Shaft Design Calculator
Design and analyze mechanical shafts with confidence. This calculator covers combined torsion and bending loads, fatigue analysis, critical speed, and angular twist — all following Shigley's MED and ASME B106.1M standards. Choose your failure theory, input your loads and material, and instantly get minimum diameter, safety factors, stress breakdowns, and standard size recommendations. Supports both metric and imperial units.
Shaft Design Calculator
Torque • Diameter • Combined Loading • Safety Factor • Power Transmission
where \(T\) = torque [N·m], \(c = d/2\) = outer radius, \(J = \pi d^4 / 32\) = polar second moment of area.
where \(I = \pi d^4/64\) = second moment of area, \(c = d/2\).
Use when horizontal and vertical bending moment components are known separately.
\(K_m\) = bending shock factor, \(K_t\) = torsion shock factor (see ASME B106.1M Table).
Recommended safety factors: \(n = 1.5\)–\(2.0\) steady load; \(n = 2.0\)–\(3.0\) dynamic; \(n \ge 3.0\) shock/impact.
Unmodified: \(S_e' = 0.5 S_{ut}\) (steel, \(S_{ut} \le 1400\) MPa). Factors: \(k_a\) = surface, \(k_b\) = size, \(k_c\) = reliability, \(k_d\) = temperature, \(k_e\) = miscellaneous.
Operating speed should be < 75% of \(N_{cr}\) (or >125%) to avoid resonance.
| Nominal Dia. (mm) | Tolerance h6 (mm) | Keyway Width (mm) | Keyway Depth (mm) | Common Application |
|---|---|---|---|---|
| 20 | −0.013 | 6 | 3.5 | Small motors, fans |
| 25 | −0.013 | 8 | 4.0 | Light gearboxes |
| 30 | −0.016 | 8 | 4.0 | Pumps |
| 35 | −0.016 | 10 | 5.0 | Compressors |
| 40 | −0.016 | 12 | 5.0 | Medium motors |
| 45 | −0.016 | 14 | 5.5 | Gearboxes |
| 50 | −0.016 | 14 | 5.5 | Industrial drives |
| 55 | −0.019 | 16 | 6.0 | Heavy gearboxes |
| 60 | −0.019 | 18 | 7.0 | Large pumps |
| 70 | −0.019 | 20 | 7.5 | Industrial fans |
| 80 | −0.019 | 22 | 9.0 | Turbines |
| 90 | −0.022 | 25 | 9.0 | Heavy machinery |
| 100 | −0.022 | 28 | 11.0 | Steel mill drives |
| 110 | −0.022 | 28 | 11.0 | Mining equipment |
| 120 | −0.025 | 32 | 11.0 | Heavy industrial |
| Load Type | Kᵐ (Bending) | Kₜ (Torsion) |
|---|---|---|
| Gradually applied, steady | 1.5 | 1.0 |
| Gradually applied, reversing | 1.5 | 1.0 |
| Minor shocks (light impact) | 2.0 | 1.5 |
| Heavy shocks | 3.0 | 2.0 |
| Feature | Kᵐ (bending) | Kₜₜ (torsion) | Remarks |
|---|---|---|---|
| No feature (plain shaft) | 1.0 | 1.0 | — |
| Keyway — end-milled | 1.6 | 1.4–1.6 | AGMA / Shigley Ch.7 |
| Keyway — sled-runner | 1.3 | 1.2 | Less severe |
| Shoulder fillet, sharp (r/d=0.02) | 2.5–3.0 | 2.0–2.5 | Avoid if possible |
| Shoulder fillet, generous (r/d=0.1) | 1.3–1.5 | 1.2–1.4 | Preferred design |
| Retaining ring groove | 2.0 | 1.8 | — |
| Transverse through-hole | 2.4 | 2.0 | — |
| Press / shrink fit | 2.0 | 1.8 | No fretting |
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Shaft Design Calculator
Complete User Guide & Formula Reference
A step-by-step walkthrough covering every input field, every output result, and every formula used — from allowable stress to fatigue life, torsional twist, and critical speed. Metric & Imperial units supported.
What This Calculator Does — Overview
This shaft design calculator is a multi-module mechanical engineering tool that determines the minimum safe shaft diameter for rotating shafts subjected to torsion, bending, and axial loading. It covers static strength design (using Von Mises, Tresca, and ASME equivalent-torque methods), fatigue life analysis (Goodman, Soderberg, and ASME Elliptic criteria), torsional twist, lateral deflection, and critical speed prediction.
