We know that in unsymmetrical bending the applied moment can be decomposed into components aligned with the principal centroidal axes, then bending stresses produced by these moments can be combined using the Pythagoras Theorem.

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The question concerns unsymmetrical bending and how the resulting bending stresses are computed.
Option analysis begins with understanding the core idea: when a member experiences bending about orthogonal axes, the moments can be resolved into components along the principal centroidal axes, and the resulting normal stresses can be combined by a vector-like addition because the bending effects are orthogonal and the equations are linear.
Option 1 (True): This statement aligns with the superposition principle in linear elastic bending. If the applied moment is decomposed into perpendicular components along the principal axes, the bending stresses produced by each component act on orthogonal directions. In many standard treatments, the total bending stress at a point is obtained by combining the individual stresses in quadrature, i.e., using a Pythagorean combination, provided we are discussing the normal bending stresses about those principal axes and ignoring other effects such as shear coupling. The key assumptions here are linear material behavior, pure bending about the principal axes, and decoupling of the bending moments. Therefore, describing a Pythagorean combination of stresses from orthogonal bending components is consistent with typical bending theory for principal-axis decomposition.
Option 2 (False): This would be correct only if one requires consideration of factors not mentioned in the statement. For instance, in unsymmetrical bending, there can be coupling with transverse shear, warping, and possibly skewed neutral axes that complicate the stress state beyond a simple orthogonal, pure-bending decomposition. In such cases, stresses could include shear components and non-negligible coupling terms, so a straightforward Pythagorean addition of normal stresses might not capture the full stress state. Additionally, if the analysis involves non-principal axes or if the material exhibits anisotropy or large deformations, the simple orthogonal decoupling and Pythagoras rule may not strictly apply.
In summary, the statement is correct under the standard, idealized assumption of pure bending about principal axes with linear, decoupled behavior, where the normal bending stresses from each orthogonal component combine in a Pythagorean manner. It is not universally correct in all real-world scenarios where shear, warping, or coupling effects become significant, which is why the False option highlights those potential complications.

BK10A6500 Engineering Mechanics 3 - Blended teaching 6.1.2025-20.4.2025 Quiz 7.2

We know that in unsymmetrical bending the applied moment can be decomposed into components aligned with the principal centroidal axes, then bending stresses produced by these moments can be combined using the Pythagoras Theorem.

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