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Normal stresses of equal magnitude a, but of opposite signs, act at a point of a strained material in perpendicular direction. What is the magnitude of the stress on a plane inclined at 45° to the applied stresses?
  • a)
  • b)
    σ/2
  • c)
    σ/4
  • d)
    Zero
Correct answer is option 'D'. Can you explain this answer?
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Degrees to each of the normal stresses?

The stress on a plane inclined at 45 degrees to each of the normal stresses can be calculated using the formula:

σ = (σx + σy)/2 + (σx - σy)/2cos(2θ)

where σx and σy are the normal stresses and θ is the angle between the plane and the x-axis.

In this case, since the normal stresses have equal magnitude a but opposite signs, we have:

σx = a and σy = -a

Substituting these values into the formula, we get:

σ = (a - a)/2 + (a + a)/2cos(2(45°))
= a/2 + a/2cos(90°)
= a/2

Therefore, the magnitude of the stress on a plane inclined at 45 degrees to each of the normal stresses is equal to half the magnitude of the normal stresses, or a/2.
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Normal stresses of equal magnitude a, but of opposite signs, act at a point of a strained material in perpendicular direction. What is the magnitude of the stress on a plane inclined at 45° to the applied stresses?a)2σb)σ/2c)σ/4d)ZeroCorrect answer is option 'D'. Can you explain this answer?
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