Fig. 1 — Simply-supported shaft with applied torque T (twisting), bending moment M (transverse load), bearing reactions R_A & R_B, shaft diameter d, and span length L. The critical section (yellow dashed box) is where combined stresses are maximum.
The calculator is organised into five tabs: Design (minimum diameter), Power & Torque (P–T–N conversion), Fatigue (endurance limit & infinite-life check), Advanced (deflection, twist, critical speed), and Formulas (reference equations).
Choosing Your Unit System — Metric vs Imperial
Toggle between Metric (SI) and Imperial (US) using the unit buttons at the top of the calculator before entering any values. All labels and output units switch automatically.
| Quantity | Metric (SI) Unit | Imperial (US) Unit | Conversion Factor |
|---|---|---|---|
| Torque / Moment | N·m | lb·ft | 1 lb·ft = 1.3558 N·m |
| Stress / Strength | MPa (N/mm²) | psi | 1 MPa = 145.04 psi |
| Elastic Modulus | GPa | Mpsi (×10⁶ psi) | 1 GPa = 0.1450 Mpsi |
| Diameter / Length | mm | in | 1 in = 25.4 mm |
| Force | N | lbf | 1 lbf = 4.4482 N |
| Power | kW | hp | 1 hp = 0.7457 kW |
Set your unit system first. If you switch units after entering values, the numbers in the input fields do NOT auto-convert — you must re-enter them in the new unit. Always select Metric or Imperial before typing any inputs.
Input Fields Explained — Design Tab
Loading Inputs
| Field | Symbol | Units (SI) | Description & How to Obtain It | Typical Range |
|---|---|---|---|---|
| Torque | T | N·m | Torsional (twisting) moment transmitted by the shaft. Use P&T tab to compute from power & RPM if unknown. | 50 – 5000 N·m |
| Bending Moment | M | N·m | Total resultant bending moment. If loads act in two planes, enter the horizontal (Mh) and vertical (Mv) components separately; the calculator computes M = √(Mh² + Mv²) automatically. | 0 – 2000 N·m |
| Axial Force | Fa | N | Compressive or tensile force along the shaft axis (e.g. thrust from a helical gear or propeller). Enter 0 if none. | 0 – 50 000 N |
| Speed | N | RPM | Shaft rotational speed. Used for power calculation and critical-speed ratio. | 100 – 10 000 RPM |
| Shaft Length | L | mm | Distance between bearing supports (bearing span). Used for critical speed and deflection. | 100 – 3000 mm |
Material Properties
| Field | Symbol | Units | Description |
|---|---|---|---|
| Yield Strength | Sy | MPa | The stress at which the material begins to deform plastically. Select a preset material to auto-fill. |
| Ultimate Tensile Strength | Sut | MPa | The maximum stress the material can withstand before fracture. Required for Goodman & endurance calculations. |
| Elastic Modulus | E | GPa | Young's modulus — stiffness in tension/bending. Steel ≈ 207 GPa, Aluminium ≈ 69 GPa, Titanium ≈ 114 GPa. |
| Shear Modulus | G | GPa | Stiffness in torsion (shear). Steel ≈ 80 GPa. Used in torsional twist formula. |
Design Parameters
| Field | Description | Recommended Values |
|---|---|---|
| Safety Factor (n) | Overall design safety factor applied to allowable stress. Divides the material strength to give a design stress. Higher n → larger, safer shaft. | 1.5 (light duty) · 2.0 (general) · 3.0+ (heavy/shock loading) |
| Calculation Mode | Select the loading scenario: Combined (bending + torsion), Torsion Only, or Fully Reversed Bending. | Use Combined for most industrial shafts. |
| Failure Theory | The mathematical theory used to combine stresses and predict failure. See Section 4 for formulas. | Von Mises for ductile steel; ASME for standardised design. |
| Shaft Type | Solid or hollow cross-section. | Solid for simplicity; hollow saves weight (use ratio k = d_i/d_o). |
| Stress Concentration (Kf) | Factor accounting for local stress raisers such as keyways, shoulders, grooves. Defaults provided per feature type. | None = 1.0; Sled keyway = 1.3; End-mill keyway = 1.6; Sharp shoulder = 2.5 |
| Allowable Shear Stress (τ_allow) | Optional override. If left as 0, the calculator uses the formula: τ_allow = min(0.30 × Sy, 0.18 × Sut) — the ASME code default. | Leave blank (0) to use the ASME default. |
Tip — Use the Preset Materials: Selecting a material from the dropdown (e.g. AISI 1045, 4140, 6061-T6) auto-fills Sy, Sut, E, and G — and displays the endurance limit estimate. Only use "Custom" when you have measured data from a material certificate.
