SCJ:

Here, take a look at this file that gives the formula for deflection of a simply supported beam:

http://de.structural-analyser.com/Modeling_HigherOrder_DE_linear_boundaries/
The top row shows the equations to calculate the deflection of a simply supported beam with a concentrated load in the middle. (The other rows show the formulas for beams with other loading conditions.)

A "simply supported" beam is just one that's supported at it's two ends, very much like a floor joist.

The deflection at mid-span of such a simply supported beam is given by the equation:

d = (P*L^3)/(48EI)

or deflection equals P times L cubed divided by 48 times E times I

Where:

P is the load at the mid-span of the beam

L is the length of the beam

E is something called the Modulus of Elasticity, and is a measure of the strength of the material the beam is made of. E for wood varies from about 50,000 to 150,000 whereas for steel, it's about 30,000,000. For any given beam material, the Modulus of Elasticity is the same, and depends only on what material the beam is made of. So, a wooden floor joist would have the same value for E as a wooden flag pole made of the same wood.

I is something called the Moment of Inertia, and is related to the cross sectional shape of the beam. Every beam with the same cross sectional shape will have the same value for I regardless of what it's made of. So, for example, the difference between using a 2X12 as a floor joists or as a diving board is that the cross sectional shape changes with the orientation of the beam with respect to the applied force. In one case the cross sectional shape of the beam is much taller than it is wide with respect to the applied force, and in the other, the beam is much wider than it is tall with respect to the applied force. It's the difference in the value for I in those two cases that results in the 2X12 deflecting very little when used as a floor joists and it deflecting a lot when used as a diving board.

But, what's important here is that the deflection in the middle of the beam is proportional to the span of the beam

**CUBED**.

By shortening the distance between supports, the amount of deflection in the joists as a result of a load it mid-span will be:

a) (1/2) cubed if you added one new support at mid-span or 1/8 of the amount it was before, or

b) (1/3) cubed if you added two new supports each at 1/3 of the length of the beam, or 1/27th of what it was before, or

c) (1/4) cubed if you added three new supports each at 1/4 of the length of the beam, or 1/64th of what it was before.

Certainly, because of that (Length) cubed term in the deflection formula, shortening the distance between the points where your joists are supported is the most effective way of strengthening your floor.

The problem is, adding supports under your floor that are strong enough to support the joists. How are you going to ensure that the supports you add won't simply sink into the mud under your house as a result of the load put on them, or even just because of their own weight?