Discussion
The shear stress due to a transverse shear force in a linear elastic isotropic beam of rectangular cross-section
Answer: C
The transverse shear stress is maximum at the neutral axis.
For a rectangular section of depth h the shear stress is \(\tau = \frac{VQ}{Ib}\), and the first moment Q of the area beyond the level considered varies parabolically with depth:
\[ \tau(y) = \frac{6V}{bh^{3}}(h^{2}/4 - y^{2}) \]
It is zero at the top and bottom faces (\(y = \pm h/2\)) and largest at the neutral axis, \(\tau_{max} = 1.5V/(bh)\). So it is neither linear nor constant through the depth, and it is the bending stress, not the shear stress, that is zero at the neutral axis.
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