Design Tab — Diameter Calculation Formulas
The core calculation determines the minimum shaft diameter that keeps stresses below the design limit. The method used depends on your selected Failure Theory. Below are all six formulas the calculator employs, with full variable definitions.
Step 1 — Compute Allowable Design Stress
Before solving for diameter, the allowable shear and normal stresses are established. The ASME B106.1M approach limits shear stress to the lesser of:
Sy = yield strength [MPa]
Sut = ultimate tensile strength [MPa]
The design shear stress used in diameter solving = τ_allow ÷ n (safety factor applied separately)
Step 2 — Resultant Bending Moment from Two Planes
Mh = bending moment in horizontal plane [N·m]
Mv = bending moment in vertical plane [N·m]
If only a single M is entered, that value is used directly.
Step 3 — Solve for Minimum Diameter (choose theory)
σ_allow = Sy ÷ n [Pa] (normal stress allowable)
Km = shock/service factor for bending moment (1.0–3.0)
Kt = shock/service factor for torsion (1.0–3.0)
Kf = fatigue stress concentration factor (1.0–3.0)
M = bending moment [N·m]
T = torque [N·m]
τ_design = τ_allow ÷ n [Pa] (design shear stress)
All other symbols as above.
Tresca is slightly more conservative than Von Mises (≈15% larger diameter).
Use this mode when no bending moment exists (e.g. a drive coupling stub shaft).
Se' = 0.5·Sut (for Sut ≤ 1400 MPa, capped at 700 MPa)
ka = surface finish factor
kb = size factor (auto-computed from d)
kc = reliability factor
Kfs = torsion fatigue stress concentration factor (≈ Kf)
DE-Goodman uses Sut as the mean-stress limit → less conservative than Soderberg.
Step 4 — Verify Stresses at Calculated Diameter
Once d is known, the actual stresses are computed to confirm the design and calculate the true safety factor.
Step 5 — Actual Safety Factor
A result below target n triggers a red FAILURE RISK warning.
Section Properties — Reported in Results
| Property | Formula | Unit | Purpose |
|---|---|---|---|
| Polar Moment of Inertia (J) | J = πd⁴ / 32 | mm⁴ | Resistance to torsion |
| Second Moment of Area (I) | I = πd⁴ / 64 | mm⁴ | Resistance to bending |
| Polar Section Modulus (Zp) | Zp = J / (d/2) = πd³/16 | mm³ | Torque capacity per unit stress |
| Section Modulus (Z) | Z = I / (d/2) = πd³/32 | mm³ | Bending capacity per unit stress |
Power & Torque Tab — P–T–N Relationship Formulas
Use this tab to convert between power (kW or hp), torque (N·m or lb·ft), and rotational speed (RPM). You can enter any two values and solve for the third. The calculated torque can be sent directly to the Design tab with one click.
T = torque [N·m]
ω = angular velocity [rad/s]
N = rotational speed [RPM]
Imperial shortcut: T [lb·ft] = 5252 × P[hp] / N[RPM]
Important for journal bearings and seal selection.
Gear ratio input: Enter the gear ratio (output speed / input speed) to see the output shaft speed. This does NOT automatically recalculate the transmitted torque — torque scales inversely with speed and is reduced by efficiency. Calculate each shaft separately.
Fatigue Analysis Tab — Endurance Limit & Infinite-Life Criteria
Fatigue failure occurs at stress levels far below the static yield strength after many load cycles. The Fatigue tab assesses whether a shaft of known diameter will survive indefinitely (infinite life) under fluctuating (mean + alternating) loads using three internationally recognised criteria.
Marin Equation — Modified Endurance Limit (Se)
Se' = rotating-beam specimen endurance limit
ka = surface condition factor (entered by user, or select from finish type)
kb = size factor — auto-computed:
kb = 1.24 × d^(−0.107) for 2.79 ≤ d ≤ 51 mm (Shigley's)
kb = 1.51 × d^(−0.157) for 51 < d ≤ 254 mm
kc = reliability/loading factor (0.814 at 99.9% reliability)
Alternating & Mean Von Mises Stresses
Mm = mean bending moment [N·m]
Ta = alternating torque [N·m]
Tm = mean torque [N·m]
Kf = fatigue stress concentration for bending
Kfs = fatigue stress concentration for torsion (≈ Kf for simplicity)
Fatigue Failure Criteria — Three Theories Compared
Uses ultimate strength Sut as the mean-stress limit.
