See above post. please tag or notify other involved user. I cant reply to their post.
This is caused by infiltration of the hot air into the crawl vent and the condensation that results around the cold AC duct. The Duct inevitably sweats and you get water / mold damage. The giveaway is the HVAC , if you look even closer you will probably have the same on the other side of the duct. Unless your crawl moisture issue is less than mine and you only got it on one side.
10 $ says if you look around ALL your ducting you will find the same on both sides of it.
My home inspector suggested encapsulating the crawl to limit outside air from condensating in there, I believe there is also something to be said for hanging the ducting below the joists so they can have some air flow to prevent this going forward. im still looking into that though. its much cleaner looking when they are in the slot. but this is the result.
Google sistering joists , its the answer.
The tell is the dark spots on the other side of the ducting. Its water damage. dark wood has unacceptable moisture level more likely than not.
Also, id be willing to bet you all that black stuffs on the brick is mold. As it is on the wood. if its sweating the mold will activate and eat the wood. weakening it. Stop the moisture , Sister the joist , perhaps get better R rating ducting . Perhaps hang it lower away from the wood a bit with better airflow if thats in code , i havent checked yet.
Go check your attic make sure the bathroom fan is vented out the roof or gable and not the soffit or attic
Have better luck than me.