Question

For an element with stress values of 158 MPa, 158 MPa, 158 MPa, and the other stresses as zero, use the invariants of the eigenvalue problem to find the maxiμm principal stress in units of MPa.

a) 474 MPa
b) 158 MPa
c) 316 MPa
d) 632 MPa

Answer 1

The maximum principal stress in a triaxial stress state with equal stresses of 158 MPa in all directions is 158 MPa.

Step-by-step explanation:

The question is asking to determine the maximum principal stress for an element subjected to a triaxial stress state, which is a typical problem in the field of materials engineering and mechanics of materials.

Given the stress values of 158 MPa in the three principal directions (assuming a principal stress state with σ1 = σ2 = σ3 = 158 MPa), and all other stresses equal to zero, the maximum principal stress is simply one of these values, as they are all equal; therefore, the maximum principal stress is 158 MPa.

To find the maximum principal stress, we need to calculate the principal stresses using the given stress values. The formula to calculate the principal stresses for 2D stress states is σ₁ = (σx + σy)/2 + sqrt(((σx - σy)/2)² + τxy²), σ₂ = (σx + σy)/2 - sqrt(((σx - σy)/2)² + τxy²).

Since the other stresses are zero, the formula simplifies to σ₁ = σ₂ = σ₃ = 158 MPa.