Mohr's circle is used to determine the stresses on an oblique section of a body subjected to

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BPSC AE Paper 4 (General Engineering Science) 25 March 2022 Official Paper
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1. direct tensile stress in one plane accompanied by a shear stress
2. direct tensile stress in two mutually perpendicular directions
3. direct tensile stress in two mutually perpendicular directions accompanied by a simple shear stress
4. All of the above

Option 4 : All of the above
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Detailed Solution

Explanation:

Mohr's circle

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

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.

Pure shear planes are planes on which normal stress is zero

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

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

Mohr's circle is used to determine the stresses on an oblique section of a body subjected to:

• direct tensile stress in one plane accompanied by a shear stress
• direct tensile stress in two mutually perpendicular directions
• direct tensile stress in two mutually perpendicular directions accompanied by a simple shear stress
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