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ASME B106.1M-1985 — Design of Transmission Shafting
🔧 ASME B106.1M-1985 (ANSI/ASME B106.1M) is the American National Standard for the Design of Transmission Shafting, developed by the ASME Standards Committee B106 and approved by the American National Standards Institute on May 17, 1985. It presents a fatigue-based shaft-sizing procedure for rotating steel shafts — solid or hollow — subjected to the most common loading condition of combined reversed bending and steady torsion. The body of the Standard contains six sections: 1 Scope, 2 Nomenclature, 3 Design Formulas, 4 Fatigue Modifying Factors, 5 Factor of Safety (FS), and 6 Other Considerations, supplemented by Appendix A (Theoretical Background), Appendix B (Materials and Properties), and Appendix C (Sample Problem).
💡 Since the withdrawal of the old ASA-B17C code in 1954, it has become widely recognized that most shaft failures are not caused by a lack of static strength but by progressive fatigue-crack propagation under fluctuating load. B106.1M was written to reflect that understanding with a fatigue-strength design method.
1. Scope and Design Philosophy 📌
As the Foreword explains, the earlier ASA-B17C design method was based on the static yield strength of the shaft material under combined bending and torsional loads. It proved overly conservative in some cases and incomplete in others. It is now well accepted that most shaft failures result from progressive crack propagation caused by fluctuating loads — commonly called “fatigue failure.” Accordingly, the purpose of this Standard is to provide a design method based on the fatigue strength of the shaft for the most common shaft loading condition: combined reversed bending and steady torsion.
The Standard takes into account many modern theories and has been substantiated, in part, by laboratory testing. It is not intended as a textbook; it is written for use by those skilled in the art of shaft design and stress calculations, providing a common basis for discussion and understanding among persons involved in shaft design.
⚠️ B106.1M covers only rotating steel shafts under combined reversed bending and steady torsion — the most common condition. It does not address non-steel materials, non-rotating shafts, or highly unusual load spectra; engineers should judge applicability for each case.
2. Design Formulas and the Combined-Stress Criterion 🔩
Section 3 of the Standard provides the core diameter equation. The design applies an “elliptical” combined-stress criterion: the reversed bending stress is checked against the fatigue (endurance) strength, while the steady torsional shear stress is checked against the yield strength, and the two are combined in an elliptical relationship. For a solid round shaft, the diameter d is determined from:
d³ = (32·FS / π) · √[ (kf·M / S′n)² + (kt·T / Sy)² ]
where M is the resultant bending moment; T is the transmitted torque; kf is the fatigue stress concentration factor in bending; kt is the fatigue stress concentration factor in torsion; S′n is the modified endurance limit at the shaft section; and Sy is the yield strength. Note that for torsional shear checking the shear yield strength is commonly taken as about 0.5 times the tensile yield strength; the exact treatment follows the equations in the Standard. For a hollow shaft, the solid-section modulus (π/32)·d³ must be replaced by the hollow-section expression involving (do⁴ − di⁴)/do.
💡 In practice the bending moment M is treated as the fluctuating component — each surface fiber of the rotating shaft experiences one tension–compression cycle per revolution — and the torque T as the steady component, consistent with the “reversed bending + steady torsion” assumption. If the torque itself fluctuates, use the combined-stress fatigue test data approach of Appendix A.
3. Fatigue Modifying Factors 🔬
Section 4 requires that the rotating-beam endurance limit of the material (Sf, from polished specimens at room temperature) be modified by a set of factors before use in design. The modified endurance strength is:
S′n = ka · kb · kc · kd · Sf
where ka is the surface finish factor (a function of surface condition and tensile strength, Fig. 3); kb is the size factor (Figs. 1 and 2 give recommended size-effect factors for unnotched steel shafts); kc is the reliability factor (Table 1); and kd is the temperature factor (Table 2). These are “derating” factors — ignoring any of them overestimates the fatigue strength.
| Reliability | Reliability Factor kc | Comment |
|---|---|---|
| 50% | 1.000 | Average-level requirement only |
| 90% | 0.897 | General mechanical drives |
| 95% | 0.868 | More critical shafting |
| 99% | 0.814 | Critical transmission shafts |
| 99.9% | 0.753 | Safety-sensitive applications |
| 99.99% | 0.702 | Extremely low failure rates |
| Temperature (°F, based on 70°F / 23°C) | Temperature Factor kd (typical) |
|---|---|
| 70°F and below | 1.000 |
| 200°F | 1.000 |
| 300°F | 0.99 |
| 400°F | 0.96 |
| 500°F | 0.92 |
| 600°F | 0.86 |
| 800°F | 0.72 |
| 1000°F | 0.55 |
⚠️ Do not ignore the size effect: the larger the shaft diameter, the lower the endurance limit, and kb falls well below 1. Applying a small-specimen Sf directly to a large shaft significantly overestimates fatigue strength; always apply the size factors of Figs. 1/2.
