A beam has a triangular cross-section having base b & altitude h.

| A beam has a triangular cross-section having base b & altitude h. If the section of the beam is subjected to a shear force F, the shear stress at the level of neutral axis in the cross-section is given by :

A. \(\frac{{4F}}{{3bh}}\)

B. \(\frac{{3F}}{{4bh}}\)

C. \(\frac{{8F}}{{3bh}}\)

D. \(\frac{{3F}}{{8bh}}\)

Please scroll down to see the correct answer and solution guide.

Right Answer is: C

SOLUTION

Concept:

Shear stress distribution in the triangular section:

The relation between neutral axis shear stress and average shear stress is given by:

\({{\bf{\tau }}_{{\bf{neut}}}} = \frac{4}{3}\times{{\bf{\tau }}_{{\bf{avg}}}} = \frac{4}{3}\times\frac{F}{A} = \frac{4}{3}\times\frac{F}{{\frac{1}{2}bh}}\)

\(\therefore {{\bf{\tau }}_{{\bf{neut}}}} = \frac{{8F}}{{3bh}}\)

Cross-section	\(\frac{{{\tau _{max}}\;}}{{{\tau _{avg}}}}\)	\(\frac{{{\tau _{NA}}\;}}{{{\tau _{avg}}}}\)
Rectangle	\(\frac{3}{2}\)	\(\frac{3}{2}\)
Circle	\(\frac{4}{3}\)	\(\frac{4}{3}\)
Triangle	\(\frac{3}{2}\)	\(\frac{4}{3}\)
Diamond	\(\frac{9}{8}\)	1