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When two mutually perpendicular principal stresses are unequal but like, the maximum shear stress is represented by
- a)The diameter of the Mohr's circle
- b)Half the diameter of the Mohr's circle
- c)One-third the diameter of the Mohr's circle
- d)One-fourth the diameter of the Mohr's circle
Correct answer is option 'B'. Can you explain this answer?
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When two mutually perpendicular principal stresses are unequal but lik...
Explanation:
When two mutually perpendicular principal stresses are unequal but like, the maximum shear stress is given by half the diameter of the Mohr's circle. This is explained in the following points:
Mohr's circle:
Mohr's circle is a graphical representation of the state of stress at a point. It is constructed by plotting the normal stresses on one axis and the shear stresses on the other axis. The circle is drawn by plotting points corresponding to the different states of stress at a point.
Principal stresses:
Principal stresses are the maximum and minimum normal stresses that act on a plane at a point. They are mutually perpendicular and are represented by the diameter of the Mohr's circle. The maximum principal stress is represented by the rightmost point on the circle, and the minimum principal stress is represented by the leftmost point on the circle.
Maximum shear stress:
The maximum shear stress is the difference between the two principal stresses divided by two. It is represented by the radius of the circle. The maximum shear stress occurs on a plane inclined at 45 degrees to the principal planes.
Unequal but like principal stresses:
When two mutually perpendicular principal stresses are unequal but like, they are represented by a point on the right-hand side of the circle. The diameter of the circle represents the difference between the two principal stresses. Since the principal stresses are like, the maximum shear stress occurs on a plane inclined at 45 degrees to the principal planes. Therefore, the maximum shear stress is given by half the diameter of the Mohr's circle.
Conclusion:
Hence, the correct answer is option 'B', which states that the maximum shear stress is represented by half the diameter of the Mohr's circle.
When two mutually perpendicular principal stresses are unequal but like, the maximum shear stress is given by half the diameter of the Mohr's circle. This is explained in the following points:
Mohr's circle:
Mohr's circle is a graphical representation of the state of stress at a point. It is constructed by plotting the normal stresses on one axis and the shear stresses on the other axis. The circle is drawn by plotting points corresponding to the different states of stress at a point.
Principal stresses:
Principal stresses are the maximum and minimum normal stresses that act on a plane at a point. They are mutually perpendicular and are represented by the diameter of the Mohr's circle. The maximum principal stress is represented by the rightmost point on the circle, and the minimum principal stress is represented by the leftmost point on the circle.
Maximum shear stress:
The maximum shear stress is the difference between the two principal stresses divided by two. It is represented by the radius of the circle. The maximum shear stress occurs on a plane inclined at 45 degrees to the principal planes.
Unequal but like principal stresses:
When two mutually perpendicular principal stresses are unequal but like, they are represented by a point on the right-hand side of the circle. The diameter of the circle represents the difference between the two principal stresses. Since the principal stresses are like, the maximum shear stress occurs on a plane inclined at 45 degrees to the principal planes. Therefore, the maximum shear stress is given by half the diameter of the Mohr's circle.
Conclusion:
Hence, the correct answer is option 'B', which states that the maximum shear stress is represented by half the diameter of the Mohr's circle.
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When two mutually perpendicular principal stresses are unequal but like, the maximum shear stress is represented bya)The diameter of the Mohr's circleb)Half the diameter of the Mohr's circlec)One-third the diameter of the Mohr's circled)One-fourth the diameter of the Mohr's circleCorrect answer is option 'B'. Can you explain this answer?
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