No offense intended but there are a couple of serious errors with this thread I am sorry to say.
None taken, this is a discussion and I am not the authority on engineering. I am but a mere fish nerd.
1. What you call the "weakest link" is actually the strongest part of the stand. The vertical supports are being compressed parallel to the grain not perpendicular. The compression strength is 4800 psi not 440. The horizontal frame is being compressed perpendicular to the grain. If the weight was all on the center of the horizontal frame you would not want to exceed 440 psi. Fortunately aquariums have their weight distributed evenly across the frame or on the corners so that shouldn't be an issue. However the longer of the span you have the more weight is put on the center and the more easily it can break.
Nice catch. I believe you're the first person to see that. I will have to fix these numbers and calculate this again.
2. The green boards (or something like them) are necessary as they prevent the stand from folding. While the stand has an excessive amount of support from a force load vertically, a lateral force (pushing the stand from side to side) can cause the connectors (screws, nails, glue, etc...), if they are all coming from a direction parallel to the vertical supports, to loosen and the stand can fold over. This is because all the connecting hardware between the vertical support and the horizontal frame is in the same vector (Y axis). Add in the green boards with screws coming from the back to the front and and the connecting hardware is now in a different vector (X), 90 degrees from the other hardware and this keeps the stand from folding. The boards don't have to be there to provide any vertical support but they are a convenient way to add hardware from a different vector. There are other options to doing this besides boards as well. The most common of these being metal plates that overlap the seam between the vertical supports and horizontal frame and use 3-5 screws on each side to hold the seam together.
What boards are definitely not necessary are the purple boards facing the front and back of the stand. They are not necessary for vertical support and do not add any additional vectors of support not provided by the purple boards on the side and the green boards. Although they would make the stand look better aesthetically.
Personally I prefer dado cutting the vertical supports so they are under and around the horizontal frames. This way the screws that come in from the side provide the X axis connection and there is no need for any Y axis connection.
On this point, I will agree and disagree at the same time. Yes, the green boards will provide additional support to keep the frame from folding, but the additional purple boards will do the same. You can add additional screws between the two purple boards in order to have the screw providing the X axis connection. Either way about it, you are relying on the screws to prevent horizontal movement.
I have built countless stands without the green boards and have never had a bit of movement. Of course, the entire build depends on how you attach everything together. I do not see this being a huge issue considering the actual loading and the fact that we are talking about extreme weights that most stands will never see. If the stand is under 36" tall, I doubt you will see much movement at all, even with a 300G sitting on it.
I forgot to add that the combined compression vertical support strength of this stand is calculated by measuring the square inches from the narrowest dimension that can make a perfect square. (1.5" in the case of a 2x4). This is because the failure will happen in the vector of the narrowest dimension. A good example of this is if you take a ruler and hold it so the flat part is facing up and then bend it up and down. It bends very easily. Now hold it so the edge is facing up and try to bend it. You probably can't.
In the case of our model stand the verticals have a combined support square inches (1.5" x 1.5") x 8 = 18 square inches and can support a combined weight of 86,400 lbs or 21,600 lbs per leg. Of course this is only realistic if the stand is only about a foot or so tall.
Interesting. I will research and add this as well.
Now here is where it gets complicated. The longer the legs are the more they are going to bow from the weight applied. If the legs are really long or there is a lot of weight they can bow out in the direction facing the narrowest dimension and eventually shear. This is where the second purple leg facing the front and back of the stand becomes important. This leg, if connected to the legs on the side prevents that leg from bowing by essentially adding the strength of it's longest dimension to the narrowest dimension of the side leg. Now you essentially have a leg with a footprint of 3.5" x 3.5" which will make it considerably stronger than before with little risk of bowing from even extreme weights placed on it.
The 3.5"x3.5" would be applicable only if they were side by side making in essence, a 4x4. Please correct me if my logic is off on this one.
While I agree that a wooden frame can support MUCH more weight than most people think, it's not just the static downward force that you need to worry about.
When you think about how the stand could potentially fail, it will never be simply squashed flat, unless you run over with a bulldozer or something. It will fail by either folding over or the uprights being deformed so they no longer support the full downward force.
Watch this video.
http://www.youtube.com/watch?v=EjOvI0TOx98
OK that's a bit extreme, but the shelves were holding the static load of all those cases of vodka just fine, until someone deformed one support, and then the sideways force bought it all down like a house of cards. A relatively small earthquake can have the same effect. A few ornaments bouncing off the shelf is a nuisance, a 300 gal fish tank collapsing becomes a disaster. We recently had a mag 7.1 near hear and a lot of warehouse storage made like that video clip.
Main disaster was the big beer warehouse. :eek3:
What can you do about that? Bracing!!!!
What your drawing doesn't show is the bracing the stand should have to prevent it folding up. That could be diagonal braces, steel corner pieces or probably the simplest, plywood. Generally a stand is clad in something. Make that some structural plywood and you have a something that's both going handle the static weight AND any sideways stress as well.
I think this drawing does a solid job of bracing. If you build to this design, I don't think you will have much to worry about.
Ian
Responses in red.