Question

On the element shown in the given figure, the stresses are:
${\sigma }_x=110MPa$

${\sigma }_y=30MPa$

${\tau }_{xy}={\tau }_{yx}=30MPa$

${\sigma }_1,{\sigma }_2$

The radius of Mohr's circle and the principal stresses ${\tau }_1,{\tau }_2$ are (in MPa)

• A.

  Radius = R	${\sigma }_1$	${\sigma }_2$
  50	120	20

• B.

  Radius = R	${\sigma }_1$	${\sigma }_2$
  55	30	110

• C.

  Radius = R	${\sigma }_1$	${\sigma }_2$
  60	140	20

• D.

  Radius = R	${\sigma }_1$	${\sigma }_2$
  70	140	20

Answer 1

The correct option is A

Radius = R	${\sigma }_1$	${\sigma }_2$
50	120	20

Centre of Mohr's circle,

$C=\frac{{\sigma }_x+{\sigma }_y}{2}=70MPa$
Radius of Mohr's circle,

$R=\sqrt{{\left(\frac{{\sigma }_x-{\sigma }_y}{2}\right)}^2+{\tau }_{xy}^2}=50MPa$
Major principal stress

${\sigma }_1=C+R=70+50=120MPa$
Minor principal stress

${\sigma }_2=C-R=70-50=20MPa$