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) \[{{\sigma }_{1}}=\pm \,{{\sigma }_{yp}}\]