Question

The shear stress due to a transverse shear force in a linear elastic isotropic beam of rectangular cross-section

• A. varies linearly along the depth in the transverse direction of the beam
• B. is zero at the neutral axis
• C. is maximum at the neutral axis
• D. remains constant along the depth in the transverse direction of the beam

Hint:

Remember: In rectangular beams, bending stress is maximum at the outer surface, but shear stress is maximum at the neutral axis and follows a parabolic variation.

Answer 1

The Correct Option is C

For a rectangular cross-section subjected to a transverse shear force \(V\), the shear stress distribution is given by:
\[ \tau(y) = \frac{3V}{2bh}\left(1 - \frac{4y^2}{h^2}\right) \] This equation represents a parabolic distribution across the beam depth. The shear stress is:
- Maximum when \(y = 0\), i.e., at the neutral axis
- Zero at the top and bottom surfaces \((y = \pm h/2)\) Thus, the shear stress reaches its highest value at the neutral axis and decreases toward the outer fibers.