EAS4200 Aerospace Structures, Lecture 18, 2026 fall

Overview

Ting Dong explains how notch sensitivity connects theoretical stress concentration, Kt, to fatigue stress concentration, Kf, using q = (Kf − 1)/(Kt − 1). The lecture applies the method to a fully reversed bending problem for a steel shaft, showing how geometry, material strength, unit consistency, and the S–N curve enter a fatigue-life estimate.

Key takeaways

Notch sensitivity converts static geometry effects into a fatigue factor through q = (Kf − 1)/(Kt − 1), with q constrained between 0 and 1.
The fatigue factor is Kf = 1 + q(Kt − 1); therefore, Kf must lie between 1 and Kt for a valid notch-sensitivity value.
Notches include more than holes: grooves, fillets, abrupt cross-section changes, and structural discontinuities all require attention to their local radius.
The empirical √a polynomial requires strength in ksi, while √a carries square-root-of-length units; mixing units can invalidate the calculation.
For the steel shaft example, the 38 mm-to-32 mm diameter ratio is about 1.19, the chart estimate is Kt ≈ 1.65, and the resulting fatigue factor is about Kf ≈ 1.55.
A supplied fully corrected endurance limit represents the actual structure’s conditions, including size, surface, temperature, and loading effects; the simplified endurance-limit model is more appropriate for steel than aluminum.

Chapters

0:00 Notch Sensitivity Relates Static and Fatigue Stress Concentration

Theoretical stress concentration factors describe geometric effects under static loading, while fatigue factors are generally lower.
For normal stress, q = (Kf − 1)/(Kt − 1); the same relationship applies to shear using the corresponding shear factors.
The notch sensitivity index q ranges from 0 to 1.

5:00 The Meaning of q = 0 and q = 1

At q = 0, Kf = 1, so the material is insensitive to the notch in fatigue even though the geometry may have a static stress concentration.
At q = 1, Kf = Kt, representing full notch sensitivity.
Most practical fatigue cases fall between these limits, with Kf below Kt.

7:00 Empirical Notch Sensitivity Depends on Radius and Material

An experimentally fitted equation estimates q from the notch radius and a material parameter √a.
The value of a depends on material strength and loading mode, including bending, axial loading, or torsion.
The polynomial fit is empirical rather than a direct physical law; Ting Dong notes that the required equation will be supplied on quizzes and exams.

10:00 Holes, Grooves, and Abrupt Geometry Changes Count as Notches

Fastener holes, grooves, fillets, abrupt cross-section changes, and other structural discontinuities can act as notches.
Use the local radius of the feature that creates the stress concentration when evaluating notch sensitivity.
A geometry change that concentrates stress under static loading also creates a stress concentration relevant to fatigue.

12:00 Convert q into Fatigue Stress Concentration Factors

Once q is known, calculate the normal-stress fatigue factor with Kf = 1 + q(Kt − 1).
For shear, use the corresponding equation with the theoretical and fatigue shear stress concentration factors.
The empirical √a polynomial for torsion differs from the bending or axial form, and the strength input must use ksi as specified by the fit.

15:00 Steel Shaft Example and Corrected Endurance Limit

The worked problem concerns a steel shaft in fully reversed bending, with shoulder diameters of 38 mm and 32 mm.
The problem supplies a nominal stress and a fully corrected endurance limit for the actual structure.
A corrected endurance limit accounts for differences from standardized laboratory specimens, such as size, surface finish, temperature, and loading; it should not be recalculated as half the ultimate strength once supplied.
The lecture notes that the simplified horizontal endurance-limit model is useful for steel but does not strictly describe aluminum, which lacks a true endurance limit.

25:00 Read Kt from Shaft Geometry Before Estimating Life

The fatigue-life workflow begins by finding theoretical Kt from a chart using the large-to-small diameter ratio and fillet-radius-to-small-diameter ratio.
For the 38 mm and 32 mm shaft sections, the diameter ratio is approximately 1.19.
Chart readings are estimates; Ting Dong gives an example Kt of about 1.65 and says a reasonable nearby reading is acceptable.

31:00 Calculate √a and q with Consistent Units

For the bending example, use the bending-specific empirical expression with the material ultimate strength, given as 100 ksi.
The polynomial fit was developed using strength in ksi, so convert strength before applying it.
The notch sensitivity q is dimensionless, while √a has units of the square root of length and must match the radius units used in the equation.
Ting Dong emphasizes that engineers must track units consistently across hand calculations and simulation software.

39:00 Apply Kf to Nominal Stress and the S–N Curve

The example combines the estimated q with Kt ≈ 1.65 to obtain a fatigue stress concentration factor of approximately Kf = 1.55.
A valid result should not exceed Kt when q lies between 0 and 1.
Multiply the nominal fully reversed stress by Kf to obtain the stress used in the fatigue-life calculation.
Use the S–N relation for fully reversed loading, together with its constants and the applicable endurance limit, to estimate cycles to failure.

45:00 Exam Guidance and Clarifications on the Example

Ting Dong says students do not need to memorize the stress-concentration chart because it will be provided for the exam.
The preceding calculations mainly determine the dimensionless Kf, so subsequent fatigue calculations can use a consistent stress unit such as MPa or ksi.
A closing question clarifies that the bending example uses normal stress as its nominal stress.

Summary, takeaways, and chapters were generated by AI from the video's transcript and may contain errors. The video belongs to its creator, Ting Dong.