[Solved] If Width Of A Rectangular Cross Section Beam Is Increased By

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Concept:

For a rectangular section:

\(\tau_{max}=\frac{3}{2}\tau_{avg}\)

\(\tau_{avg}=\frac{Shear\;force}{Area}\)

\(\therefore {\rm{\tau }} = \frac{{\rm{V}}}{{\rm{A}}} = \frac{{\rm{V}}}{{{\rm{bd}}}}\)

where b = breadth, d = depth and V = shear force.

So, as the cross-sectional area remains unchanged so there will no change in average shear stress as well as in maximum shear stress.

Mistake/ Confusion Point:

If the area is not kept constant then maximum shear stress will be inversely proportional to the width.

∴ The maximum shear stress would reduce by 10 times.

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