How to calculate square tube size for your tank stand

Discussion in 'D.I.Y.' started by TankMaster, May 31, 2018.

  1. TankMaster
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    Reposted here based on this thread - http://www.apsa.co.za/xenforo/threads/dual-tank-stand-build.17063/


    So I decided to look into this and do some calculations, just in case others want to find out if a certain steel tube size is enough to hold up 'x' amount of weight. Although I did study engineering briefly, the following is based on advice given to me by a qualified engineer. Go through the calculations again, just in case I missed anything. This is not my area of expertise. I am just one of those people who spends time researching everything, so please also feel free to correct me.

    I am using online calculators to actually make the math simpler. So you don't need to know much engineering math to do this.

    To calculate this we want to determine the following.
    • Tank Size & total Mass on 1 tier/shelf.
    • Weight (see definition below)
    • Stand Size based on your tank size
    • Section Modulus of your square tube. (Definition Below)
    • Bending Moment ( Local Extremum) based on stand width without center support.
    • Bending Capacity of your chosen steel tube.
    • Conclude if the steel will suffice or if center supports are needed
    • Bending moment with center support

    Let's just relate this with Brenton's (TheGrissom) example and assume all stands are built with welds as shown. With D being the depth and L being the length. Height does not need a definition (Kinda obvious).

    [​IMG]

    • 1.
    Tank Size & Mass - http://theaquatools.com/building-your-aquarium/
    Tank size - 900x300x300 (mm)
    Tank glass+water mass - 93 kg (0.093 ton)

    We then want to decide how many of those tanks we want per tier and the orientation we want to place them on each tier. In Brenton's case, it's just one tank placed with the long side of the tank facing forward. So that makes the total mass per tier 93 kg.

    Mass - 93 kg (0.093 ton)

    • 2.
    Determine the weight - http://www.endmemo.com/physics/force.php

    So by now you may be confused between weight and mass. So here's a quick quote.

    "The mass of an object is a measure of the object's inertial property, or the amount of matter it contains. The weight of an object is a measure of the force exerted on the object by gravity, or the force needed to support it. The pull of gravity on the earth gives an object a downward acceleration of about 9.81 m/s^2."

    So to calculate the weight we simply use the calculator linked above.

    Mass - 93 kg
    Acceleration - 9.81 m/s^2
    Weight - 0.91233 kN (Please use the dropdown menu in the calculator to change from N to kN)


    • 3.
    Stand size

    Ideally, you want the shelf dimensions (D and L) to match your tank D and L. This will provide the most efficient and safe load bearing.

    If you are using a board across each shelf, this becomes less of an issue but may cause problems over time if the wood swells with water.

    Brenton decided to go with a Length of 1.2m and use boards on each shelf. The Depth of the stand wasn't defined but is not needed to qualify your steel of choice. Most of the load bearing is done by the the longer horizontal beams and vertical colums if your tanks are positioned correctly as shown.

    [​IMG]

    We want to assume that the tanks are NOT positioned correctly and that all load bearing is done by the front and back horizontal beams (beams that form the length). This will be the case with MOST multi tank stands with tank orientation front-to-back or left-to-right.

    Front-to-back and positioned on a board away from load bearing beam edges.

    [​IMG]


    If you use this method with 8-12mm plywood and the tanks are positioned more than 50mm away from the edge of the closest load bearing beam, you will need a 3rd horizontal support along the length or depth to prevent the ply from flexing under load like shown here.


    [​IMG]

    So just be mindful of this when designing your stand.

    Brenton's tank length - 1.2m


    • 4.
    Section modulus of your square steel tube - https://www.engineersedge.com/calculators/section_square_case_10.htm

    Definition quote

    "Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include area for tension and shear, radius of gyration for compression, and moment of inertia and polar moment of inertia for stiffness."

    Simply use the linked calculator to determine the Section Modulus value. In this example, we are using 38mmx38mm with a wall thickness of 2mm. We don't really need the other values but are nice to have if you want to tinker.

    Bar profile -
    Our External width and height is the same - 38mm
    and our internal width and height is the same - 34mm

    Section modulus as derived from the calculator using above profile - 3284.21053 mm^3


    Unfortunately, this is where some form of 'smarticles' is involved but, I will guide you through using this calculator. We want to determine how much the steel bars flex under the load of the tanks+water (weight not mass).

    Firstly, to use this we need to remember our weight that we calculated earlier and the length of our stand.

    Weight - 0.91233 kN
    Brenton's tank length - 1.2m

    Now that we know the above we can calculate the bending moment at x= length/2 (pretty much the halfway point of the beam)

    We also must remember that the front and back horizontal beams share the weight so our weight value must be divided by at least 2.

