Metal tube strenght

[Anonymous No.751136]

I'm planing on doing some welding and I need some advice on the sizes and strength of square steel tubes. So let's say we need to build a thing limited by weight but not the size. Then what dimensions of square metal tubes we should use to get the most possible strength from the same weight?
For example which 1 meter long tube would be stronger (width x height x wall thickness all in millimetres):
40 x 40 x 5
50 x 50 x 4
100 x 100 x 2
200 x 200 x 1
And by stronger I mean 3 things pictured in diagram I just created: bending when force is concentrated in one point, bending when force is distributed all over the length of tube and lastly crushing from the top when tube is vertical and placed on solid surface.
Is there golden ratios of width*height*thickness? I am oversimplifying this and I should study engineering for 4 years to understand those things? Or I am overcomplicating this and we would get almost identical strength from the same weight (amount) of steel? Also I think we should add that there are not only square tubes but also rectangle, so to increase the resistance against bending we could also use for example 30 x 70 x 4. Maybe rectanglyness is the only thing that noticeably increase strength?

I'm not native English speaker and my knowledge of technical terms is very poor so I couldn't Google any useful information related to the topic.

So if it is simple please post some formulas and charts. If it's not so simple then give me some links where I could read more about it. And please tell me to GTFO if it is super complicated and I need to study few years just to get the basic knowledge of the topic.

[Anonymous No.751147]

All those measurements does not give an equal amount of surface area, meaning that the 200 x 200 x 1 (796mm^2) would weigh more than the 40 x 40 x 5 (700mm^2).

[Anonymous No.751149]

>>751147
(200+200+200+200)*1=800
(40+40+40+40)*5=800
???

[Anonymous No.751150]

>>751149
Each side becomes sidelength-thickness, because they intersect at corners, so basically you are counting the area of each corner twice.
(40-5)*5*4=35*20=700
(200-1)*1*4=199*4=796

[Anonymous No.751162]

>>751136
This stuff can get pretty complex with a lot of equations, however since they are all tubes I can make this a bit simpler for you.

There is a certain term in material mechanics called the 2nd moment of intertia, I. You don't need to know much about it, except for that fact that most material mechanics equations for structural terms such as stress, load, etc are structured in some form similar to this:

answer = terms/(terms*I)

This usually means that the larger your moment of interia is, the weaker your material. The equation for I is as follows:

I = base*height^3/12

This is for a solid object, for a square tube you just subtract the moment of interias of the outer and inner square. ex:

40x40x5

I = 40*40^3/12 -35*35^3/12 = 8.83e4

[Julez No.751212]

Engineering technican here, I used to do these calculations all day long in school. Also not native English speaker.
Yes, that shit is fairly complicated, so I'm gonna simplify it a bit.

Generally, stiffness rises linearly with the width of a square tube. Double the width, get double the stiffness.

It also rises to the 3rd power with heigth. Make it double the heigth, get 2^3=8 times the stiffness.

It also rises linearly with the wall thickness. Double the wall thickness, get double the stiffness.

So it might seem like a good idea to make the tube as narrow and high as possible. But here, dent resistance will come and bite you in the ass. As long as the tube will not keep its structural integrity, theoretical stiffness will not help you. You need some minimum wall thickness to get the desired dent resistance. And 1mm thin metal is awful to weld, too.

So, 30 x 70 x 4 sounds perfectly alright for bending forces. For axial loads, I'd prefer a round tube, or at least a symmetrical square tube.

If you want to calculate stuff:

http://www.calculatoredge.com/civil%20engg%20calculator/beam.htm#tube

"Calculate Deflection for Hollow Rectangular Beams"

More sophisticated:

Calculate "Wy", 3rd last formula:

http://de.wikipedia.org/wiki/Widerstandsmoment

Or use this:

http://www.mobile-soft.at/widerstandsmoment-berechnung.html

Calculate bending momentum "Mb"

http://www.cnc-lehrgang.de/biegebeanspruchung/

Use drawings in the middle of the 3x2 chart.

Calculate stress:

sigma b = Mb / Wy

Multiply stress with safety factor, like 2.
Is that stress less than your steel is rated for? Then you're good. Around 100N/mm2 is a conservative rating, especially if welding is involved. If something expensive or dangerous is involved, make your safety factor 5-7.

For your axial load, buckling resistance is important, but I'm too lazy to explain that now.

http://en.wikipedia.org/wiki/Buckling