Nugentcn:
You CAN sister your floor joists. Doing so will double the strength and rigidity of the floor, and that will halve the deflection of the floor under any given weight.
However, you can strengthen your floor much more easily and at much lower cost if you're willing to sacrifice some headroom in the space below.
Take a look at the drawings on this web site:
http://www.uoregon.edu/~struct/courseware/461/461_lectures/461_lecture40/461_lecture40.html
They depict beams with both uniform and concentrated loads supported in different ways, and the formula for "DeltaMax" under each drawing tells you the maximum deflection of the beam under those conditions.
Notice that in EVERY situation the maximum deflection equation always has the group "EI" in the denominator.
E is the modulus (or a measure of the strength) of the material the beam is made of. For a steel beam, E would be about 30,000,000 psi, whereas for wood it would be a lot lower (I don't know what it is).
I is the "Moment of Inertia of the beam, and this is entirely dependant on the shape of the beam's cross section. For a rectangular shape like a joist, I = b*h*h*h/12, or the Moment of inertia of a rectangular beam is equal to it's width multiplied by the cube of it's height, all divided by 12.
The following web site includes the sentance: "Two useful examples, especially for wooden beams, are the rectangular beam of height h and width b, and the circular beam of diameter d. The moment of inertia of area of the rectangular beam about a centroidal axis parallel to the width is I = bh3/12, and for a circular beam, I = πd4/64."
http://mysite.du.edu/~jcalvert/tech/beam.htm
So, increasing E or I or both of your floor joists will strenthen your floor, resulting in less deflection of your floor joists.
We can't change E unless we change the material the joists are made of, like sistering the joists with joists made of stronger wood, or stronger material, like sandwiching the existing joists between steel plates.
But, we can easily change I.
By sistering your joists, you effectively double the width of the floor joists, and that doubles the value of b in that bh3/12 equation, which in turn doubles the value of I. That will reduce the deflection by 50 percent.
However, we can double the value of I by increasing the height of the joists too. If you have 2X10's now (which are 9 1/2 inches high) then h cubed is 857.4 cubic inches. If we double that to get 1714.75 and take the cube root, we get 11.97, or 12 inches.
That means that if you were to increase the height of your joists to 12 inches by adding 2 1/2 inches of wood to their bottoms, you would have the same increase in strength as sistering the joists.
All that you need to ensure is:
A) that the wood you add to the bottoms of the joists is as strong or stronger than the wood your existing joists are made of, and
B) the bond between the original wood and the wood you add has to be as strong or stronger than the original wood, and
C) there can be no slippage between the new wood and old wood. That is, the bond between them has to be rigid so that they behave like a single piece of wood. That means you need to glue the new wood to the old wood, not just nail or screw it.
If you do that, it's essentially the same as rebuilding the house with 2X12 floor joists instead of 2X10 floor joists.
And, if you don't believe me, just print off this post and take it to the Faculty of Engineering at your local University, and stop any 3rd or 4th year mechanical or civil engineering student and ask him/her to confirm. Or, consult with any engineering or architectural consulting firm, even over the phone.
LePage's boasts that their PL Premium construction adhesive not only achieves a bond strength 3 times higher than competitive construction adhesives, it achieves that bond strength within 24 hours. If you were to remove all the furniture from the floor so that there's no initial bending of your floor joists, glue and screw wood to the bottoms of your floor joists, you could double the strength of your floor much more easily than sistering all your joists.
Maybe engage the services of an engineering or architectural consulting firm since your house is your single biggest investment, and you don't want to screw it up just because you followed the advice of someone you've never met on a DIY forum.
PS1: If you can find out the value of E for the kind of wood joists you have, you can determine the actual deflection of the floor under a 800 pound concentrated load (350 pound tub, 200 pound person and 250 pounds of water) with the equations on this web page:
http://www.engineersedge.com/beam_bending/beam_bending3.htm
PS2: I think we should keep in mind that Randall was simply trying to help, and that by ridiculing him we are discouraging other people from posting when they think they can be of help as well. Everyone who's tiled their bathroom floor figures that they've learned a lot from the experience and wants to share their knowledge with others.