Project ForgeStrength of Materials
Stress & Strain
GATE 2023
Medium
The principal stresses at a point P in a solid are 70 MPa, −70 MPa and 0. The yield stress of the material is 100 MPa. Which prediction(s) about material failure at P is/are CORRECT?
- AMaximum normal stress theory predicts that the material fails
- Maximum shear stress theory predicts that the material fails
- Maximum normal stress theory predicts that the material does not fail
- DMaximum shear stress theory predicts that the material does not fail
Explanation
Maximum normal stress (Rankine) theory: failure if max|σi| exceeds σY. Here max|σi|=70<100, so it predicts NO failure (option C correct, A wrong). Maximum shear stress (Tresca) theory: failure if τmax=(σmax−σmin)/2 exceeds σY/2. Here τmax=(70−(−70))/2=70>100/2=50, so it predicts failure (option B correct, D wrong).
Source: GATE ME 2023 Official Paper (2023)
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