Will my 2x8 floor joists hold my cast iron bathtub filled with water and a person?

If you can see joist and have access to run bracing joist to joist under where legs are this should be fine. Your subfloor is spreading weight already, but there is more weight where legs are. It would not hurt to cross brace under legs.

Better before the tub is in the room.

12' is a bit long for an 8" joist. If you contemplate a ~1000 lb. Concentrated load, I'd reinforce IIWY.

I'd want 2x12 floor joists holding up that much weight. I may even sister up the ones taking most the load. Remember: those old tubs were installed in houses using 4x10 or larger oak joists.

The type of wood and lumber grade of the existing joist are a big factor in whether the existing floor joists would be adequate. The sub-floor and floor materials and the adequacy of their attachment also has an effect on the strength. Lumber grades considered were Hemlock-Fir, Douglas Fir, SPF, and Southern Pine.

Grades considered were Select Structural, No.1 and No. 2. Allowable loads are described as Dead Load (DL) which is the weight of the structure and fixed loads and Live Load (LL) which is movable loads such as furniture, wind, snow and similar loads.

The allowable loadings are limited to a maximum allowable deflection of the span in inches divided by 360. 144"/360 = .4" or 13/32" inches in 12'. (The following is based on 12' span length and 16" centers.) Hemlock-Fir Select has a max. Span of 12'-10" LL = 40 lb/sf DL = 27 lb/sf, Douglas Fir Select has a max span of 13'-7" LL = 40 DL = 27, SPF Select 12'-0" LL = 40 DL = 10, So.

Pine No 2 12'-10 LL 40 DL 10 and No1 12'-2" LL 50 DL 20. Using the load supported by 3 joist 48" wide area 12' long you would have an area of 48 sq ft. With a 950 lb load you would have 950/48 = 19.8 lbs/sq ft. Without consideration for any structural load this would indicate the tub would be eating significantly into the allowable LL and probably absorbing all the dead load capacity that is available.It would appear that full length sister joist could be installed on the three or four joist directly under the tub. They should be full length and rest on the same plates as the existing joist.

The sister joist can be cut as long as the shortest piece at one of the ends is no longer than 3'. They must be nailed securely to the joist and must be secured by the sub-floor, floor members. Cross bracing must be reinstalled to resist any twisting by the floor joist.

Cross bracing holds the joist in a vertical position, they are not considered in the joist loading capacity since they are not there to distribute loads. The sub- floor, floor materials, strength and attachments to the joist does effect the floor capacity and is assumed to be adequate to carry the loads to the joist. Nothing has been provided regarding the floor so this is an unknown.

( There is a chance the existing joist would hold up the tub, there is a greater chance the floor deflection would be considerably more than allowable.) Depending on what is under the tub area, possibly an alternate system of installing a couple double 2 x 8's or 10's at each end of the tub perpendicular to the joist with some 4 x 4 posts resting on spread footings would be easier. The floor joist would not require supplementing if this could be done. The adequacy of the floor would still be in question.

These are just some of the issues involved. Anyone that gives you "this is the way to proceed guidance" without seeing the conditions would be way out of line. The previous is just for thought and potential planing.

You need to have an engineer look at the situation and give you accurate guidance to reduce all the variables. Info from handymen and carpenters with many years experience are not trained to resolve these issues and will not guarantee their design input.

40 years in construction, BSCE, retired, smart enough to not tell you how this can be completed but also smart enoght to tell you where you can go to solve the issues. (Loading values tabulated in Thomas Glover Pocket Reference from Span Tables for Joist and Rafters, American Standard Sizes, American Wood Council. ).

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.