What are the three stress invariants (in MPa) respectively in a body under the stress states of σx = 10, σy = 8, σz = -5, τyz = τzy = 5, τzx = τxz = -4, and τxy = τyx = -8, where all stresses are in MPa?
- A23, -128 and 125
- B13, 115 and -138Correct
- C115, 13, -128
- D138, 23, 125
Solution
Concept
Stress invariants I1, I2 and I3 do not change with axis rotation. They come from the stress tensor.
Formula
I1 = σx + σy + σz; I2 = σxσy + σyσz + σzσx - τxy2 - τyz2 - τzx2; I3 = determinant of stress matrix
Step-by-step solution
1. I1 = 10 + 8 - 5 = 13 MPa. 2. σxσy + σyσz + σzσx
Correct answer: B) 13, 115 and -138