Equation of a straight line from Se on the alternating axis to Sut on the mean axis (Goodman line).
Soderberg is always more conservative than Goodman. Rarely used in practice but specified by some government/defence standards.
Generally gives slightly higher nf than Goodman for the same loading.
If ny < 1.0, the shaft yields before any fatigue consideration.
Reading the Goodman Diagram: The operating point (red star) represents your actual (mean, alternating) stress state. If the point lies below and left of the Goodman line, the design is safe for infinite life. If it is above the Goodman line but below the Langer line, the shaft will fail by fatigue before yielding. If it is above the Langer line, first-cycle yielding is predicted.
Advanced Tab — Torsional Twist, Deflection & Critical Speed
Torsional Twist Angle
T = applied torque [N·m]
L = shaft length [m]
G = shear modulus [Pa]
J = polar moment of inertia [m⁴]
Limit: Most design codes recommend < 0.25°/m (0.3°/ft) for general machinery. Precision machine tool spindles require < 0.05°/m.
Lateral (Bending) Deflection — Simply Supported, Central Load
F = transverse (radial) force at mid-span [N]
L = bearing span [m]
E = elastic modulus [Pa]
I = second moment of area [m⁴]
Rule of thumb: δ should not exceed L/1000 for most rotating machinery. Gear and coupling misalignment can cause problems above L/2000.
Critical Speed (Rayleigh–Ritz Method)
δ = static deflection at mass centre [m]
This is the Rayleigh approximation for a single-mass simply-supported shaft.
Design rule: Operating speed N_op must be either:
N_op < 0.75 × N_cr (run below critical — most shafts), OR
N_op > 1.25 × N_cr (run above critical — turbine shafts, flexible couplings required)
Critical Speed Warning: If the speed ratio N_op/N_cr falls between 75% and 125%, the calculator shows a red resonance alert. Operating near critical speed causes catastrophic shaft whirl and bearing failure within seconds. Always design with at least 25% margin from the first critical speed.
Stiffness Properties
Understanding Your Results — Complete Output Reference
-
Overall Status Indicator — SAFE / NEAR LIMIT / FAILURE RISK
The coloured banner at the top of results shows the design status based on the utilisation ratio (σ_eq / Sy). ✓ SAFE = utilisation < 67%. ⚠ NEAR LIMIT = 67–90%. ✗ FAILURE RISK = > 90%. The stress gauge bar shows the utilisation percentage visually.
-
Minimum Required Diameter (d_min)
The theoretically smallest diameter that satisfies the selected failure criterion at the design safety factor. Do not use this raw value for procurement — always round up to the next standard size shown below it.
-
Next Standard Size / Recommended Size
The nearest commercially available shaft size that equals or exceeds d_min. The standard size table below the cards shows the safety factor achievable at each candidate size — including one size below (marked "Undersized") and three sizes above.
-
Actual Safety Factor (n_actual)
Computed as Sy ÷ σ_eq (Von Mises). This is the margin your shaft has at the calculated minimum diameter. When you step up to a standard size, the actual safety factor will be larger. The Tresca safety factor is also reported (slightly lower, more conservative).
-
Twist per Metre (°/m) — Torsional Rigidity Check
Checks the angular twist rate. Values below 0.25°/m are highlighted green. Values above 0.25°/m are highlighted amber — consider a larger diameter or a higher-G material (e.g. upgrade from aluminium to steel).
-
Maximum Transmissible Torque (T_max)
The maximum torque this shaft can carry at the design allowable stress. Useful for checking sudden overload scenarios. Computed as: T_max = τ_design × J / r = τ_design × Zp.
-
Power Transmitted (kW / hp)
Back-calculated from T and ω. Confirms the power rating of your drive system. If this differs from your motor nameplate, check that your torque input is correct.
Common Mistakes & Input Validation Tips
Mistake 1 — Wrong units for torque.
If using metric, torque must be in N·m, NOT N·mm or kN·m.
Converting: 1 N·mm = 0.001 N·m | 1 kN·m = 1000 N·m.
A torque of 500 000 N·mm should be entered as 500 N·m.
Mistake 2 — Elastic modulus entered as MPa instead of GPa.
The E and G fields expect GPa (metric) or Mpsi (imperial).
