Question

The state of stress at a point under plane stress condition is σ_xx = 60 MPa, σ_yy = 120 MPa and τ_xy = 40 MPa

The radius of Mohr’s circle representing the given state of stress in MPa is

1. 40
2. 50
3. 60
4. 120

Answer 1

Correct Answer - Option 2 : 50

Concept:

The radius of the Mohr's circle is given by the value of maximum in-plane shear stress.

Maximum and minimum values of normal stresses occur on planes of zero shearing stress. The maximum and minimum normal stresses are called the principal stresses, and the planes on which they act are called the principal plane.

\({\sigma _{max,\;min}} = \frac{{{\sigma _{xx}} + {\sigma _{yy}}}}{2} \pm \sqrt {{{\left( {\frac{{{\sigma _{xx}} - {\sigma _{yy}}}}{2}} \right)}^2} + \tau _{xy}^2} \)

Maximum shear stress is given by 

\({\tau _{max}} = \frac{{{\sigma _{max}} - {\sigma _{min}}}}{2} = \sqrt {{{\left( {\frac{{{\sigma _{xx}} - {\sigma _{yy}}}}{2}} \right)}^2} + \tau _{xy}^2} \)

which is equal to the radius of the Mohr's Circle.

Calculation:

Given σxx = 60 MPa, σyy = 120 MPa and τxy = 40 MPa;

The radius of the Mohr's circle will be 

\({\tau _{max}} = R = \sqrt {{{\left( {\frac{{{60} - {120}}}{2}} \right)}^2} +40^2} \)

⇒ R = 50 MPa