Project ForgeStrength of Materials
Stress & Strain
GATE 2018
Hard
The state of stress at a point, for a body in plane stress, has σx=100 kPa and τxy=50 kPa acting on the element. If the minimum principal stress is 10 kPa, then the normal stress σy (in kPa) is
- A9.45
- B18.88
- 37.78
- D75.50
Explanation
Principal stresses: σ1,2 = (σx+σy)/2 ± √(((σx−σy)/2)²+τxy²). Testing σy=37.78: average=(100+37.78)/2≈68.89, half-difference≈31.11, √(31.11²+50²)=√3468.8≈58.9, σmin≈68.89−58.9≈9.99≈10 kPa — matches, so σy=37.78 kPa.
Source: GATE ME 2018 Session 1 (Set 1) (2018)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.