Question

The first moment of the total cross-sectional area taken about the neutral axis must be?

Answer 1

The first moment of the total cross sectional area taken about the neutral axis must be zero.

As with non-composite beams, the neutral axis (NA) is the location where the bending stress is zero. The location of the NA depends on the relative stiffness and size of each of the material sections.

Generally, the NA location is determined relative to the bottom surface of the beam. However, this is not mandatory, and the location can be relative to any location. If the bottom is used, then the NA axis is a distance "h"

The distance h can be determined by recalling that the stresses through the cross section must be in equilibrium.

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Answer 2

The first moment of the total cross-sectional area taken about the neutral axis must be zero.

A member that resists bending has a neutral axis in its cross-section along which there are no longitudinal stresses or strains. The neutral axis lies at the geometric centroid if the section is symmetric, isotropic, and does not curve before a bend. The neutral axis is not under any strain. Therefore, the neutral axis has no bending moment. Because the neutral axis is not affected by the applied stresses, there is no bending stress. At the neutral axis, no stress is created. The line in the cross-section of a beam where there is neither longitudinal compression nor tensile stress is known as the neutral axis for that beam. The neutral axis is typically regarded in the study of wood beams to be at the centroid of the beam.

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