This question was previously asked in

PY 1: GATE ME 2020 Official Paper: Shift 1

Option 2 : a point on the σ axis at a distance of 10 units from origin

CT 1: Ratio and Proportion

2672

10 Questions
16 Marks
30 Mins

__Concept:__

General Mohr Circle for biaxial stress condition:

Principal stresses are given by

\({{\sigma }_{1,~2}}=\frac{{{\sigma }_{x}}+{{\sigma }_{y}}}{2}~\pm ~\sqrt{{{\left( \frac{{{\sigma }_{x}}-{{\sigma }_{y}}}{2} \right)}^{2}}+\tau _{xy}^{2}}\)

Radius of circle (Mohr’s circle) \(=\sqrt{{{\left( \frac{{{\sigma }_{x}}-{{\sigma }_{y}}}{2} \right)}^{2}}+\tau _{xy}^{2}}\)

__Calculation:__

Given state of stress is represented by

∴ σ_{x} = 10 MPa. σ_{y} = 10 MPa τ_{xy} = 0

For this the Mohr Circle will be a point:

∴ σ_{1} = σ_{2} = 10 MPa

Radius of circle (Mohr’s circle) will be zero.

The co-ordinate of the centre of Mohr’s circle on σ-axis at a distance of 10 units from the origin.