Question

Mohr's circle for the state of stress defined by $\left[\begin{array}{cc}30& 0\\ 0& 30\end{array}\right]$ MPa is a circle with

• A. centre at (0,0) and radius 30 MPa
• B. centre at (0, 0) and radius 60 MPa
• C. centre at (30, 0) and radius 30 MPa
• D. centre at (30, 0) and zero radius

Answer 1

The correct option is D centre at (30, 0) and zero radius

State of stress
$\left[\begin{array}{cc}30& 0\\ 0& 30\end{array}\right]=\left[\begin{array}{cc}{\sigma }_{xx}& {\tau }_{xy}\\ {\tau }_{yx}& {\sigma }_{yy}\end{array}\right]$
${\sigma }_{xx}=30$
${\sigma }_{yy}=30$
${\tau }_{xy}=0$

Co-ordinate of centre of Mohr circle,

$(x,y)=(\frac{30+30}{2},0)=(30,0)$
radius $r=\sqrt{(\frac{{\sigma }_{xx}-{\sigma }_{yy}}{2}{)}^2+{\tau }_{xy}^2}$
$=\sqrt{{\left(\frac{30-30}{2}\right)}^2+0^2}$
$=0$