Calculate beam moment of inertia using the parallel axis theorem.
The moment of inertia about an offset can be calculated by
`Ix = Il + Y AX^2 `
`Iy = Im + X AX^2 ::Hxy = Hlm + X Y AX^2 `
where :
Ix = moment of inertia about X axis
Iy = moment of inertia about Y axis
Il = moment of inertia about L axis
Im = moment of inertia about M axis
Hxy = product of inertia about offset
Hlm = product of inertia about the centroid
X = offset length from Y axis to centroid
Y = offset length from X axis to centroid
AX = cross section area
X and Y are perpendicular axes passing through the offset. L and M are perpendicular axes passing through the centroid and parallel to X and Y. The X and Y axes pass through the offset point.
For principal axes the product of inertia equals zero. Axes which are an axis of symmetry are principal axes. If the moment of inertia for a principal axis is equal to the moment of inertia of any other axis, all moments of inertia through that point are equal.
For rotated axes, the rotation is calculated relative to either the X axis or the L axis (anti clockwise is positive). Use the Result Plot option to plot the rotated moments of inertia and product of inertia versus the rotation angle.
Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill
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