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At a point in a strained body carrying two unequal unlike principal stresses p1 and p2 (p1 > p2), the maximum shear stress is given by
- a)p1/2
- b)p2/2
- c)(p1 - p2)/2
- d)(p1 + p2)/2
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
At a point in a strained body carrying two unequal unlike principal st...
The maximum shear stress is given by,
Now, σ1 = +p1
σ2 = -p2
∴
Now, σ1 = +p1
σ2 = -p2
∴
Most Upvoted Answer
At a point in a strained body carrying two unequal unlike principal st...
>p2), the maximum shear stress occurs on a plane inclined at 45 degrees to the principal planes.
This can be explained by the Mohr's Circle of stress. Mohr's circle is a graphical representation of stress states at a point in a material. In Mohr's circle, the principal stresses are represented by the diameter of a circle, and the shear stresses are represented by the distance from the center of the circle to a point on the circle.
For a strained body carrying two unequal unlike principal stresses p1 and p2, the Mohr's circle will be an ellipse. The major axis of the ellipse represents the maximum principal stress (p1), and the minor axis represents the minimum principal stress (p2). The center of the ellipse represents the mean stress.
Now, to find the maximum shear stress, we need to draw a line on the Mohr's circle at 45 degrees to the principal planes. This line represents a plane on which the shear stress will be maximum. The distance from the center of the circle to the point where the line intersects the circle represents the maximum shear stress.
Since the principal stresses are unequal and unlike, the Mohr's circle will be elongated in one direction. This means that the maximum shear stress will occur on a plane that is inclined at 45 degrees to the principal planes.
Therefore, at a point in a strained body carrying two unequal unlike principal stresses p1 and p2 (p1>p2), the maximum shear stress occurs on a plane inclined at 45 degrees to the principal planes.
This can be explained by the Mohr's Circle of stress. Mohr's circle is a graphical representation of stress states at a point in a material. In Mohr's circle, the principal stresses are represented by the diameter of a circle, and the shear stresses are represented by the distance from the center of the circle to a point on the circle.
For a strained body carrying two unequal unlike principal stresses p1 and p2, the Mohr's circle will be an ellipse. The major axis of the ellipse represents the maximum principal stress (p1), and the minor axis represents the minimum principal stress (p2). The center of the ellipse represents the mean stress.
Now, to find the maximum shear stress, we need to draw a line on the Mohr's circle at 45 degrees to the principal planes. This line represents a plane on which the shear stress will be maximum. The distance from the center of the circle to the point where the line intersects the circle represents the maximum shear stress.
Since the principal stresses are unequal and unlike, the Mohr's circle will be elongated in one direction. This means that the maximum shear stress will occur on a plane that is inclined at 45 degrees to the principal planes.
Therefore, at a point in a strained body carrying two unequal unlike principal stresses p1 and p2 (p1>p2), the maximum shear stress occurs on a plane inclined at 45 degrees to the principal planes.
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At a point in a strained body carrying two unequal unlike principal stresses p1 and p2 (p1 > p2), the maximum shear stress is given bya)p1/2b)p2/2c)(p1- p2)/2d)(p1 + p2)/2Correct answer is option 'D'. Can you explain this answer?
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