Shaft Stress Concentration Factor Calculator

Calculator

Unit system *

Stress output: MPa (metric) or psi (imperial).

Loading case *

Kt for normal stress; Kts for shear stress.

Notch sensitivity q (0–1) *

Used for fatigue factors: Kf = 1 + q(K - 1).

Large diameter D *

mm

Should satisfy 1.01 <= D/d <= 3.0.

Small diameter d *

mm

Fillet radius r *

mm

Recommended 0.002 <= r/d <= 0.30.

Axial force F *

Ignored if axial is not selected.

Bending moment M *

Nominal: sigma_nom = 32M/(pi d^3).

Torque T *

Nominal: tau_nom = 16T/(pi d^3).

Tip: For fatigue, use q < 1 to model notch sensitivity.

Example Data Table

Scenario	D	d	r	D/d	r/d	Kt (bend)	Kt (axial)	Kts (torsion)	Key output (metric)
Combined	50 mm	40 mm	2 mm	1.250	0.050	2.298	2.743	1.621	sigma_max(total)=226.5 MPa, von Mises=236.2 MPa
Bending only	60 mm	40 mm	1 mm	1.500	0.025	2.997	—	—	sigma_max(bend)=166.9 MPa
Torsion only	80 mm	40 mm	6 mm	2.000	0.150	—	—	1.289	tau_max=43.1 MPa

Example outputs are generated using the same built-in curve-fit equations.

Formula Used

D/d = large-to-small diameter ratio.
r/d = fillet radius ratio.
K = A + B·(r/d)^-C (coefficients depend on loading and D/d).
Nominal stresses (solid round shaft, based on d):

Bending

sigma_nom = 32M / (pi d^3)

sigma_max = Kt · sigma_nom

Axial

sigma_nom = 4F / (pi d^2)

sigma_max = Kt · sigma_nom

Torsion

tau_nom = 16T / (pi d^3)

tau_max = Kts · tau_nom

The curve-fit coefficients are tabulated for 1.01 <= D/d <= 3.0, split at r/d = 0.05. Interpolation is applied between tabulated D/d values.

How to Use This Calculator

Select your unit system and the loading case.
Enter D, d, and r for the stepped shaft fillet.
Provide the relevant loads: F, M, and/or T.
Set q (0–1) if you also want fatigue factors Kf.
Click Calculate. Results appear above the form.
Use Download CSV or Download PDF for documentation.

Practical Notes on Shaft Stress Concentration

1) What the factor represents

Stress concentration factor (Kt or Kts) scales nominal stress to peak stress near a geometric discontinuity. In a stepped shaft, the shoulder and fillet radius amplify stress locally. This tool estimates that amplification for bending, axial loading, and torsion using calibrated curve-fit coefficients.

2) Geometry inputs that drive the result

Two ratios control the model: D/d (step severity) and r/d (fillet softness). The built-in tables cover 1.01 to 3.0 for D/d and recommend 0.002 to 0.30 for r/d. Small radii and large steps typically raise the factor quickly.

3) Typical ranges you can expect

For a moderate step (D/d about 1.5) and a small fillet (r/d about 0.02), the curve fits produce bending Kt near 3.21 and torsion Kts near 2.09. Increasing the fillet to r/d = 0.10 can reduce them to roughly 1.80 and 1.38.

4) Why bending often governs

Bending produces a linear stress distribution across the section, so the highly stressed surface at the shoulder is the first to benefit from a larger fillet radius. For example, at D/d = 2.0 and r/d = 0.05, bending Kt is about 2.34, while torsion Kts is about 1.64 in the same geometry.

5) Nominal stress matters as much as K

Even a high K may be acceptable if nominal stress is low. This calculator reports both: nominal stress from classic solid-round formulas and maximum stress after applying Kt or Kts. It also shows a conservative combined result and a von Mises estimate when you select the combined loading case.

6) Fatigue use: Kf and notch sensitivity

For fatigue, the effective factor is often Kf rather than Kt. The relation Kf = 1 + q(Kt − 1) uses notch sensitivity q between 0 and 1. With q = 0.6 and Kt = 2.34, the effective Kf becomes 1.80, reducing peak alternating stress predictions.

7) Staying inside valid limits

The tool warns when ratios fall outside recommended ranges. Values below D/d = 1.01 or above 3.0 and extremely small or very large r/d can shift the behavior away from the fitted curves. If you must operate outside these ranges, validate using a detailed chart source or finite element analysis.

8) Reporting and verification

Use the CSV download for quick traceability in spreadsheets, and the PDF export for design reviews. Keep a record of geometry ratios, the selected loading case, and the computed peak stresses. A simple sanity check is to increase r and confirm K decreases, which should occur for a shoulder fillet.

FAQs

1) What shaft shape does this calculator assume?

It assumes a stepped, solid, round shaft with a shoulder fillet radius r transitioning from diameter d to D.

2) What is the difference between Kt and Kts?

Kt applies to normal stress (bending and axial). Kts applies to shear stress in torsion.

3) Why does the tool ask for D/d and r/d limits?

The curve-fit coefficients are calibrated for specific ranges. Staying within the recommended D/d and r/d limits keeps results closer to the intended accuracy.

4) How should I pick notch sensitivity q?

Use q near 1 for larger parts or brittle materials, and lower values for small radii, ductile materials, or when micro-scale effects reduce sensitivity. When unsure, run a range (0.5 to 1.0).

5) Does the combined case add stresses correctly?

It uses conservative superposition for normal components and then computes a von Mises estimate using the combined normal stress and torsional shear. For detailed fatigue or multiaxial loading, use a dedicated method.

6) Can I use this for hollow shafts?

The nominal stress formulas shown are for solid circular sections based on d. For hollow shafts, compute nominal stresses using the correct section properties and then apply the same K factors cautiously.

7) Why do my factors look high for tiny radii?

When r/d becomes very small, the shoulder behaves like a sharp notch and stress intensifies rapidly. Increasing r is usually the most effective way to reduce Kt and Kts.