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ISRO Refrigeration and Air Conditioning 2015 Official

Option 3 : equal to radius of Mohr’s circle

ISRO Scientist ME 2020 Paper

1538

80 Questions
240 Marks
90 Mins

**Explanation:**

Mohr's circle is very useful in determining the relationships between normal and shear stresses acting on an inclined plane at a point in a stressed body. It is helpful in finding maximum and minimum principal stresses, maximum shear stress, etc.

Major Principal stress is given as:

\({\sigma _{p1}} = \frac{{{\sigma _1} + {\sigma _2}}}{2} + \sqrt {{{\left\{ {\frac{{{\sigma _1} - {\sigma _2}}}{2}} \right\}}^2} + {\tau _{xy}}^2} \)

Minor Principal stress is given as:

\({\sigma _{p2}} = \frac{{{\sigma _1} + {\sigma _2}}}{2} - \sqrt {{{\left\{ {\frac{{{\sigma _1} - {\sigma _2}}}{2}} \right\}}^2} + {\tau _{xy}}^2}\)

Maximum Shear stress is given as:

\({\tau _{max}} = \frac{{\left( {{\sigma _{1}} - {\sigma _{2}}} \right)}}{2}\)

**The radius of Mohr’s circle is given as**:

\(R= \frac{{\left( {{\sigma _{1}} - {\sigma _{2}}} \right)}}{2}\)

So

**The radius of Mohr’s circle is equal to Maximum Shear stress.**