Help with calculating weight that steel tubing can handle

[King_triton]

Hello everyone...

Would firstly like to say that I'm new to this forum so please forgive me if i posted this in the wrong place.

I am currently busy with a marine tank build and need some help as the title says.

I have 2mm thick 2"x2" steel square tubing which i am thinking of using for the stand. I just need help to find out if this steel will be strong enough to hold the weight of the tank. when filled the tank should weigh more or less around 1600kg.

The stand dimensions is : L = 1500mm, W = 1000mm, H = 1000mm ( sorry for metrics.. I'm from SA)

I have attached a pic of the stand so you guys can see where it will be braced as well. The bottom part of the stand will be for a sump tank, which will weigh a lot less as it will be shallow hold a lot less water.

Thanks in advance for the help

P.S. I have tried the online calculators and its all greek for me as I am not in the engineering field.. hence my search for help here...

 

[Stargazer19385]

Strength of structures and materials is something I'm good at. I don't know how strong your tank is, which will affect the loads the stand will be taking, but I'll partially answer it from what you've given.

The four legs carry column load, whereas the middle beams carry cantilever load, which is much weaker. How strong is your tank? If your tank is very rigid when full, the four columns will take the load. If your tank bends and sags in the middle, then the horizontal beams will also take the load.

You need to google and calculate the radius of gyration and Euler buckling and second moment of area column strength. The maximum strength of this structure is complex because it depends on how your joints are set up. Tubes get crushed sideways more easily than axially, so you want the sides of your horizontal tubes to attach from the sides, not on top of, your vertical tubes. It will ask you what the modulus of elasticity is, but since the tubes are so wide, I doubt it will matter, since that is just to see if it is stiff enough to reach the load maximum.

What kind of steel alloy is it? Chromolly can take 200,000 psi in a short column, and mild steel about 60,000, off the top of my head, though you should google the alloy number. 2mm is 1/12 inch, x 4 sides is 1/3 inch, x 4 legs is and 2inch wide is 8/3 of a square inch, means you're total weight is well bellow the theoretical maximum no matter what alloy you are using.

1000mm high, divided by 25 mm per inch, = 40 inches. 2 inches wide, = 20 times as tall as wide. I bet you are in the kneeling range (google it), not the Euler range. The legs will not fail from standard compression.

Next, the other two ways this can fail is if the horizontal tubing crushes (if on top of the legs) or the stand tips to the side, or it bends in the middle.

Even if the horizontal tubing is on top of the vertical, it still has half the surface are as the column does, which is well above the strength of the load. I doubt it would crush.

Next, in cantilever. Modulus of elasticity may come into play here to see if it is stiff enough to reach its maximum load, but I'll start with a ball park estimate. Your load is spread out over the whole top, so it is not like it is all in the center. Let's approximate it as half the load being in the center. The load is more complex than this, but this will give us an idea. 1500 mm is 5 feet, or 60 inches. The central edges of the leg columns will take more load than the other four edges, but it should still hold. So it is 30 inches from the center of the stand to the edges, and the beams are 2 inches thick, so 30:1 leverage, and 750 kg or about 1600 lb, divided by 4 breams is 400 pounds on each cantilever, x 30:1 leverage is 12000 pounds of tension underneath and 12000 pounds of compression on top for each one. The web will take some of the load too, but I ignore that for a safety factor and simplicity. The top of a beam has 2mm (1/12 in) x 2 inch of steel, which is 1/6 square inch. 12000 divided by 1/6 is 72,000 psi. So you want steel that can handle at least 72,000 psi. Find out what kind of steel it is, and google mild steel. My estimates were based on half loads, which may or may not be a good model. You would have a better safety factor with stronger steel.

Another thing that matters with the cantilever lead is not just what the maximum is, but also what the sag is. Mild and alloy steel have the same stiffness to a point, before irreversible bending. I don't know how to calculate the sag at maximum load, but if it is high, it would indicate that the table would fail by another method, below.

Finally, it could fail by tipping over, or by local compression where one tube crushes into the other tube at the joints on top. I would have to draw a picture to show the possibilities. The joints also need to handle any lateral loads if the stand tipping, which should be small as long as the process does not start, since it is based on the torque of gravity on a very small shadow.







I attached a picture of the joint. I think you should reinforce it by putting slabs of metal inside the ends. The problem is that only a wield would be strong enough, unless you use a solid piece. And a wield will take the temper out of the steel, making it mild and weak unless you put the whole thing in a furnace again to temper it. Definitely ask someone else if the joints will handle those forces so the tubes don't crush.

 

[King_triton]

Wow.. this is a lot to take in.. and all greek to me(i'm in IT), but I'm trying to understand what you mean.. how would i find out the radius of gyration and Euler buckling and second moment of area column strength

 

[Stargazer19385]

You don't have to. As I said, the columns will not fail. If anything fails, it will be the joints or the top horizontal beams. If you really want to do the column calculations yourself, you can look up the second moment of area for a square tube. I believe it is outer edge to the fourth power minus inner edge to the fourth power, and that difference divided by 12. All steel has the same modulus of elasticity, about 30 million pounds per square inch. The radius of gyration equation can be found on Efunda.com. I do not think the column will be in the Euler buckling range. I think it will be in the kneeling range, and simply using the yield strength times the area of the cross section will give the maximum load, which the tank is much less than.

If your tank is strong enough to handle the water weight while supported on four corners by bricks, then your stand will very likely handle it. If the glass underneath breaks under the weight of the water, then the stand probably would not have been able to support it. Without knowing what the tank is made out of, and how thick the walls are, I can't say more than that. The walls have half as much load on them as the bottom does, and the walls don't need support, so my guess is the bottom is strong enough. The walls also give rigid cantilever strength. I suspect your stand will do just fine with the tank.

 

[King_triton]

You don't have to. As I said, the columns will not fail. If anything fails, it will be the joints or the top horizontal beams. If you really want to do the column calculations yourself, you can look up the second moment of area for a square tube. I believe it is outer edge to the fourth power minus inner edge to the fourth power, and that difference divided by 12. All steel has the same modulus of elasticity, about 30 million pounds per square inch. The radius of gyration equation can be found on Efunda.com. I do not think the column will be in the Euler buckling range. I think it will be in the kneeling range, and simply using the yield strength times the area of the cross section will give the maximum load, which the tank is much less than.

If your tank is strong enough to handle the water weight while supported on four corners by bricks, then your stand will very likely handle it. If the glass underneath breaks under the weight of the water, then the stand probably would not have been able to support it. Without knowing what the tank is made out of, and how thick the walls are, I can't say more than that. The walls have half as much load on them as the bottom does, and the walls don't need support, so my guess is the bottom is strong enough. The walls also give rigid cantilever strength. I suspect your stand will do just fine with the tank.

Thank you Stargazer... The tank will be strong enough, as it will be made of 10mm thick glass. The base of the tank will be a double base. The tank height will be 600mm high, with the water level at 550mm. 10mm glass is sufficient for this, and only if the water level raises higher than 600mm will it create a problem, and then will need to use thicker glass. The total area of the tank base will sit on the stand as it is the same area as the stand. hope this info helps.

 

[Stargazer19385]

I looked up the yield strength of mild steel. Yield strength is the load it can carry elastically, and return to its previous shape when the load is removed. For mild steel, this is about 36,000 psi. 2mm is about 0.08 inches.

I ran through the calculations again. If the tank was divided into point masses in the middle of each upper beam, it might just barely carry the load. But as rigid as that tank is, the weight will be put on the corners. The legs will easily carry the load.