Stress Concentration Factor (Kt) Simulator

The Stress Concentration Factor (Kt) Simulator visualises how geometric discontinuities — holes, notches, fillets, and grooves — amplify local stress compared to the nominal (average) stress. It implements Peterson’s chart curve fits for 8 common geometries covering flat plates and round shafts under tension, bending, and torsion. The canvas displays a colour-mapped stress field showing exactly where peak stress occurs.

The stress concentration factor Kt is defined as σ_max = Kt × σ_nom. A plate with a small central hole under tension has Kt ≈ 3.0, meaning the stress at the hole edge is three times higher than the average stress across the plate. Understanding Kt is essential for preventing fatigue cracks, optimising fillet radii, and designing safe components.

The simulator opens in Simulate mode with the “Hole” geometry (plate with central hole under tension). The top canvas shows a colour-mapped stress field, and the bottom canvas plots the Kt vs. geometry ratio curve from Peterson’s charts. A readout panel displays Kt, σ_nom, σ_max, and the current geometry ratio.

Click any of the 8 geometry buttons (Hole, Notch, Fillet-T, Fillet-B, Shaft-T, Shaft-Tor, Groove, Trans-Hole) to switch between configurations. Each geometry has its own set of dimension sliders that appear in the controls panel. Adjust sliders to see how Kt changes with the geometry ratio.

The 8 geometries are: (1) Plate with centre hole — tension, (2) Plate with edge notch — tension, (3) Plate with shoulder fillet — tension, (4) Plate with shoulder fillet — bending, (5) Round shaft with fillet — tension, (6) Round shaft with fillet — torsion, (7) Round shaft with groove — tension, (8) Round shaft with transverse hole — tension.

Each geometry has sliders for the key dimensions (e.g., hole diameter d, plate width D, fillet radius r). As you adjust a slider, the Kt value updates based on Peterson’s polynomial curve fit, the colour-mapped stress field redraws, and a marker moves along the Kt chart curve. The nominal stress σ_nom uses the net cross-section (after removing the discontinuity) for plates, or the full cross-section for shafts depending on the convention.

A larger fillet radius always reduces Kt — sharp corners (r → 0) create very high stress concentrations, while generous fillets bring Kt closer to 1.0.

Explore mode provides educational content in four categories: Fundamentals (definition of Kt, nominal stress conventions, stress raiser concept), Plate Geometries (hole in plate, edge notch, shoulder fillet), Shaft Geometries (stepped shaft, groove, transverse hole), and Design Methods (notch sensitivity, fatigue Kf, Peterson’s chart usage, mitigation strategies).

Pay particular attention to the distinction between the theoretical Kt (geometry-only) and the fatigue Kf = 1 + q(Kt − 1), which accounts for material notch sensitivity. For fatigue design, Kf is more relevant than Kt.

Practice mode generates random problems asking you to calculate σ_max given Kt and σ_nom, or to look up Kt from given geometry ratios. Enter your numeric answer, click Check, and use Show Solution for a step-by-step walkthrough. Click Next for another problem. Your running score is displayed.

Quiz mode presents 5 questions per session covering Kt lookup, σ_max calculation, geometry identification, and design recommendations. After completing all questions, your score and detailed review are displayed.

• A small hole in a wide plate under tension has Kt ≈ 3.0. This is the most frequently cited stress concentration case.
• Increasing the fillet radius is the most effective way to reduce Kt at a shoulder transition. Even a small radius dramatically lowers peak stress.
• For fatigue design, use Kf instead of Kt: Kf = 1 + q(Kt − 1), where q is the notch sensitivity (0 to 1). Ductile materials have lower q for large radii.
• Under static loading of ductile materials, stress concentration is less critical because local yielding redistributes the stress. Under cyclic loading, it is critical.
• The Kt chart curve for each geometry is a polynomial fit from Peterson’s data. Verify your hand-calculated Kt against the simulator’s curve.
• Try all 8 geometries and compare Kt values at similar dimension ratios to understand which configurations produce the highest stress concentrations.
• Use σ_max = Kt × σ_nom as your starting point, then apply safety factors appropriate to your loading type (static vs. fatigue).