Plane stress analysis: compute the maximum normal stress (principal stress) for a biaxial state with shear A body is under σ_x = 1200 MPa (tension) and σ_y = 600 MPa (tension) on mutually perpendicular planes. A shear stress τ_xy = 400 MPa acts on the same planes. Determine the maximum principal (normal) stress.

Givenσ_x = 1200 MPa, σ_y = 600 MPa, τ_xy = 400 MPa.

ApproachPrincipal stresses for plane stress: σ_1,2 = (σ_x + σ_y)/2 ± √{ [ (σ_x − σ_y)/2 ]² + τ_xy² }.

Step-by-step calculationσ_avg = (1200 + 600)/2 = 900 MPa.Δ = (σ_x − σ_y)/2 = (1200 − 600)/2 = 300 MPa.Radical = √(300² + 400²) = √(90,000 + 160,000) = √250,000 = 500 MPa.σ₁ = 900 + 500 = 1400 MPa; σ₂ = 900 − 500 = 400 MPa.

VerificationMohr’s circle would have center at 900 MPa and radius 500 MPa, consistent with σ₁ and σ₂ above.

Final Answer1400 MPa.