Find the average shear stress for a rectangular cross -sectioned beam of 100 mm × 250 mm, subjected to a maximum shear stress of 3 N/mm².

Concept:

Relation between maximum shear stress and average shear stress for rectangular section;

\(\tau_{max}={3\over 2}\tau_{ave}\)

\(\tau_{ave}={V\over bd}\)

Where \(\tau_{max}\) = maximum shear stress, \(\tau_{ave}\) = average shear stress, V = shear force, b = width of section, and d = depth of section.

Calculation:

Given

Beam cross-section = 100 mm × 250 mm

Maximum shear stress (\(\tau_{max}\)) = 3 N/mm²

\(\tau_{max}={3\over 2}\tau_{ave}\)

\(3={3\over 2}\tau_{ave}\)

\(\tau_{ave}=2\, N/mm^2\)

Hence option (3) is correct.