Even if you have actually read this far without getting bored it is about to get a whole lot worse. Here is what really happens when you put an aquarium on the floor:
"Kevin is a structural engineer so he knows exactly to the pound how strong his floor framing is." Well we can get close and we can be safe but we really don't know exactly what load will cause the floor will collapse. Man did not manufacture wood from basic elements under controlled conditions as we do steel. Mother nature made wood according to her whim. Oak is stronger than southern pine but not all southern pine trees are identical. Wood has several "grades" based upon its' physical condition but it is usually visually graded. That means a man at the mill looks at the linearity, grain, knots, splits etc and then says: "I think that I'll call this a no 2 grade" Then we structural engineers look in a book which tells us only approximately how strong it is.
This is the material that is between your floor joists. It might be a solid 2 x 10 blocking. X-braced wood slats or X-braced metal straps. Bridging does two things. It helps to distribute concentrated floor loads to more joists (If they deflect together then they share the load.) than the ones directly below the load. And it also keeps the floor joists in a verticle position so that they don't tip over on their side. (Lateral-torsional buckling)
Strength and Stiffness:
These two items are completely different properties of a material that are indeed related to each other. This single point is definitely the source of a lot of confusion. Strength is obviously how strong something is. Stiffness is how much it bends, deflects, flexes etc.
If you were to hold a pencil at the edge of a table and then strike it just past the edge of the table you might shear it off. In your floor joists, the shear stresses in the wood joists are the greatest right at the face of the supporting bearing wall. If you have a shear failure in your floor joists it will be a horizontal split, at mid-depth of the joists, parallel to the grain in the wood, near the supporting wall or beam.
When you hold that pencil in both hands and rotate each hand in oposite directions you will bend the pencil. The pencil should break near the middle. The bending stresses put tension into one side of the pencil and that is where you can see the wooden pencil start to split apart. If you have a bending failure in your floor joists then the wood will pull apart at the bottom of the joist near the mid-span of the joist.
First the weight of your aquarium bears on the subfloor. For the most part this is of little concern unless it permanently puts a dent into your beautiful hardwood floors. It takes an incredible amount of pressure (in psi) for the leg of an aquarium stand to poke a hole through your floor. This type of failure is called punching shear and most plywood or tongue and groove plank subfloors are very strong in punching shear. It could happen, it is just not very likely to happen at all. The subfloor carries the aquarium leg load to the floor joists. Remember that your primary floor structure is the wood joists and that is what was designed to support 40 psf, not the subfloor. The subfloor has to be able to resist the common concentrated loads from refrigerators, water beds, and chairs, etc. and it can do so easily enough since it only has to span the 16 inches between the floor joists. So the subfloor can resist a very large bearing pressure without puncturing the plywood and that is why it is not the bearing pressure that is the greatest concern to us.
"I weigh 250 pounds and can stand on one foot anywhere on the floor without crashing through the floor. My foot is about 36 square inches (0.25 sq ft) so that is 1000 psf. Therefore Kevin's 40 psf makes no sense." Like I said above, the subfloor is very strong in punching shear. And an isolated bearing pressure of 1000 psf on the subfloor has nothing at all to do with a uniform floor design load of 40 psf on the floor joists. The floor joists must be able to support the 250 lb man not the 1000 psf foot pressure. The subfloor easily supports the 1000 psf in punching shear and carries the 250 lb weight to the floor joists.
Structural framing might be designed for this theoretical uniform 40 psf but it probably doesn't reflect the real world loading conditions in any room of your house. The most likely way for a residential wood floor to fail would be because of excessive shear stresses or excessive bending stresses in the floor joists. So let's say I have a 125 gallon tank and the All-Glass web site says that it weighs 1400 lbs and is 6 ft long. The aquarium is oriented perpendicular to the joists and my floor framing is wood joists spanning 12 ft. So this 6 ft by 12 ft portion of the floor was designed to safely support a total live load of at least 6 ft x 12 ft x 40 psf = 2880 pounds total and may actually be much stronger than that, as discussed above. (And keep in mind that this 2880 pounds includes the weight of any people, furniture, bookshelves etc that are located in that 12 ft x 6 ft area) Does this have much value to you? Yes, but only a little bit. The bending stresses and the shear stresses are distributed much differently due to a large concentrated load like an aquarium than they are when distributed uniformly. Aquariums located close to the wall generate high shear stresses and very low bending stresses. Aquariums located in the middle of the span generate extremely high bending stresses and much lower shear stresses at each supporting wall. But you know that it was easier to break that pencil by bending it, so up against the wall is still the preferred aquarium location.
I think one of the best sources of estimating the weight of your aquarium is to visit the All-Glass web site
. Basically you can figure that water weighs 8.34 pounds per gallon or 62.4 pounds per cubic ft. Then there is the weight of the aquarium itself and the weight of the rocks and substrate and stand. You know that the density (weight per unit volume) of rock is greater than the density of water. That's why the rock doesn't float. Depending upon the rock that you use, the density might vary from 120 pounds per cubic ft (pcf) to 180 pcf. The all-glass web site says that a 125 gallon tank weighs 206 lbs (empty) and the total estimated weight of a full aquarium is around 1400 lbs. Let's say that you are adding 210 lbs of limestone rock and gravel to a tank. The density of limestone is around 140 pcf. If this was a solid rock it should be around (210/140 = )1 1/2 cubic ft in size. If it were all gravel it would not all fit into a 1 1/2 cubic ft box but that is because there are lots of pockets of air in that cube of gravel. So 210 pounds of limestone whether solid or gravel should displace about 1 1/2 cubic ft of water. The "bouyant weight" of rock is the weight of the rock minus the weight of the water that it displaces. So this rock has added about (1.5)(140-62.4) = 116 pounds to the aquarium weight. The water in the aquarium weighs (125)(8.34) - (1.5)(62.4) = 950 pounds. So if that aquarium stand weighs 44 pounds, then this is how this works out. Total weight = 206 lb (tank) + 950 lb (water) + 210 lb (rocks) + 44 lb (stand) = 1400 lbs. (Note that since I subtracted out the volume of water that is displaced by the rock, I must use the total weight of the rock and not the bouyant weight.)
Another often unrecognized structural concept is that the duration of the load can be a factor in whether a wood structure collapses or not. Anyone that has ever used a chain saw to cut part way through a tree knows that. You can push on the tree and the tree does not break and fall down immediately unless you use a lot of force. Or you can use less force and sustain it for a longer period of time to make it fall down. A floor failure that I investigated occurred at 3:00 am on Monday morning due to an excessive load that was placed on a wood framed floor on the previous Friday afternoon. So if an entire professional football team crowds around to admire your large beautiful aquarium, it might not be any cause for concern unless they stand there all weekend.