Principal Stresses in Plane Stress
Mediumprincipal stressesplane stress
At a point in plane stress, σx = 80 MPa, σy = 20 MPa, and τxy = 0. What are the two in-plane principal stresses?
- A50 MPa and 50 MPa
- B80 MPa and 20 MPa
- C100 MPa and 0 MPa
- D60 MPa and 40 MPa
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Answer: B. 80 MPa and 20 MPa
Because τxy = 0, the x and y planes are already principal planes. Equivalently, σ₁,₂ = (80 + 20)/2 ± √[((80 − 20)/2)² + 0²] = 50 ± 30 = 80 and 20 MPa.
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