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An element in a stressed body is subjected to normal stresses on mutually perpendicular directions as shown in fig.

An element in a stressed body is subjected to normal stresses on mutually perpendicular directions as shown in fig. Determine the normal tangential and resultant stresses on plane P-P inclined as shown. Either use analytical method or graphical method.

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From above figure, we get,

$P_1 = 100 \ Mpa$ (tensile)

$P_2 = 60 \ Mpa$ (tensile)

$\theta = 30°$

A] Normal stress on P – P Plane.

$\sigma_n = \frac{P_1 + P_2}{2} + (\frac{p_1 –p_2}{2}) \ cos \ 2 \ \theta $

$= \frac{100 + 60}{2} + (\frac{100 – …

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