Combined Stress — Minimum Principal (Normal) Stress A body is under a direct tensile stress of 300 MPa in one principal plane and a simple shear stress of 200 MPa. Determine the minimum normal (principal) stress.

Introduction:
Using principal stress transformation, we can find the minimum principal stress for a combined state of direct tension and shear.

Given Data / Assumptions:

• σx = 300 MPa, σy = 0 MPa.
• τxy = 200 MPa.
• Plane stress; linear elastic behavior.

Concept / Approach:
Principal stresses are: σ1,2 = (σx + σy)/2 ± sqrt( ((σx - σy)/2)^2 + τxy^2 )

Step-by-Step Solution:
Average = (300 + 0)/2 = 150 MPa.Radius = sqrt(150^2 + 200^2) = sqrt(62500) = 250 MPa.σ2 = 150 - 250 = -100 MPa (minimum principal stress).

Verification / Alternative check:
Sum of principal stresses equals σx + σy = 300 MPa, so σ1 + σ2 = 400 + (−100) = 300 MPa. Checks out.

Why Other Options Are Wrong:

• 250 MPa: Radius, not a principal stress.
• 300 MPa: Applied direct stress, not the transformed minimum principal value.
• 400 MPa: This is the maximum principal stress.

Common Pitfalls:
Sign errors when subtracting the radius or interchanging σ1 and σ2 are frequent mistakes.

Final Answer:
-100 MPa