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In a two-dimensional stress analysis, the state of stress at a point is shown in the figure. The values of lengths of PQ, QR, and RP are 4, 3, and 5 units, respectively. The principal stresses are ______. (round off to one decimal place)

1. σx = 26.7 MPa, σy = 172.5 MPa
2. σx = 54.0 MPa, σy = 128.5 MPa
3. σx = 67.5 MPa, σy = 213.3 MPa
4. σx = 18.0 MPa, σy = 138.5 MPa

Correct answer: σx = 54.0 MPa, σy = 128.5 MPa

Solution

The given lengths form a 3-4-5 triangle, which is typically used to infer the stress components from the figure. After resolving the stress state, the principal stresses are obtained using the plane stress transformation equations or Mohr’s circle. The correct pair is 54.0 MPa and 128.5 MPa.

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