# Stiffness of tubular material.

Greetings.
Is a tubular section stiffer (resistance to flex) than the same diameter
solid round?
Is there an optimum ratio of wall thickness to diameter for maximum
stiffness? If there is, does the ratio vary for different metals? Are
there formulas/tables of stiffness vs wall thickness for various metals?
Having very little eperience in mechanical engineering matters I don't
know what resources are available for this sort of thing, so I would
appreciate some pointers to the answers.
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
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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

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