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Is it in the same direction of the applied load or in the co-planar perpendicular direction to the load applied?

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    $\begingroup$ The direction that resists the bending? $\endgroup$ – Solar Mike May 28 at 6:30
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Bending moment of inertia or second moment of inertia is taken on the surface of the beam parallel to applied loads' vertical component and perpendicular to the long axis of the beam, about a horizontal line on that surface, called neutral axis.

When loads are applied to a beam they want to bend the beam into a deflected down curve. They create bending moment in the beam which is countered by tension stresses on the lower part and compression stresses on the upper part of the beam.

Moment of inertia is a characteristic property of the beam section which defines how that cross section bends and how much stress both tension and compression it takes to bend, and how this stress is distributed on that section of the beam.

It is a engineering representation of the stiffness of the beam at that point. In prismatic beams, extruded shapes, moment of inertia or I is constant along the length of the beam. But if the Beam's cross section varies along its length, then the I varies along the length of the beam.

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