that rock wall plan isn’t fully supported by the joists. A lot of the weight is held by the studs and floor it’s resting against.

I’ve built two separate home climbing walls. The biggest lesson I learned was securing it against the wall is really important. The swinging forces generated by climbing won’t work if it’s just supported at one end. I tried to build a freestanding wall and it was impossible to make fully secure.

My current wall is small, one 4x8 sheet of plywood. I have 1 4ft 2x6 for connecting it to the wall and one attaching it to the joists, each are secured to 3 studs/joists. This is very stable. I’m like 150lbs and I can make dynamic movements on it all day and it doesn’t move at all.

I'd feel safe with it. I've built a house by hand before including a roof and ceiling joists are fucking beefy, an adult could probably play with whatever you're setting up without issue assuming that you build it in such a way that the weight is distributed across several joists instead of all on one. That's assuming you don't have anything insanely heavy on the top floor and the boards aren't damaged or rotten or anything.

Yup! Thought I was just about done once we got to the drilling and t-nut phase. Wasn’t prepared for the exhaustion of drilling thousands of holes and sinking thousands of t-nuts. We went with ones you had to sink manually too. After setting with holds and backing out took too long, resorted to hammering hundreds in. Exhausting work.

2nd this i build this exact plan on a steeper incline and 3/4 ply is a must. Metolius has the best climbing package to buy i think its a few hundred bucks and it comes with a step by step guide

You may not have been using proper whisky. I found that having a good quality whiskey helps with repetitive tasks like this. Also, I did all of my drilling and hammering with the plywood up on a workbench so my back wasn't toast

Note how the vertical boards have a top board that attaches to all of the joists. That will help spread the load.

As for a swing, I used the swing hangers from menards and my 200lbs didn't create any scary creaking noises.

If you have two points on two joists you should be good.

Just commenting to emphasize the 3/4 plywood and agree with everything this post states.

I don't think most people know that you can/should lubricate a drill bit

If you are going to be inverted on the ceiling holds I would never trust lag bolts or any other vertically screwed anchor. You risk them pulling straight out of the wood and falling on your head/neck.

The only truly safe ceiling anchors are thru-bolted through the joists horizontally so you rely on the shear strength of the anchor bolt. Just make sure its anchored in the upper 1/3 of the joist so there is plenty of wood below the bolt.

If you must do some sort of vertical fastener then Climbing gym setups are the ideal solution for thru-bolting. I think they use at least 3/4" plywood with rear metal anchors that bolts screw into. They are Best for a angled or vertical walls because you are using the shear strength of the bolt. But because they have a metal backing they are probably also ok for ceiling mounts. You could try to get extra large metal backings with a large washer to mitigate any potential pull through risk.

Attach the plywood to the joists with carriage bolts (lots of them). That will distribute the load across the whole plywood and not just a single lag like the monkey bars in the link you posted.

You'll have to self tap all the screw holes for the metal anchors on the back side tho. Search custom rock climbing walls for lots of tutorials.

Also you may want to double check your homeowners insurance. They may not cover damage to the house structure if you happen to deform or break anything because of your use case.

Not trying to be a downer but a person I knew fell from aerial equipment that failed and ended up partially paralyzed.

I remember that pain, but I bought some 16 inch drill bits and stacked and clamped my plywood together and drilled through 5 or 6 sheets at a time.

There are some great construction guides on the internet for for rock climbing walls that would be a great help for some specifics. I built one using a guide to a T and it’s SO sturdy.

Not for wood

Not with oil*

I recommend the Bosch Daredevil bit for t-nut holes.

I have built multiple home climbing walls. Lag bolts (properly installed) are fine for attaching the main structure. Standard timber screws are fine for attaching the ply.

Just use lots of them. The plywood spreads out the force. It also helps if your vertical walls support the ceiling sections.

The individual holds are attached with t-nuts and M10 (3/8 inch) socket head cap screws and bolts. They WILL NOT pull through 3/4" (19mm) ply.

What do you mean by "self tap the metal anchors"?

Self tap: individually drill holes for each t-nut.

Self tap were the wrong words to say what I meant.

I understand.

That is some severe over-engineering in my opinion. No point in making the climbing wall10 times stronger than the structure it is attached to.

And think of all that extra weight!