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Two-dimensional state of stress at a point in a plane stressed element is represented by a Mohr circle of zero radius. Then both principal stresses
- a)Are equal to zero
- b)Are equal to zero and shear stress is also equal to zero
- c)Are of equal magnitude but of opposite sign
- d)Are of equal magnitude and of same sign
Correct answer is option 'D'. Can you explain this answer?
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Two-dimensional state of stress at a point in a plane stressed element...
Explanation:
When the Mohr circle of zero radius is obtained, it means that the principal stresses are equal and have the same magnitude. Let's analyze the options to understand why option D is the correct answer.
a) Are equal to zero:
If the principal stresses were equal to zero, then the Mohr circle would not exist because the Mohr circle represents the state of stress at a point in a plane stressed element. Therefore, option A is incorrect.
b) Are equal to zero and shear stress is also equal to zero:
If both principal stresses were equal to zero and the shear stress was also equal to zero, then the Mohr circle would not exist because the Mohr circle represents the state of stress at a point in a plane stressed element. Therefore, option B is incorrect.
c) Are of equal magnitude but of opposite sign:
If the principal stresses were of equal magnitude but of opposite signs, then the Mohr circle would not have a zero radius. The radius of the Mohr circle represents the difference between the principal stresses. Therefore, option C is incorrect.
d) Are of equal magnitude and of the same sign:
When the Mohr circle has a zero radius, it means that the principal stresses are equal and of the same sign. In this case, the principal stresses have equal magnitudes and are both tensile or both compressive. This is represented by a single point on the Mohr circle, which is the center of the circle. Therefore, option D is the correct answer.
To summarize, when the Mohr circle has a zero radius, it indicates that the principal stresses are of equal magnitude and of the same sign. This means that both principal stresses are equal and represent either pure tensile or pure compressive stress at the point in the plane stressed element.
When the Mohr circle of zero radius is obtained, it means that the principal stresses are equal and have the same magnitude. Let's analyze the options to understand why option D is the correct answer.
a) Are equal to zero:
If the principal stresses were equal to zero, then the Mohr circle would not exist because the Mohr circle represents the state of stress at a point in a plane stressed element. Therefore, option A is incorrect.
b) Are equal to zero and shear stress is also equal to zero:
If both principal stresses were equal to zero and the shear stress was also equal to zero, then the Mohr circle would not exist because the Mohr circle represents the state of stress at a point in a plane stressed element. Therefore, option B is incorrect.
c) Are of equal magnitude but of opposite sign:
If the principal stresses were of equal magnitude but of opposite signs, then the Mohr circle would not have a zero radius. The radius of the Mohr circle represents the difference between the principal stresses. Therefore, option C is incorrect.
d) Are of equal magnitude and of the same sign:
When the Mohr circle has a zero radius, it means that the principal stresses are equal and of the same sign. In this case, the principal stresses have equal magnitudes and are both tensile or both compressive. This is represented by a single point on the Mohr circle, which is the center of the circle. Therefore, option D is the correct answer.
To summarize, when the Mohr circle has a zero radius, it indicates that the principal stresses are of equal magnitude and of the same sign. This means that both principal stresses are equal and represent either pure tensile or pure compressive stress at the point in the plane stressed element.
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Two-dimensional state of stress at a point in a plane stressed element...
Radius in principle plane gets zero so according to the formula (sigma 1 - sigma 2 )÷2 = 0
sigma 1 = sigma 2
sigma 1 = sigma 2
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Two-dimensional state of stress at a point in a plane stressed element is represented by a Mohr circle of zero radius. Then both principal stressesa)Are equal to zero b)Are equal to zero and shear stress is also equal to zeroc)Are of equal magnitude but of opposite signd)Are of equal magnitude and of same signCorrect answer is option 'D'. Can you explain this answer?
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