Stress concentration around an elliptical hole in a plate under tension Plate with a central elliptical hole: semi-major axis a is perpendicular to loading; semi-minor axis b is along the loading direction. Let σ be the nominal (no-hole) stress. Find the maximum stress at the hole edge.

Given• Plate in tension with an elliptical hole (semi-major axis a ⟂ load, semi-minor axis b ∥ load).• Nominal stress (no hole) = σ.

ConceptThe stress concentration factor at the ends of the minor axis for an elliptical hole isK = 1 + 2(a/b)⇒ σ_max = K · σ = σ (1 + 2a/b)

Step-by-step1) Identify orientation: a ⟂ load → the high-stress points lie on the ends of b.2) Use the classic elasticity result for an ellipse in an infinite plate.3) Multiply nominal stress by K to obtain σ_max.

Common pitfallSwapping a and b reverses the factor; ensure correct axes relative to the loading direction.

Final Answerσ (1 + 2a/b)