What is a stress concentration factor (Kt)?

The stress concentration factor (Kt) is the ratio of maximum local stress to the nominal stress at a geometric discontinuity. For example, a plate with a small central hole under tension has Kt = 3.0, meaning the stress at the hole edge is three times the average stress. Kt depends on geometry ratios like r/d and D/d.

How do you calculate maximum stress using Kt?

Maximum stress is calculated as sigma_max = Kt x sigma_nom, where sigma_nom is the nominal stress (P/A for tension, Mc/I for bending, Tc/J for torsion). For example, if Kt = 2.5 and sigma_nom = 100 MPa, then sigma_max = 250 MPa at the stress raiser.

How does fillet radius affect stress concentration?

Increasing the fillet radius reduces the stress concentration factor. A sharp corner (r approaches 0) creates very high Kt values, while a generous fillet (large r/d ratio) brings Kt closer to 1.0. This is why engineers specify fillet radii at shaft shoulders, keyways, and other geometric transitions.

Stress Concentration Factor (Kt) Simulator

Visualize stress concentration for 8 geometric discontinuities using Peterson's charts

Mode

Geometry

Kt 3.000

σ_nom 100.0 MPa

σ_max 300.0 MPa

Ratio d/D = 0.200

Understanding Stress Concentration Factors in Mechanical Design

Stress concentration is one of the most critical concepts in mechanical engineering design. Whenever a structural member contains a geometric discontinuity such as a hole, notch, fillet, or groove, the local stress near that feature can be many times higher than the average (nominal) stress. The ratio of this peak stress to the nominal stress is called the stress concentration factor, denoted Kt. Understanding and calculating Kt is essential for preventing fatigue failures, designing safe components, and optimizing material usage in everything from aircraft fuselages to automotive crankshafts.

Peterson's Stress Concentration Charts

The most widely used reference for stress concentration factors is Peterson's Stress Concentration Factors, first published by Rudolf Peterson in 1953. Peterson compiled experimental and analytical data for hundreds of geometric configurations, presenting them as Kt versus geometry ratio curves. For example, a flat plate with a central circular hole under uniform tension has Kt = 3.0 when the hole is infinitesimally small compared to the plate width. As the hole diameter increases relative to the plate width, Kt changes according to the polynomial Kt = 3.0 - 3.13(d/D) + 3.66(d/D)^2 - 1.53(d/D)^3. This simulator implements curve fits from Peterson's charts for 8 common geometries covering plates and round shafts under tension, bending, and torsion loads.

From Kt to Real-World Design: Notch Sensitivity and Kf

While Kt is a purely geometric factor, real materials do not always develop the full theoretical stress concentration. The fatigue stress concentration factor Kf accounts for material notch sensitivity: Kf = 1 + q(Kt - 1), where q is the notch sensitivity factor (0 to 1). Ductile materials under static loading may yield locally at the stress raiser, redistributing stress and making Kt less critical. However, under cyclic (fatigue) loading, even ductile materials are sensitive to stress concentrations, making Kt and Kf essential for fatigue life prediction. This simulator helps students visualize how geometry changes affect Kt and understand the relationship between nominal stress, maximum stress, and the geometry ratios that control stress concentration.

Who Uses This Simulator?

This stress concentration visualizer is designed for mechanical engineering students, design engineers, and technical educators. It is particularly useful in courses on strength of materials, machine design, and fatigue analysis. Students can experiment with different geometries and dimensions to build intuition about how fillet radii, hole sizes, and notch depths affect stress concentration. The practice and quiz modes reinforce calculation skills needed for professional engineering exams and real-world design work.

Explore Related Simulators

If you found this stress concentration simulator helpful, explore our Stress-Strain Diagram Trainer, Mohr's Circle Stress Analysis, Fatigue Testing Virtual Lab, and Shaft & Torsion Simulator for more hands-on practice.