> Does anyone know the origin of this term? Why it refers to a
> radius and/or what is gyrating? It just seems to specific to be
> simply obscure… yet I've never found anyone who knows. So, anyone
> on here know?
My god, man--Never found *anyone* who knows? Have you never studied
strength of materials or physics?
There are two definitions, the first having to do with rotational
motion, the second applies to beam theory by extension.
Applying Newton's 2nd law to rotational motion about a fixed axis, it
turns out that the torque required
to produce an angular acceleration is
Torque = moment of inertia x angular acceleration or T = I x alpha.
The moment of inertia, I, is the sum of the squares of the masses of
the particles making up
the body x the square of the distance, R, from the fixed axis to each
particle. It's expressed as an integral:
I = integral(R^2dm).
As an example (look this up in your physics book) the moment of
inertia of a thin rod with mass, m, and length, L, about an axis at
one end is mL^2/3.
By definition the radius of gyration, Rg^2 x mass = I or Rg = sqrt(I/
mass). So T = mass x Rg^2 x alpha. Lots of times it's convenient to
characterize rotational inertia with the radius of gyration. You can
think of a rotating physical object as a particle with the same mass
as the body placed at a distance Rg from the axis of rotation.
Extending the notion to the moment of inertia of a cross-section of a
beam or column you define the radius of gyration as
I = sqrt(moment of inertia/area). For example the radius of gyration
of a rectangular area with base, b, and depth, d, as
r = sqrt[(bd^3/12)/bd] = d/sqrt(12). It turns out that Euler buckling
and the natural frequencies of beams are expressed conveniently in
terms of the ratio of the span to the radius of gyration of the
section. You should verify this in your strength of materials book if
you ever hope to convert that EIT into a PE any time soon.
The rotation, BTW, refers to rotation of a particle about a fixed
axis in regard to angular motion. I supose you can think of the
rotation in respect to beam and column design as the rotation of a
member cross section when a beam bends.
This is really basic stuff you should have learned as a sophomore.
Christopher Wright P.E. |"They couldn't hit an elephant at
chrisw@skypoint.com | this distance" (last words of Gen.
.......................................| John Sedgwick, Spotsylvania
1864)
http://www.skypoint.com/members/chrisw/
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