For steel: E = 207 GPa (not 207 000 MPa). If you accidentally type 207000,
deflections will be 1000× too small and critical speed will be 31× too high.
Mistake 3 — Not entering bending moment when loads act in two planes. Use the Mh and Mv fields if your shaft has gear forces or belt pulls acting in different planes. Entering only one component will under-predict the resultant M and give an unsafe result.
Mistake 4 — Using Kf = 1.0 (none) when a keyway is present. Keyways are severe stress raisers — a standard end-mill keyway has Kf ≈ 1.6 at the runout. Always select the appropriate stress concentration from the dropdown. Using Kf = 1.0 for a keyed shaft can result in premature failure at 62% of the predicted load.
Mistake 5 — Setting safety factor n = 1.0 for a "perfectly known" load. Even with precise load data, a minimum of n = 1.5 is recommended to account for material variability, manufacturing tolerances, and load variations. Use n = 2.0 as a starting point for general industrial shafts.
Reminder — Pure Torsion mode ignores bending. The "Torsion Only" calculation mode sets M = 0. If your shaft is also being bent by gear reactions, belt tensions, or its own weight, switch to "Combined" mode and enter the appropriate bending moment. A shaft that appears safe under pure torsion may fail when bending is included.
Quick Sanity Check: After calculating, compare the Power result to your motor rating. If the calculated power is significantly higher or lower than expected, your torque or speed input is likely incorrect. P = 9.55 × T[N·m] × N[RPM] ÷ 1000 [kW] is a reliable back-of-envelope check.
Valid Input Ranges — Metric (SI)
| Input | Min Valid | Max Valid | Warning if Outside Range |
|---|---|---|---|
| Torque T | 0 N·m | 500 000 N·m | Negative torque not physical; enter magnitude only |
| Bending Moment M | 0 N·m | 500 000 N·m | If M > 10× T, check units — moments are often confused |
| Yield Strength Sy | 100 MPa | 2500 MPa | Values >2000 MPa are rare special alloys — verify source |
| Safety Factor n | 1.0 | 10.0 | n < 1.25 is considered reckless; n > 5 suggests over-engineering |
| Speed N | 1 RPM | 100 000 RPM | Ensure critical speed is evaluated at high speeds |
| Hollow ratio k | 0.0 | 0.90 | k > 0.85 gives very thin walls — check buckling separately |
| Reliability factor kc | 0.62 (99.9999%) | 1.0 (50%) | 0.814 = 99% reliability; 0.868 = 95% (default) |
Accuracy Statement & Limitations
About the Accuracy of This Calculator
All formulas in this calculator are implemented directly from Shigley's Mechanical Engineering Design, 10th Edition (Budynas & Nisbett) and ASME Standard B106.1M. Calculations follow accepted analytical methods used in industry and university-level mechanical design courses worldwide.
The following simplifications are made:
- The critical speed formula uses the Rayleigh single-mass approximation; multi-mass systems require Dunkerley's method or FEA.
- Lateral deflection assumes a simply-supported shaft with a single central point load; distributed loads (shaft weight) and off-centre loads require beam superposition or FEA.
- Fatigue Marin factors (ka, kc) must be selected by the user — incorrect surface or reliability factors will alter Se by up to ±40%.
- Stress concentration factors are typical values. Actual Kf depends on the notch radius-to-diameter ratio and must be confirmed from notch sensitivity charts (Shigley's Fig. 6-20) for critical designs.
- This tool does not account for combined variable-amplitude loading, fretting fatigue, corrosion fatigue, or thermal effects.
Recommended use: This calculator is suitable for preliminary sizing, design exploration, and educational purposes. For final production designs, validate critical results with Finite Element Analysis (FEA) and/or physical proof testing in accordance with relevant industry standards. The authors assume no liability for design decisions made solely on the basis of this tool.
Frequently Asked Questions (FAQ)
Von Mises (Distortion Energy) is the most accurate theory for ductile materials and is recommended for general steel and aluminium shaft design. It has been validated extensively against experimental data and typically predicts failure within 5% of test results.
Tresca (Maximum Shear Stress) is slightly more conservative (predicts ≈15% lower capacity) and is preferred when additional safety margin is desired or when the loading conditions are uncertain.
ASME B106.1M uses the equivalent torque method with shock service factors Km and Kt. It is the right choice when designing to a contractual ASME standard or when your shock/service factors are specified by a code.
For fatigue-critical applications (fluctuating loads, high-cycle operation), switch to DE-Goodman instead.
