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If a body is subjected to stresses in xy plane with stresses of 60N/mm² and 80N/mm² acting along x and y axes respectively. Also the shear stress acting is 20N/mm²Find the maximum amount of shear stress to which the body is subjected.
- a)22.4mm
- b)25mm
- c)26.3mm
- d)27.2mm
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If a body is subjected to stresses in xy plane with stresses of 60N/mm...
Explanation: τ(max)=√( [σ(x)-σ(y) ]²/2² + τ²).
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If a body is subjected to stresses in xy plane with stresses of 60N/mm...
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in x direction, 40N/mm2 in y direction and 20N/mm2 in xy direction, calculate the maximum shear stress and the maximum normal stress on the body.
To calculate the maximum shear stress, we can use the formula:
τmax = (σx - σy)/2 + sqrt((σx - σy)2/4 + τxy2)
where σx, σy, and τxy are the stresses in the x, y, and xy directions, respectively.
Plugging in the values we get:
τmax = (60 - 40)/2 + sqrt((60 - 40)2/4 + 202) = 10 + sqrt(400) = 30 N/mm2
Therefore, the maximum shear stress on the body is 30 N/mm2.
To calculate the maximum normal stress, we can use the formula:
σmax = (σx + σy)/2 + sqrt((σx - σy)2/4 + τxy2)
Plugging in the values we get:
σmax = (60 + 40)/2 + sqrt((60 - 40)2/4 + 202) = 50 + sqrt(400) = 70 N/mm2
Therefore, the maximum normal stress on the body is 70 N/mm2.
in x direction, 40N/mm2 in y direction and 20N/mm2 in xy direction, calculate the maximum shear stress and the maximum normal stress on the body.
To calculate the maximum shear stress, we can use the formula:
τmax = (σx - σy)/2 + sqrt((σx - σy)2/4 + τxy2)
where σx, σy, and τxy are the stresses in the x, y, and xy directions, respectively.
Plugging in the values we get:
τmax = (60 - 40)/2 + sqrt((60 - 40)2/4 + 202) = 10 + sqrt(400) = 30 N/mm2
Therefore, the maximum shear stress on the body is 30 N/mm2.
To calculate the maximum normal stress, we can use the formula:
σmax = (σx + σy)/2 + sqrt((σx - σy)2/4 + τxy2)
Plugging in the values we get:
σmax = (60 + 40)/2 + sqrt((60 - 40)2/4 + 202) = 50 + sqrt(400) = 70 N/mm2
Therefore, the maximum normal stress on the body is 70 N/mm2.
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