Structural engineers: Please HELP with 7 foot DIY stand build.

[oreo54]

Sure - we can run through a simple calculation based on that.

The only number that we need for the beam calc is the pound force on the beam and the length of the beam
You have defined that as 200 lbs/ft and 84 inches

2x8 lumber.
1.5" x 7.25" nominal (less when fully dry, sadly)

Moment of inertia for a solid rectangle with a vertical force
Iy = height * width^3 / 12
l = 47.63 in4

Young's Modulus
SPF #2 lumber - properly graded and avg. moisture content using NLGA.ORG values with no modifier for moisture or other factors.
E = 1,400,000 PSI

84 Inch Span
L = 84

200 lbs/ft - we are working in inches (PSI for Young's and in4 for Inetrtial Moment) so we need to convert
w = 16.67 lbs/in


Simply support beam with uniform load
Formula to apply for bending moment, solving for deflection.

Deflection = (5 * 16.67 * 84^4) / (384 * 14000000 * 47.63)

Max Deflection at center of span = .16 inches


Hope that helps a bit. I am not sure of that matches the calculator that you listed or not, but I am confident in the formulae that I have applied given your constraints.

Please excuse unit symbolization - don't have easy access to formatters for this type of math and symbol sets right now.

0.16 vs 0.146 (0.15)

 

[BeanAnimal]

0.16 vs 0.146 (0.15)

It it were me, trusting that page, I would run a wildly different set of parameters and double check those as well. But it does sound like the are using the apply the proper formulas.

As for the variance. I did not pay attention to significant digits in my calculations and not sure how or if they do rounding in any portion, etc.

But if we assume both calculations are good to three decimal places.

0.162 vs 0.146 doesn't sound like much, but it is almost a 10% difference and that is significant (no pun). Neither value is right or wrong it just means slight different assumptions were used. I may not have used the same value for the Moment of Inertia calc or (as mentioned) there was some rounding done somewhere in one of the calculations, either on purpose or as a side effect of the script language, etc.

 

[oreo54]

It it were me, trusting that page, I would run a wildly different set of parameters and double check those as well. But it does sound like the are using the apply the proper formulas.

As for the variance. I did not pay attention to significant digits in my calculations and not sure how or if they do rounding in any portion, etc.

But if we assume both calculations are good to three decimal places.

0.162 vs 0.146 doesn't sound like much, but it is almost a 10% difference and that is significant (no pun). Neither value is right or wrong it just means slight different assumptions were used. I may not have used the same value for the Moment of Inertia calc or (as mentioned) there was some rounding done somewhere in one of the calculations, either on purpose or as a side effect of the script language, etc.

Either way both are above the "internet threshold" of 1/16" or less.
Wonder what deflection " retail" stand builders use?


2x10's seem the threshold for that large of a free span.

Anyways the o/p has come to the conclusion that most have, supports are good!

 

[BeanAnimal]

Either way both are above the "internet threshold" of 1/16" or less.
Wonder what deflection " retail" stand builders use?

Assume that most don’t do any math Regarding their stands or for that matter their tanks.

 

[BeanAnimal]

I hesitate to get any deeper into this thread...

But, back to the point of steel.

We can use the same process to determine how a steel tube profile would react to the same load.

We need a different calculation for the Second Moment of Inertia for the cross section of a rectangular tube.

I will save showing the work, as it is obvious and straight forward.

Typically ASTM A36 steel is what will be used. So we can go look up the Modulus of Elasticity for A36 Steel.
This is typically listed as 29,000 ksi
Notice the change in units? We want to change that now because we are still working in pounds and inches for everything else.

1 ksi is simply 1000 PSI
E = 29,000,000
L = 84"
W = 200

We will use the same bending moment calculations for deflection as we did wood, as the application and load are the same. So all that has changed is the elastic properties of the material and its stiffness per cross section profile (hollow rectangle vs solid rectangle)

 

[BeanAnimal]

Perfect example of a very well done page with wonderful explanations of Second Moment, etc.

BUT at least one of the calculators on the page provides insanely wrong values for Second Moment Area (I)

If you look at the simple calculator code, whoever wrote this used the Javascript ParseInt() function to read the values from the input form!!!

