Parallel Axis
Theorem
In a
Nutshell: Use the parallel axis theorem to transform
the moment of inertia through the centroid to any
other parallel axis ( or vice-versa). In
the figure below let y and
z be any axes parallel to axes y1 and z1
which pass through the centroid , C, of the
area. Then the moments of inertia Iyy , or Izz equal
the moments of inertia calculated about the centroidal
axes plus the area times the distance between the parallel axes as shown in
the table below.
where Iyy
and Izz are the moments of inertia of area about
axes y
and z Iy1 and Iz1 are the moments of inertia of area about
the centroidal axes
A is the total cross-sectional area ybar and zbar
are the distances between the parallel axes.
The parallel axis theorem is frequently applied to
composite areas once each area, each centroid, and
distances between the parallel axes are known. If the area happens to be a void, then the negative value applies to the moment of
inertia calculation. |
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