For an unsymmetrical thin-walled beam bending about arbitrary centroidal axes $x$ and $y$, the axial direct stress $\sigma_z$ vanishes along the neutral axis, which is defined by:

(A) A straight line passing through the centroid whose inclination depends on moments $M_x$, $M_y$ and section product of inertia $I_{xy}$

(B) The principal axis corresponding to maximum moment of inertia exclusively

(C) The geometric perimeter of the skin contour

(D) A parabolic curve tangent to the shear center

Answer Key:

A

### Solution: Setting direct stress $\sigma_z = \left(\frac{M_x I_y - M_y I_{xy}}{I_x I_y - I_{xy}^2}\right)y + \left(\frac{M_y I_x - M_x I_{xy}}{I_x I_y - I_{xy}^2}\right)x = 0$ yields a straight line through the centroid $(0,0)$ with slope depending on $M_x, M_y$ and $I_{xy}$. Correct: A.

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