Stiffness of tubular material.

Dear edson:
On an inch-per-inch basis, no. On a pound-per-pound basis (or volume-per-volume), yes.
Search for "moment of area" and for kinetics "moment of inertia"
Given a certain outside diameter, the member wil simply get stiffer and stiffer as you decrease the inside diameter. The "optimum" comes from motion, cost, weight, and manufacturability constraints.
"Young's modulus"
David A. Smith

Thanking you.

No. A solid cylinder is always stronger and stiffer than a tube of the same material. Think about it. If the tube was stronger than the cylinder, that means that filling in its hole makes it *weaker*.
The stiffness of a beam is determined by its "moment of inertia", which is a property of its cross section. Material that is out toward the edges (farthest from the axis of bending) is more important and adds more strength per unit area than material closer to the axis. That's why I-beams have thick steel at the top and bottom, but only a thin membrane holding them together.
The inner material still adds to the stiffness, just not as much as the outer material. It gets down to cost and weight. A tube isn't as strong as a solid cylinder, but it is cheaper and lighter.
The formula for the moment of inertia I of a tube being flexed is
I = pi/64 * (D^4 - d^4)
where D is the OD and d is the ID of the tube. The larger this number, the stiffer the tube, for a given material.
The other factor to consider is the material itself. Every material has a "modulus of elasticity" E, which is a number that you can look up in tables. The higher the number, the stiffer the material, or the more force it takes to flex it a given distance. Note that this is not the same as the "strength" of the material. In other words, a material can be stiff and hard to flex, but still break, or get permanently bent, before another material that is less stiff.
To calculate the deflection exactly for a given tube gets a little more complicated than you're probably willing to delve into, but if you multiply the moment of inertia by the modulus of elasticity (E * I), you can get a relative figure that tells you which design is stiffer than another. A higher EI is "stiffer" than a lower one.
Hope this helps.
Don Kansas City

stiffness? If there is, does vs wall thickness for what resources are material. Think in its hole makes property of its cross bending) is more axis. That's why holding them together. material. It gets is cheaper and stiffer the tube, for "modulus of elasticity" the stiffer the this is not the same and hard to flex, but complicated than you're the modulus of is stiffer than Be aware that the Modulus of Elasticity, E, is not the same for all steel alloys AND temperature affects the value also. For example, per the text below, Low Carbon Steel at -325 degrees F, E = 30,000,000 PSI; at 70 degrees F, E = 29,000,000 PSI; at 1000 degrees F, E = 15,400,000 PSI. The curve is not a straight line and should not be interpolated.
Although there are several sources for this information, you could find some of this information in "Handbook of Engineering Fundamentals", Eshbach, Wiley Handbook Series, ISBN 0-471-24553-4. This text is a very good reference and supports the answers given by other posters.
Jim Y

/// /// /// Using Don's formula, you will see that in comparison with a solid shaft, a shaft hollowed out to half its diameter loses about 6% of its stiffness and about 25% of its weight.
This option is often attractive in weight sensitive applications.
Brian Whatcott Altus OK