4. Stress Concentration and Keyways ⚠️
Fig. 4 of the Standard presents the notch sensitivity q; Figs. 5, 6, and 7 give stress-concentration geometries for a round shaft with a shoulder fillet in bending, a grooved round bar in bending, and a round shaft in bending with a transverse hole. The fatigue stress concentration factor kf is related to the theoretical factor kt through the notch sensitivity: kf = 1 + q·(kt − 1). Table 3 of the Standard lists typical kf values for keyways; typical engineering values are:
| Keyway Type | Bending kf (typical) | Engineering Guidance |
|---|---|---|
| Sled-runner keyway | ~1.6 | Milled with a round end; lower stress concentration — preferred |
| Standard (end-milled) keyway | ~2.0 | Common on ordinary shafting; must be accounted for |
| Profile keyway | ~2.0 and up | Highest stress concentration; avoid where possible |
| Smooth shaft without keyway (reference) | 1.0 | For comparison only |
🚨 Keyways, shoulder fillets, annular grooves, and transverse holes are the most common sites of fatigue-crack initiation on transmission shafts. Prefer sled-runner keyways, generous fillet radii at shoulders, and no sharp corners — otherwise a shaft may crack early at a stress raiser even if the computed diameter is adequate.
5. Factor of Safety and Engineering Practice 🛠️
Section 5 discusses selection of the factor of safety (FS). FS should reflect the confidence in load determination, scatter of material properties, severity of failure consequences (personnel safety, downtime losses), and ease of repair/replacement. FS ≈ 2–3 is typical for general machine shafting; use higher values when loads are uncertain or consequences are severe.
- 🔍 Design workflow: determine loads (bending moment M, torque T, and dynamic character) → select material and heat treatment → derive the modified endurance strength from Sf via ka, kb, kc, kd → establish kf at keyways/shoulders → solve for diameter → round up to a standard size and recheck.
- 🔧 Surface condition: ground/polished surfaces give ka near 1; machined surfaces about 0.8; hot-rolled surfaces as low as about 0.5. Shot peening or rolling can raise fatigue life, but the Standard conservatively does not credit such enhancement in the design value.
- 📊 Critical speeds: keep the operating speed away from critical speeds — usually below the first critical speed with margin, or in an acceptable window between criticals with acceptable dynamic response.
- 📋 Stiffness checks: fatigue strength is not the end of design; also check deflection, slope (they affect gear meshing and bearing life), and torsional twist.
- 📚 Appendix C sample problem: a complete worked example walks from the load diagram (Fig. C1) to the final shaft diameter — the best way to learn the method.
✅ Good practice: after sizing with the fatigue formula, re-evaluate the local stress at stress raisers (keyways, shoulders) using the section’s own kf and local bending moment; if the local margin is inadequate, enlarge that diameter or improve the geometry (larger fillet radius, sled-runner keyway).
6. Frequently Asked Questions ❓
❓ Q: Why does B106.1M emphasize fatigue design instead of traditional static-strength design?
A: Failure statistics and analyses show that most shaft failures are caused by progressive fatigue-crack propagation under fluctuating load, which has little to do with static yield strength. The old method (ASA-B17C) was sometimes overly conservative and sometimes incomplete; B106.1M uses fatigue strength as the basis and matches the real failure mechanism.
A: Failure statistics and analyses show that most shaft failures are caused by progressive fatigue-crack propagation under fluctuating load, which has little to do with static yield strength. The old method (ASA-B17C) was sometimes overly conservative and sometimes incomplete; B106.1M uses fatigue strength as the basis and matches the real failure mechanism.
❓ Q: What is the difference between kf (fatigue stress concentration factor) and kt (theoretical stress concentration factor)?
A: kt is a purely geometric elastic factor, while kf is the factor that actually affects fatigue life after converting through the notch sensitivity q: kf = 1 + q·(kt − 1). Brittle materials and sharp notches push q toward 1; for ductile materials and blunt notches kf is clearly smaller than kt.
A: kt is a purely geometric elastic factor, while kf is the factor that actually affects fatigue life after converting through the notch sensitivity q: kf = 1 + q·(kt − 1). Brittle materials and sharp notches push q toward 1; for ductile materials and blunt notches kf is clearly smaller than kt.
❓ Q: How do I apply the formula to a hollow shaft?
A: Replace the solid-section modulus (π/32)·d³ with the hollow expression (π/32)·(do⁴ − di⁴)/do; the fatigue modifications and stress-concentration treatment are the same. Hollow shafts give more stiffness and strength per unit weight, but beware of local buckling and keyway depth limits when the wall is thin.
A: Replace the solid-section modulus (π/32)·d³ with the hollow expression (π/32)·(do⁴ − di⁴)/do; the fatigue modifications and stress-concentration treatment are the same. Hollow shafts give more stiffness and strength per unit weight, but beware of local buckling and keyway depth limits when the wall is thin.
🔍 Q: How should the factor of safety FS be chosen?
A: Section 5 provides selection principles rather than a fixed value: the poorer the confidence in loads and material data, and the more severe the consequences of failure, the larger FS should be. FS ≈ 2–3 is common for general machine drives; increase it for impact loads, unpredictable dynamics, or safety-critical duties.
A: Section 5 provides selection principles rather than a fixed value: the poorer the confidence in loads and material data, and the more severe the consequences of failure, the larger FS should be. FS ≈ 2–3 is common for general machine drives; increase it for impact loads, unpredictable dynamics, or safety-critical duties.