    Weight per beam will therefore be 0.91233 kN / 2 = 0.4561 kN

    Step 1 - In the calculator make sure your units of measurement is Meters (m) and your units of force is Kilonewton (kN). Change it if it appears differently.

    Step 2 - Next, you want to look at "Setting the support of beam" section. Once you find it, click on the first little icon that looks like a santa hat. That is a Pin support. Once you click it, it will ask where you want to place it. Select ON THE LEFT.

    Step 3 - Then look at the icon that looks like handcuffs. That's a Roller support. Once you click on it, it will ask you where you want to place it. Select ON THE RIGHT.

    Step 4 - Next, focus to your top-right and find the box that says "Setting loads of beam".

    Step 5 - Once you find it, click on the icon that looks like a garden fork. This is the Uniform distributed load button. Once you click it, it will ask you to define values for -

    • Start Location - Use Zero
    • End Location - Use Stand Length (in this case 1.2m)
    • Load/Magnitude - Which is our Weight divided by the length - 0.91233/1.2 = -0.07602kN/m (Make sure the value is negative to define that the direction of the load is from above.
    • Click add and you're done with that.
    Step 6 - Focus on the box below "Setting the bending diagrams of beams". You want to make sure all boxes are checked (Just so there is consistency between our steps)

    Step 7 - Click "SOLVE"

    Step 8 - Scroll Right Down to the Bottom of the calculations and find the solution titled "Local extremum at the point x = 0.66". This is the halfway point of the 1.2m beam. The solution is 0.01 (kN*m)


    • 6.
    Bending Capacity of your chosen steel tube

    You want to know the bending capacity of your chosen square tube to know how much of load it can bare per meter.

    To calculate this -

    Section Modulus x Steel yield strength of 275 N/mm^2 (Standard)

    Our section modulus was calculated earlier and the solution is - 3284.21053 mm^3

    So,

    3284.21053 mm^3 x 275 N/mm^2 = 903157.89575 Nmm

    (Take note of Exponent Rules*, N/mm^2 is the same as Nmm^-2 , so exponents are added 3 + (-2) = 1 .....)

    903157.89575 Nmm / 1000 = 903.157Nm

    Therefore 903.157/1000 = 0.90315kNm


    Now that we know the bending capacity in kNm (kilonewton*meter) We can use this value to find the minimum load (Yield) that it will take to bend the tube anywhere along it's length. Read more about it here - https://www.cmrp.com/blog/faq/how-is-section-modulus-used-in-bending-steel.html


    So now we can compare the bending moment of the steel (Local extremum) which we calculated earlier to the bending yield.




    Bending moment - 0.01kNm vs 0.90315kNm - Yield

    Just by looking at the above comparison we can see that it would take 90 x the EVENLY DISTRIBUTED load for each beam (front and back) bend critically. If our bending moment was greater or equal to the yield, we will need to add a center vertical support to each beam at 0.66m and our bending moment will have to be recalculated as shown but, this time using an overall length of 0.66m. The Local extremum will naturally be at 0.33m.

    If the bending moment is STILL greater than the yield, you may want to consider choosing a larger size of square tube. In this case, we would go from 38mm to 50mm square is the bending moment was greater.

    The minimum square tube size for Brenton's example would have been 12mm square (1.6mm wall) with a yield of 0.056kNm. You can safely double that to get a safe minimum of 25mm with a wall thickness of 1.6mm which will have a yield of 0.3020kNm - AKA OVERKILL. This is assuming that the load is placed on the stand correctly and evenly distributed.

    When stacking tiers to make multiple levels, you will also need to consider column buckling. Honestly, after doing calculations, there's no way you'll ever get to those limits with home aquariums.

    I know that the above is a lot to go through and I may have not been accurate with some numbers (please correct) but, I hope this helps you design your tank stands correctly.

    DISCLAIMER: As much as I've tried to provide information that is both helpful and accurate as I could possibly get, the above is just a guide. You will need to review this and calculate this based on your needs. Your steel may have manufacturing defects and may fail at lower yields. The above does not account for these defects. The above assumes that all steel is BRAND NEW and not some rusted crap you had laying outside from the 90's.

    Use the above guide responsibly and position tanks over ALL load bearing beams and columns to ensure the best safety. You may also want to WELD joints where possible. The above guide assumes that you will be welding and not using connecting blocks as those will have a different yield and may be a fail-point.

    You are responsible for your own stupidity. Try and be as accurate as possible with calculations. I can't be responsible for changes to the above calculators and/or inaccurate solutions (either by miscalculation or by software error) that result in failure.

    Review your numbers and make safe choices!
     
    Trev Pleco likes this.

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