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Strength of Materials
Stress & Strain
GATE 2022
Medium

A structural member under loading has a uniform state of plane stress which in usual notations is given by σx=3P, σy=−2P and τxy=√2 P, where P>0. The yield strength of the material is 350 MPa. If the member is designed using the maximum distortion energy theory, then the value of P at which yielding starts (according to the maximum distortion energy theory) is

  • 70 MPa
  • B90 MPa
  • C120 MPa
  • D75 MPa

Explanation

Von Mises equivalent stress: σe=√(σx²−σxσy+σy²+3τxy²) = √(9P²−(3P)(−2P)+4P²+3(2P²)) = √(9P²+6P²+4P²+6P²) = √(25P²) = 5P. Setting σe equal to yield strength: 5P=350, so P=70 MPa.

Source: GATE ME 2022 Session 2 (ME-2) (2022)

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