This calculation is as simple as it gets, no order of operations dependence (other than final division) so no parenthesis to mess up. No unit conversion, etc. and they messed it up. This could be because the author knows the math but had somebody else write the code, or they wrote the code themselves but don't really know how to code. Etc.

Anyway - if we take our 2 x 6 in the above examples, with an actual value of 1.5 by 7.25
The Moment area for a solid rectangle would (properly be)
7.25 * 7.25 * 7.25 * 1.5 = 47.63 in4

However, the calculator parses the decimal input values to integers and the math becomes
7 * 7 * 7 * 1 = 28.58 in4

That is a HUGE error - Worse, the simple code is exposed on the page and therefore every other nitwit who builds a calculator for Second Moment can (will) copy it and build a flawed calculator.

The internet is amazing... but things like this are rampant and hard to undo. How do you argue with somebody when 73 calculators on 73 different sites say they are "correct" even if they are nowhere close? We could fill an entire reddit with examples like this.

That is why - hesitate to add more calculations here... I don't want an error that I make to be propagated for eternity or used for something critical by somebody who does not know how to verify the results

 

[mjovic]

Perfect example of a very well done page with wonderful explanations of Second Moment, etc.

BUT at least one of the calculators on the page provides insanely wrong values for Second Moment Area (I)

If you look at the simple calculator code, whoever wrote this used the Javascript ParseInt() function to read the values from the input form!!!

This calculation is as simple as it gets, no order of operations dependence (other than final division) so no parenthesis to mess up. No unit conversion, etc. and they messed it up. This could be because the author knows the math but had somebody else write the code, or they wrote the code themselves but don't really know how to code. Etc.

Anyway - if we take our 2 x 6 in the above examples, with an actual value of 1.5 by 7.25
The Moment area for a solid rectangle would (properly be)
7.25 * 7.25 * 7.25 * 1.5 = 47.63 in4

However, the calculator parses the decimal input values to integers and the math becomes
7 * 7 * 7 * 1 = 28.58 in4

That is a HUGE error - Worse, the simple code is exposed on the page and therefore every other nitwit who builds a calculator for Second Moment can (will) copy it and build a flawed calculator.

The internet is amazing... but things like this are rampant and hard to undo. How do you argue with somebody when 73 calculators on 73 different sites say they are "correct" even if they are nowhere close? We could fill an entire reddit with examples like this.

That is why - hesitate to add more calculations here... I don't want an error that I make to be propagated for eternity or used for something critical by somebody who does not know how to verify the results

OK now you're freaking me out with all the maths, haha! I was confident before, but now I'm like f it, let's just overengineer this thing! Currently deciding between just going HAM on 2x4 uprights or biting the bullet and going with an aluminum stand like these guys. Pricey, but I can assemble easily on site: https://www.framingtech.com/solutions/aquarium-stands

 

[mjovic]

OK now you're freaking me out with all the maths, haha! I was confident before, but now I'm like f it, let's just overengineer this thing! Currently deciding between just going HAM on 2x4 uprights or biting the bullet and going with an aluminum stand like these guys. Pricey, but I can assemble easily on site: https://www.framingtech.com/solutions/aquarium-stands

Update. I threw my back out pretty badly and recovering so that killed the idea of building a stand myself. I decided to bite the bullet and order an extruded aluminum stand. Went with a company out of Ohio called AluFab. It will be constructed using 3x3" posts. It will be overbuilt for my needs. Thanks for all your help. It's been truly educational and next time I go to build a stand I will be that much more knowledgable.

Here are the plans:

 

[mjovic]

Here are some shots of the tank being built.

 

[BeanAnimal]

Thank you for the update - good choice!
Good luck with the back and the tank!

For the rest of you following along or looking at units and calculators and still confused... I went ahead and wrote that article that I have been putting off for ~15 years...

It has not been proofread - so you have been warned! Building the graphics and illustrations was time consuming. I will proofread in a few days, or after somebody points out the terrible errors that I have made!

Beam Deflection – Easy Engineering for Aquarists | BeanAnimal's Reef

This easy to understand engineering lesson uses layman's terms and simple math to allow anybody calculate beam deflection for aquarium stands or other projects.

beananimal.com

I need to add a bit about unit conversion and maybe some common E values

I will build a calculator to go along with the article - but not sure when that will happen.

@RocketEngineer - Maybe one day I will use a parametric animation with your colorful stand model and exploded view along with a calculator...