When do bathtubs require reinforcing floor joists?

As the subject suggests, I am wondering if my first floor bath remodel requires reinforcing my floor joists. I'll probably end up asking an engineer I'll be consulting anyway, but I would like to have some idea how these calculations work. The details:
The bathtub weighs 376 lbs and can hold 47 gallons. If a pint's a pound the world around, that would be another 376 lbs when full. If two 300 pound people are in the bathtub (worst case), that would make a total load of 1350 lbs. The bathtub's dimensions are 32" by 66".
The floor system consists of 2" x 9.5" (old nominal 2x10) joists 16" o.c. spanning 12 feet from the exterior wall to a girder. The joists run parallel to the bathtub, so there are only two of them directly underneath. The bathtub is basically centered over the span, as it is 3 feet from the exterior wall. The subfloor is 7/8" thick T+G 1x4s, on top of which will be 3/8" ACX plywood and linoleum, then the tub.
Does this floor system need reinforcing, and if so, how? Note that I will be careful not to cut away any of the joists when installing the plumbing. The sidewall of the bathtub will eventually be an interior shear wall, as it is over one of the concrete retaining walls of my half basement, in case that would be of value.
Thanks, Wayne
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Just a point, but I don't think the tub would 47 gallons AND 300 pounds of people. I would be 47 gallons and what ever 300 pounds of people would displace by volume.
TS

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You reinforce the area by "sistering" the joists, which is where you attach new joist to the existing joist, and bolt the two together.
After you do that, you have to replace the x bracing between the joists, since the gap is smaller.
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How often should they be bolted? The span is 12 feet. I assume the bolts (1/2"?) should go through the center line.
Since the bathtub is over just two joists, would it be useful to add blocking between those two joists and the adjoining joists, to spread the load over four joists? That would be easier.
As to whether the joists need reinforcing, here's a stab at an answer: the 32" x 66" bathtub is 14.7 square feet. The extreme load of 1350 pounds I calculated comes out to 92 pounds per square foot. Looking at a span table for 100 psf live load and 10 psf dead load for 2x10 southern yellow pine gives a span of 12-7 for SS, 12-1 for No. 1, and 10-10 for No. 2. Of course, my joists are not southern yellow pine, I guess they may be douglas fir. But they are also a full 2" thick, not 1.5" thick.
This computation makes it sound like the existing floor system is borderline, depending on the grade of the lumber and effect of 2" thick douglas fir versus 1.5" thick southern yellow pine. Did I do this analysis correctly?
Thanks, Wayne
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They should be bolted about every 12" in a zig-zag pattern approx 3" from the top and bottom.

Blocking won't be effective in spreading the bathtub load horizintally to the flanking joists.

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Thanks for all the help! I'll probably end up sistering each of the two joists, to be on the safe side.
Cheers, Wayne
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No, like the other guy said, spread them out. The bolts don't have to be that big, there job is holding the two joists together.

No, blocking is to keep the joists from twisting, and to tie them into a single structure, not to spread load.

I'm no engineer, I can barely spell it. <G> I'm just answering your question on sistering. What you can look at, is the difference between a 2x10 and a 4x10, since that is what sistering the joist is doing.

I dunno, I'm a software guy, so I'd load it to the hilt, and when it crashed through the floor, build is stronger next time. <G>
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"Uhhhh... my tub crashed."
"Ummm, did you try re-building it?"
"Yea and it's still crashing."
"OK Hit Crushed Ice + Oven Set + Dark toast simultaniously and try re-booting the house..."
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