Which of the plot(s) shown is/are valid Mohr’s circle representations of a plane stress state in a material? (The center of each circle is indicated by O.)

Answer :

Solution :

• For case-1: Plane stress state means there should be existance of two stress components. So for case 1 there is two equal and opposite stresses exists so M₁ represent the plane stress condition. 
• For case-2: It is clearly seen that Mohr circle did not cut σ - axis , there is no stress component exists.
• For case-3: Here σ₁ = 0 and σ₂ = diameter of Mohr circle. So it is a plane stress condition. 
• For case-4: Mohr circle is tangential to σ - axis so only one stress exist. Which is equal to zero. It does not represent plane stress condition.