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If a body carries two unlike principal stresses, what is the maximum shear stress?
- a)Half the difference of magnitude of the principal stresses
- b)Half the sum of the magnitude of principal stresses
- c)Difference of the magnitude of principal stresses
- d)Sum of the magnitude of principal stresses
Correct answer is option 'B'. Can you explain this answer?
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If a body carries two unlike principal stresses, what is the maximum s...
The principal stress given are unlike i.e if one is tensile and other is compressive. Let σ1 be tensile and σ2 be compressive, then
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If a body carries two unlike principal stresses, what is the maximum s...
Explanation:
When a body carries two unlike principal stresses, the maximum shear stress can be calculated using Mohr's circle. Mohr's circle is a graphical method used to determine the state of stress at a point in a material. The circle is constructed using the principal stresses as coordinates.
To find the maximum shear stress, we need to find the diameter of the Mohr's circle. The diameter of the circle represents the difference between the two principal stresses. The maximum shear stress occurs at the midpoint of the diameter.
Therefore, the maximum shear stress can be calculated as:
Option B: Half the sum of the magnitude of principal stresses.
Shear stress = 1/2 (σ₁ - σ₂)
where σ₁ and σ₂ are the principal stresses.
The sum of the principal stresses represents the diameter of the Mohr's circle. Dividing it by 2 gives the radius, which represents the maximum shear stress.
Hence, option B is the correct answer.
Summary:
- Mohr's circle is used to determine the state of stress at a point in a material.
- The diameter of the circle represents the difference between the two principal stresses.
- The maximum shear stress occurs at the midpoint of the diameter.
- The maximum shear stress can be calculated as half the sum of the magnitude of principal stresses, using the formula Shear stress = 1/2 (σ₁ - σ₂).
When a body carries two unlike principal stresses, the maximum shear stress can be calculated using Mohr's circle. Mohr's circle is a graphical method used to determine the state of stress at a point in a material. The circle is constructed using the principal stresses as coordinates.
To find the maximum shear stress, we need to find the diameter of the Mohr's circle. The diameter of the circle represents the difference between the two principal stresses. The maximum shear stress occurs at the midpoint of the diameter.
Therefore, the maximum shear stress can be calculated as:
Option B: Half the sum of the magnitude of principal stresses.
Shear stress = 1/2 (σ₁ - σ₂)
where σ₁ and σ₂ are the principal stresses.
The sum of the principal stresses represents the diameter of the Mohr's circle. Dividing it by 2 gives the radius, which represents the maximum shear stress.
Hence, option B is the correct answer.
Summary:
- Mohr's circle is used to determine the state of stress at a point in a material.
- The diameter of the circle represents the difference between the two principal stresses.
- The maximum shear stress occurs at the midpoint of the diameter.
- The maximum shear stress can be calculated as half the sum of the magnitude of principal stresses, using the formula Shear stress = 1/2 (σ₁ - σ₂).
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If a body carries two unlike principal stresses, what is the maximum shear stress?a)Half the difference of magnitude of the principal stressesb)Half the sum of the magnitude of principal stressesc)Difference of the magnitude of principal stressesd)Sum of the magnitude of principal stressesCorrect answer is option 'B'. Can you explain this answer?
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