OT - bending analysis

Wonder if anyone can tell me offhand which of the two steel structures will be more rigid with a vertical force applied in the middle… Either a simple tube 42mm in diameter with 2mm wall thickness, or a 3 level welded structure of flat steel bars 40mm x 8mm, 224mm in depth. Both are fixed to the side walls only. My feeling is that the flat bar structure will not flex more than the tubes due to the rigid welded joints, but maybe I’m completely confused…

Bending.3dm (234.7 KB)

Is this the kind of thing I can do with Scan&Solve? (no idea how to use it though)

Thanks, --Mitch

Projected a curve. The rectangular rods give a cumulative area of 960 square millimeters, and the tube - 1385 square millimeters. I bet on the tube if it is not hollow.

The tube IS hollow - wall thickness 2mm only. --Mitch

My gut is betting on the tube too based on the weight of the structure and heat generated when welding the flat bars, I can’t be sure but I’d guess the weld would be a weak point and it’s more likely to fold before the tube buckles…

Is it a very narrow point load or something a little wider like a wooden board?

This is something like a handrail… It will never have enough load to buckle, I am mainly concerned with the amount of flex (imagine a human pushing on it either laterally or vertically in the middle)…


It depends also on how well they are fastened to the walls. The disadvantage of the tube is that once it is bent you can not restore the shape. (Sorry for not being attentive.)

Hi Mitch,

I did some Scan&Solve analysis on your file assuming that it was stainless steel. Later I saw that you want it to be anodized aluminum.

However please find attached the results and the file.
I used a vertical force of 500N and the max. displacements are:
Rod = 4.29012 mm
Flat = 24.2564 mm

When you open the html documents of both analysis, I you can find out yourself.
Furthermore the file contains two extra layers that show the deflection of both objects as a mesh. This is a 5x magnification of the real deflection.
In rendered display you can also see the nice colors of the loacation of the deflection.

That’s it for now.

Mitch.zip (8.1 MB)

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OK, thanks Gerard, that is very useful! Both are stainless structures. Wouldn’t have imagined a 24mm deflection with a ~50Kg load… I was trying to get away without putting a “foot” on the middle support that actually touches the floor.

The issue here is visual, I actually need two 42mm tubes one over the other (but not connected) in this case, which create a combined visual obstruction of 84mm, as opposed to the flat bars which have much less horizontal view blockage. But if the tubes are better structurally - they will also be less expensive to fabricate - I might go with them. It’s either that or add back in the “foot” on the flat bar structure.

Cheers, --Mitch

Nice to read a little more about your thoughts regarding the desired solution.
The tubes are much stronger than the bar and probably much cheaper.

Yeah without the ‘foot’ on the bars, I doubt the assembly would be appreciably stiffer than a single bar, that little vertical isn’t going to usefully distribute any forces, compared to the tube which is inherently the stiffest shape there is, and whether or not the scan n solve numbers are specifically correct–and I don’t think those structures fall under the type of thing scan & solve handles best–it certainly would be exponentially stronger than a bar.

Yep, the accuracy of any Fem analysis is arbitrary to the users experience with strength analysis.

Simple beam analysis is sufficient for this comparison. The hollow tube will be almost 10 times stiffer in vertical bending than the three flat bars. This is based on the assumption that the ends of the tube are fixed so that they can not rotate, and the ends of the flat bars also can not rotate due to the welded connection…

The single connection between the flat bars in the middle of the span results in the three bars together being three times stiffer than each bar individually.

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Hi David,

You know the fundamentals! That’s valuable.
I forgot them over time and have to rely on S&S for a fast indication now :wink:

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if in the lower construction the bars are turned 90° either the whole thing or each bar or even just one of them, you will have more structural potential. also depends if this still looks good for you. the round hollow tube would have compared to that no chance.

There’s a third option, a compromise given that one of your constraints is visual obstruction, namely placing the flat bars at an angle while keeping the welded bits in the middle, like so: / / / ( rotate it 90 degrees of course).

The angle could be in the direction which obstructs visibility the least. Increasing the vertical “height” of the flat bars’ (while keeping the middle bits) will increase the stiffness.

Compare the strength for different orientations of the flat bars in the following three cases:

_ (flat horizontal - weakest)
|  (flat vertical - strongest)
/  (45 degrees, a compromise - think Sine(45) = "70%" strength 
    of the flat vertical. Well, not in reality but as a pointer for what 
    gives the better strength given your constraints)

If it wasn’t for the visual obstruction, also the following orientation would give even more strength, given that 90 degree vertical orientation (of the individual bars) would simply obstruct visibility too much (again, rotate 90 degree):

/ \ /

// Rolf


  1. Rhino has the AreaMoments command for determining Moments of Inertia which is very easy and handy for comparing the strength and stiffness of structural parts like this. It also include the Radii of Gyration which is needed in case something like a column is being considered.
  2. The restraints used in Scan&Solve will have a big effect on the results. Take care that they represent the true situation. It’s easy to include more restraint than really exists, resulting in overly optimistic results.
  3. Gerard’s comment is excellent… “the accuracy of any Fem analysis is arbitrary to the users experience with strength analysis”.

Finally, just to let everyone know, we went with the 42mm tubes - mainly because the cost to fabricate and install my flat bar model (with the middle “foot” for stability) was going to be double that of fabricating and installing the tubes… Kinda figured as much, as there’s no jigging/welding necessary with the tubes. Oh well…

Thanks again for all the input! --Mitch

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