The principal stresses at a point across two perpendicular planes are 100 MPa (tensile and horizontal) and 60 MPa (tensile and vertical). Determine the normal shear and resultant stresses in magnitude and direction in a plane, the normal of which makes an angle of 30 degree with the direction of maximum principal stress. Use either analytical method or graphical method.

Analytical Method:-

Data:

Principal stresses:

$P_1 = 100 \ Mpa$ (tensile)

$P_2 = 60 \ Mpa$ (tensile)

The above fig. shows the principal stresses at the point. On a plane at 30° with the maximum principal plane.

A] Normal stress is $\sigma_n/Pn$

$\therefore \ Pn/ \sigma_n = \frac{P_1 + P_2}{2} + [\frac{P_1 …