A body is subjected to a direct tensile stress of 300 MPa in one plane accompanied by a simple shear stress of 200 MPa. The maximum normal stress on the plane will be

Concept:

The maximum and minimum normal stress id given by

\({\sigma _{max,\;\;min}} = \frac{{{\sigma _x} + {\sigma _y}}}{2}\; \pm \sqrt {{{\left( {\frac{{{\sigma _x}\; - \;{\sigma _y}}}{2}} \right)}^2} + \tau _{xy}^2} \)

Where, σ_x and σ_y are direct stress and τ_xy is the shear stress

Calculation:

Given, Direct stress σ_x = 300 MPa, τ_xy = 200 MPa

Now maximum normal stress  

\({\sigma _{max}} = \frac{{{\sigma _x} + {\sigma _y}}}{2} + \sqrt {{{\left( {\frac{{{\sigma _x}\; - \;{\sigma _y}}}{2}} \right)}^2} + \tau _{xy}^2} \)

\({\sigma _{max}} = \frac{{300}}{2} + \sqrt {{{\left( {\frac{{300}}{2}} \right)}^2} + {{200}^2}} = 400\;MPa\)