• # question_answer If the principal stresses corresponding to a two-dimensional state of stress are ${{\sigma }_{1}}$ and ${{\sigma }_{2}}.$  If ${{\sigma }_{1}}$ is greater than ${{\sigma }_{2}}$ and both are tensile, then which one of the following would be the correct criterion for failure by yielding, according to the maximum shear stress criterion? A) $({{\sigma }_{1}}+{{\sigma }_{2}})/2=\pm \,{{\sigma }_{yp}}/2$B) ${{\sigma }_{1}}/2=\pm \,{{\sigma }_{yp}}/2$C) ${{\sigma }_{2}}/2=\pm \,{{\sigma }_{yp}}/2$D) ${{\sigma }_{1}}=\pm \,{{\sigma }_{yp}}$

According to maximum shear stress theory $\frac{{{\sigma }_{1}}+{{\sigma }_{2}}}{2}=\frac{{{\sigma }_{yp}}}{2}$