Question

The principal stresses ${}^{\prime }{\sigma }_1^{\prime }$ and ${}^{\prime }{\sigma }_2^{\prime }$ for the plane stress tensor $\left[\begin{array}{cc}14& -2\\ -2& 6\end{array}\right]$ are

• A. 14.472 MPa, 5.528 MPa
• B. 5.2MPa, 12.6MPa
• C. 29.6MPa, - 9.6 MPa
• D. None of the above

Answer 1

The correct option is A 14.472 MPa, 5.528 MPa

${\sigma }_x=14,{\sigma }_y=6;{\tau }_{xy}=-2$

${\sigma }_{1,2}=\frac{{\sigma }_x+{\sigma }_y}{2}\pm \sqrt{{\left(\frac{{\sigma }_x-{\sigma }_y}{2}\right)}^2+{\tau }_{xy}^2}$

${\sigma }_1=14.472MPa,{\sigma }_2=5.528MPa$