I wouldn’t want to be around when that thing “goes”! It’s not ‘if’ but ‘when’. Sure, you could do all the calc’s to figure it out, but that’s isn’t what you are paid for, is it? Even without the ‘hot tub’ in place, there are faults with the construction of concern, as you mentioned.
I wouldn’t get too specific as the HO will repair what you commented on, and think he’s good to go. Make generalized statements to include load calcs be obtained from the HT installer (which they never have, also the HO prolly installed himself) and if not available, should be obtained from a PE, and corrections made, prior to use.
The deck does look weel built, and most joists are shorter than usual.
I personally would make note of it, and advise that most decks are not designed or engineered for hot tubs. Further evaluation would be prudent to ensure the deck has been constructed to bear the load of a full tub including people. The sellers may have more information on recent deck construction in regards to the hot tub.
I also think the deck appears to be pretty well built, except for some of the things you mentioned.
The stringers are not attached correctly.
Personally, I would have doubled up the joists under the hot tub, and put in additional 6x6’s. But his is WV, where obesity is the norm, so we don’t use the “175 pound each person” rule. Most of the gals around here beat that weight with one leg! :|.)
One thing I see on a lot of joist hangars-8d decking nails or even roofing nails attaching the joists. saw some today that were not attached at all, they were just sitting in the hangars.
Viewing this on mobile so can’t see pics but decks are obviously built to support nominal psf live weight, I believe 55. You get to a hot tub I always advise client ask seller if they have architect/engineer plans or if not, to have one evaluate and leave it at that. Those guys have the knowledge on spans, fasteners, etc to calculate load and design. I’m sure if you wanted to spend the time looking it all up you could, but just alot of work for no real reason.
FYI - The attached diagram shows the basic method used to determine if a deck can support any load above the basic 10 psf dead load and 40 psf live load prescribed by code. The hot tub in your photo will have an impact on the section of deck depicted in the diagram. If the added load, in this case the hot tub, was supported on blocks or four legs that would concentrate the load in a very small area, then you would start by checking the deck boards to see if they could carry the concentrated load. Most hot tubs spread the load over the whole bottom area, so you can skip #1.
Start by placing 10 psf dead load over Area 1 & 2 plus 40 psf live load over Area 1 & 2, then add the weight of the hot tub over the foot print of the tub in Area 1. Using 40 psf live load over the entire deck would be more than enough to account for people in the tub.
Check the joists under the hot tub, if they pass, check the joist hangers on the tub side of beam AB and beam CD. Next check the design of beams AB & CD. Next check the load capacity of the post connections at A, B, C & D. Finish up by checking the load capacity of posts A, B, C & D, followed by the footing under each post.
The load carrying capacity will be limited by the weakest link in the load path from the deck boards down to the footings.
I do have a question(s). When you say “Check the joists under the hot tub, if they pass, check the joist hangers” etc. How do/would you determine if they pass? Same with verifying load capacity of post. Is there a “basic” formula, at least to give a general idea? More than using size of joist, post, hangers, fasteners to determine? Or should this be left to a PE to decide?
By check, I am referring to checking the load carrying capacity of each element. For example , the joists you check the bending and shear capacity and the deflection based on the engineering properties of the wood and established criteria outlined in the National Design Specifications for wood. These calculations go beyond the tables listed in the code books and clearly fall under engineering design.