For the case of plane stress problem, an element is subjected to bi-axial tensile. The normal stresses are 10 MPa and 5 MPa and shear stress is 6 MPa. If one of the principal stress is 1 MPa, then what is the other value of the principal stress?
- A5 MPa
- B7.5 MPa
- C10 MPa
- D14 MPaCorrect
Solution
Concept
First Stress Invariant
Formula
σ1 + σ2 = σx + σy
Step-by-step solution
1. Use the relation σ1 + σ2 = σx + σy 2. Substitute the values: 1 + σ2 = 10 + 5 3. Solve for σ2: σ2 = 15 - 1 = 14 MPa
Explanation
the stress invariant property: the sum of normal stresses equals the sum of principal stresses (σx + σy = σ1 + σ2). Simply add the two given normal stresses (10 + 5 = 15) and subtract the known principal stress (15 - 1 = 14).
Correct answer: D) 14 MPa