Example #$4$

At a point in a member subjected to load the stress system induced is defined by the stresses acting on the elemental prism shown in figure. Determine the maximum shearing stress acting at the point and also the normal and tangential stresses acting on plane $AB.$

${}_x=-70$MPa

${}_y=60$MPa

$=30$MPa

Example #$5$

The stresses acting on element A in the web of a train rail are found to be $42$ MPa tension in the horizontal direction and $140$ MPa compression in the vertical direction $($see figure$).$ Also, shear stresses of magnitude $60$ MPa act in the directions shown.

Determine the stresses acting on an element oriented at a counterclockwise angle of $48$ from the horizontal. Show these stresses on a sketch of an element oriented at this angle.