Can I use house framing wood to build a swing set
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It needs to be pressure treated.
No. House framing wood is not made to withstand the elements. It will warp and not hold up. Like Susie said, it has to be pressure treated wood, to last and be safe.
In addition to not being pressure treated, framing lumber is only 2 x 4. That isn't strong enough.
You could but it won't last. Pressure treated wood is best.