Both criteria assess infinite fatigue life under combined alternating and mean stresses. The difference is the limit used for mean stress:
Goodman: uses Sut (ultimate strength) as the mean-stress limit. Less conservative. The standard recommendation for most commercial machinery.
Soderberg: uses Sy (yield strength) as the mean-stress limit. More conservative — it guarantees no yielding AND no fatigue in a single criterion. Required by some military and pressure-vessel codes.
In practice, if Goodman gives nf = 2.0 and Soderberg gives nf = 1.7 for the same shaft, both indicate a safe design. Only choose Soderberg when a specific standard mandates it, as it often leads to unnecessarily heavy shafts.
For a simply-supported shaft with a single central load F over span L:
M_max = F × L / 4
For a single off-centre load at distance 'a' from the left bearing (b = L − a):
M_max = F × a × b / L
For a shaft with an overhang carrying a load F at distance 'a' beyond the bearing:
M_max = F × a
For gear forces, resolve the tangential force Wt and radial force Wr into their respective planes. Compute Mh and Mv at the critical section, then enter both into the Mh and Mv fields — the calculator will compute M = √(Mh² + Mv²) automatically.
A very small result usually means one of the following:
1. Torque is very low — check that your T is in N·m, not N·mm. A torque of 5 N·mm = 0.005 N·m would give a tiny shaft.
2. Material strength is very high — premium alloys like 17-4 PH (Sy ≈ 1170 MPa) will yield much smaller diameters than low-carbon steel. This is correct, but check that your material selection is realistic for your application.
3. Safety factor too low — n = 1.0 effectively means the shaft is right at the limit. Increase n to 1.5 or 2.0.
Also note: the calculated minimum diameter does not account for practical constraints like bearing bore sizes, coupling specifications, or key/spline standards — these often govern the final size in practice.
1. Go to the Power & Torque tab and enter the motor rated power (e.g. 15 kW) and speed (e.g. 1450 RPM).
2. Click Calculate. The torque result (e.g. 98.8 N·m) will appear.
3. Click Send to Design Tab. The torque is automatically transferred to the Design tab's torque field.
4. Add the bending moment and other parameters, then run the Design calculation.
Note: if there is a gearbox, work out the output shaft torque separately. Output torque = Input torque × gear ratio × efficiency. Design each shaft independently for its own load.
Km (bending moment shock factor) and Kt (torsion shock factor) are service/shock multipliers from ASME B106.1M that account for dynamic overloads beyond the steady design load:
Km = 1.0–1.5: Gradually applied loads (smooth conveyors, fans)
Km = 1.5–2.0: Suddenly applied loads, minor shocks (pumps, compressors)
Km = 2.0–3.0: Heavy shocks, reversing loads (punch presses, rock crushers)
The same classification applies to Kt. Both factors are multiplied directly into the equivalent moment/torque before the diameter formula is applied — they effectively increase the apparent loading to cover dynamic conditions without performing a full dynamic analysis.
Yes — select "Hollow" from the shaft type dropdown and enter the wall ratio k = d_inner / d_outer (0 to 0.9). The polar moment J is replaced by J_hollow = (πd_o⁴/32)(1 − k⁴).
When to use hollow shafts:
• Weight reduction is critical (aerospace, automotive, robotics)
• A passage through the shaft is needed (hydraulic flow, instrumentation cables)
• k = 0.5–0.7 saves 25–50% weight with only 7–25% reduction in torsional strength
Caution: Thin-walled shafts (k > 0.85) are susceptible to torsional buckling — this calculator does not check for buckling. Separately verify using shell buckling criteria if k > 0.7.
Use the Hollow Shaft Optimizer in the Advanced tab to compare weight savings across different k values for a given solid shaft equivalent.
The Goodman diagram plots alternating stress (σ_a) on the Y axis vs mean stress (σ_m) on the X axis. Three boundary lines are shown:
Goodman Line (blue): From (0, Se) to (Sut, 0). The infinite-life boundary for the Goodman criterion. Points below and left = safe for infinite life.
Soderberg Line (green dashed): From (0, Se) to (Sy, 0). More conservative infinite-life boundary.
Langer Line (orange dashed): From (0, Sy) to (Sy, 0). First-cycle yield boundary. Points above this line yield immediately.
The red star is your operating point (σ_m_vm, σ_a_vm). Aim to keep it well below and left of the Goodman line. The farther it is from the line, the larger your fatigue safety factor (nf). If the star is close to the Goodman line, increase shaft diameter or choose a higher-endurance material.
