A square element is subjected to Principal stresses as shown in fig. Find the intensity of normal stress on plane BD?

A] Normal stress $\sigma_n/P_n$ : On plane BD.

From above figure, we get,

$P_1 = 100 \ Mpa$ (tensile) and $\theta = 45°$

$P_2 = - 100 \ Mpa$ (Compressive).

$\sigma_n = \frac{p_1 + p_2}{2} + (\frac{p_1 – p_2}{2}) \ cos \ 2 \theta$

$= (\frac{100 – 100}{2}) = (\frac{100 – (-100)}{2}) \ cos \ 2 \times 45$

= 0 + 15.64

$\sigma_n = 15.64 \ Mpa$