stiffness

Is there a general rule(s) that describe the stiffness of a round tubing to the stiffness of a solid rod? For instance: is 1" dia. round rod stiffer than 1
" dia. x .125" wall tubing? How much larger dia. tubing equals a solid rod of a certain dia.? Is tubing inherently stiffer because it has 2 surfaces (inside and outside) that oppose each other? Thanks.
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When you bend something the outer part of the curve is in tension, the inner part in compression. There's a plane through roughly the center called the neutral axis that is neither stretched nor compressed. The stretching or compressing of any individual tiny part ("fiber") is proportional to its distance from the neutral axis, so the inner and outer sufaces, where deformation and thus resistance to it is greatest, contribute the most to stiffness.
Tubing isn't stiffer than solid rod, but the extra metal inside the rod adds more weight without contributing proportionally as much to the stiffness since it's closer to the neutral axis, so a horizontal solid rod sags more from gravity under its own greater weight. However it supports an added external bending load better.
I haven't yet found an intuitive explanation of Beam Deflection and the derivation of its formulas on the Net. I learned (and forgot) it in college Physics class. Look for a used "Statics" textbook. I use Harry Parker's steel and timber books because Den Hartog's, though excellent, are difficult to wade through without a live instructor. (Amazon.com product link shortened)ABW389HF82EMZKC0W4 (Amazon.com product link shortened) "Written to be easily understood by readers with limited experience in engineering mechanics, structural analysis, or advanced mathematics,..."
AFAIK the answer to your quesrion is that you have to figure the stiffness of either rod or tube separately and compare them. You can plug the desired result into the formula and work backwards to the dimensions that will give it. For tubing you have to specify either the outer diameter or the wall thickness before you can calculate the other.
-jsw
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On 05/23/2015 9:18 PM, jack wrote:

"It all depends..." :) On what you really are talking about by "stiffness" in the application. For simple deflection away from yield, of a laterally-applied it's basically directly proportional to the area moment of inertia; otoh, if it's used a column with axial loading that's significant factor but the yield mechanism is different.
But, no, as a general rule a tube isn't anyways nearly as strong against lateral loading as a solid rod of the same OD.
Ibar = pi*d^4/64 for a solid cylinder, a hollow cylinder is the same thing excepting you must subtract out the inner area --
Icyl=pi*[do^4-di^4]/64
So, the cylinder is quite a lot less and gets that way much faster as the wall becomes thinner.
There's truth in the weight:strength argument above and there's complexity in a detailed answer, but the rough idea is given above.
It's the material that matters--geometry is important in comparison, but it takes actual material to stand up.
Think about how a thin wall tube crushes whereas the solid rod bends uniformly...
--




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On Saturday, May 23, 2015 at 7:18:03 PM UTC-7, jack wrote:

For a full treatment, see Roark, _Formulas for Stress and Strain_. Plan on spending a few days... For a given material, and quantity of material (pounds per foot), the tube will be stiffer as long as you keep the deflection low (don't buckle the material of the tube).
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