In unsymmetrical bending, the neutral axis always coincides with one of the principal centroidal axes.

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Question restatement: The statement asserts that in unsymmetrical bending, the neutral axis always coincides with one of the principal centroidal axes. Answer options are:
- True
- False

Option 1 (True): This claim is not generally correct. In a cross-section that is unsymmetrical, bending about multiple axes can be coupled, and the neutral axis is determined by the distribution of bending stresses across the section, which depends on the loading and the geometry. The neutral axis is the locus of points with zero normal stress, and it does not have to align with any principal centroidal axis unless the loading and geometry impart a pure, unidirectional bending about a single axis or the section exhibits symmetry that enforces such alignment. Therefore, asserting that NA always coincides with a principal centroidal axis in unsymmetrical bending overlooks these possibilities and is not universally true.

Option 2 (False): This statement correctly captures the general situation. For unsymmetrical bending, the neutral axis can be inclined relative to the principal centroidal axes, and the stress distribution can involve coupling between bending about different axes. Only under special cases—such as symmetrical sections, pure bending about one principal axis, or specific loading that preserves symmetry—would the neutral axis align with a principal centroidal axis. In the typical unsymmetrical case, there is no guarantee of such coincidence, making the statement false.

Additional notes: Recognizing the neutral axis requires analyzing the actual bending moment distribution and cross-sectional geometry. When sections lack symmetry, the principal axes themselves may not align with the geometric axes, and the NA may lie at an angle that minimizes or nullifies normal stress, rather than lying on a principal centroidal axis. This nuance is what makes the general claim false rather than universally true.

BK10A6500 Engineering Mechanics 3 - Blended teaching 6.1.2025-20.4.2025 Quiz 7.3

In unsymmetrical bending, the neutral axis always coincides with one of the principal centroidal axes.

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