Discussion
What is the maximum shear stress developed for a wooden beam of width 100 mm and depth 250 mm, subjected to shear force of 75 kN?
Answer: C
For a rectangular section the maximum shear stress is 1.5 times the average shear stress, and it acts at the neutral axis:
\[ \begin{aligned} \tau_{max} = \frac{3}{2}\cdot\frac{V}{bd} \\ &= 1.5 \times \frac{75000}{100 \times 250} \\ &= 4.5\ \text{N/mm}^2 \end{aligned} \]This is 4.5 MPa. The average shear stress is 3.0 MPa, which is not among the options, and the choices 3.5, 4.0 and 5.0 MPa do not follow from the factor of 1.5.
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