When a body is subjected to direct tensile stresses ($${\sigma _{\text{x}}}$$ and $${\sigma _{\text{y}}}$$) in two mutually perpendicular directions, accompanied by a simple shear stress $${\tau _{{\text{xy}}}}{\text{,}}$$  then in Mohr's circle method, the circle radius is taken as?

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  1. $$\frac{{{\sigma _{\text{x}}} - {\sigma _{\text{y}}}}}{2} + \tau $$
  2. $$\frac{{{\sigma _{\text{x}}} + {\sigma _{\text{y}}}}}{2} + \tau $$
  3. $$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$
  4. $$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$

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Answer: Option 3

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