Question

The moment of inertia of a symmetrical section of a beam

Answer 1

The transverse cross-section of a typical prismatic beam is illustrated. It is rectangular with x and y axes chosen parallel to the axes of symmetry of the cross-section, and the z-axis longitudinal to the beam.
This symmetry ensures that events in the x-z plane under load are completely divorced from events in the y-z plane, so that bending stresses for example may be found in each plane separately before being combined (superposed) to give the stresses due to simultaneous loading in both planes. Deflections may be treated likewise.
When the cross-section is not symmetric however - or when it is, and loading planes other than those containing the axes of symmetry are chosen - then coupling between events in orthogonal planes will occur. Thus consider the I- and Z-beams below, each loaded in the y-z plane of the web.
The bending stress resultants may be approximated by flange forces only,
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Answer 2

Moment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion. It appears in the relationships for the dynamics of rotational motion. The moment of inertia must be specified with respect to a chosen axis of rotation. For a point mass, the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, I = mr2. That point mass relationship becomes the basis for all other moments of inertia since any object can be built up from a collection of point masses.