Shafts · Keyed-joint screening
Mechanical Engineering Calculators: Shaft Key Shear / Bearing Stress Calculator
Mechanical Engineering Calculators for nominal rectangular shaft-key shear stress, bearing stress, utilization, and required effective key length.
Reference calculator #028
Enter keyed-joint torque, geometry, and allowables
Inputs stay in your browser. Values are normalized to canonical units before calculation.
Calculated output
Results
- Nominal key shear stress τ
- Nominal key bearing stress σ_b
- Shear utilization τ / τ_allow
- Bearing utilization σ_b / σ_allow
- Required effective length from shear
- Required effective length from bearing
- Governing required effective length
- Available-to-required length ratio
- Effective-length margin
- Equivalent tangential force F_t
- Nominal shear area bL_e
- Nominal projected bearing area (h/2)L_e
- Governing nominal-stress mode
Nominal rectangular-key stress calculation completed
- One straight, prismatic, rectangular sunk parallel key transmits the full entered design torque between a circular shaft and one hub.
- The entered design torque is a positive magnitude and already includes every service, application, shock, fatigue, and other factor required by the user’s design method.
- Tangential force is treated as F_t = 2T/d and uniformly distributed over the nominal shear area bL_e.
- Nominal bearing stress uses projected contact area (h/2)L_e at one shaft-or-hub interface; chamfers, radii, clearance, and incomplete contact can reduce the real area.
- Effective length excludes chamfered, radiused, tapered, relieved, or otherwise non-contact portions that do not carry the assumed uniform load.
- Friction or interference-fit torque capacity is ignored, so the single key is assigned the full transmitted torque.
- Allowable shear and bearing stresses are user-established design inputs. The defaults are illustrative and do not select a key, shaft, hub, material, heat treatment, duty factor, or safety factor.
- The model excludes keyway stress concentration and fatigue in the shaft or hub, fretting, fit and tolerance effects, deformation, yielding, multiple keys, splines, axial retention, and standards or manufacturing acceptance.
Calculation engine: shaft-key-shear-bearing-stress/1.0.0
Nominal rectangular-key equations
A single rectangular sunk key transfers torque through a tangential force at the shaft radius. The calculator treats this force as uniformly distributed over one nominal shear plane and one projected bearing interface:
τ = F_t / (bL_e) = 2T / (dbL_e)
σ_b = F_t / ((h/2)L_e) = 4T / (dhL_e)
The University of Florida lecture material presents the same tangential-force, bL, and (h/2)L projected-area model. These are nominal average stresses, not local peak stresses.
| Symbol | Meaning | Canonical calculation basis |
|---|---|---|
T |
Positive design-torque magnitude | N·m, converted to N·mm in the equation |
d |
Shaft diameter at the key | mm |
b |
Rectangular key width | mm |
h |
Total rectangular key height | mm |
L_e |
Effective load-carrying key length | mm |
τ_allow |
User-established allowable nominal shear stress | Pa |
σ_allow |
User-established allowable nominal bearing stress | Pa |
The required effective lengths are calculated independently:
L_bearing = F_t / ((h/2)σ_allow)
L_required = max(L_shear, L_bearing)
Input contract
Enter a design torque that already includes every service, shock, fatigue, or application factor required by the selected design method. The engine does not derive design torque from motor nameplate power or select a factor. It uses the magnitude only and assigns the entire torque to one key; friction or interference-fit capacity is ignored.
Use the actual shaft diameter at the keyed section and the actual rectangular key width and total height. The shared geometry selector converts all four length inputs together so a mixed mm/in state cannot be created accidentally. Allowable shear and bearing stresses also share one unit selector, but they remain independent values.
Effective length and projected contact
Overall key length is not always effective length. End chamfers, rounded ends, cutter runout, relieved portions, clearance, a short hub, or incomplete seating can reduce the region that carries the assumed load. Enter only the verified load-carrying length.
The nominal bearing model uses half the total key height at one interface. This does not prove uniform contact. Shaft and hub keyseat depth, edge radius, key chamfer, tolerances, deformation, assembly, and material stiffness can shift real pressure toward local regions.
Worked example
Use the default values:
| Input | Value |
|---|---|
| Design torque | 500 N·m |
| Shaft diameter | 40 mm |
| Key width × height | 12 × 8 mm |
| Effective length | 50 mm |
| Allowable shear stress | 60 MPa |
| Allowable bearing stress | 120 MPa |
- Convert torque:
T = 500,000 N·mm. - Tangential force:
F_t = 2(500,000)/40 = 25,000 N. - Nominal shear area:
bL_e = 12 × 50 = 600 mm². - Nominal bearing area:
(h/2)L_e = 4 × 50 = 200 mm². - Shear stress:
τ = 25,000/600 = 41.666667 MPa; utilization is0.694444×. - Bearing stress:
σ_b = 25,000/200 = 125 MPa; utilization is1.041667×. - Required lengths are
34.722222 mmfrom shear and52.083333 mmfrom bearing. - Bearing governs. The available-to-required ratio is
0.96×, so 50 mm is4% shortunder the entered nominal allowables.
The calculator reports a valid numerical result and separate engineering warnings. A warning is not a geometry recommendation: the joint still needs a realizable current-standard or controlled-drawing key size, suitable materials and allowables, and all required shaft/hub checks.
Allowables and warning interpretation
The tool does not infer allowables from a generic material name. Heat treatment, property direction, key and keyseat materials, fatigue loading, reversals, temperature, surface condition, fit, reliability, and the governing code or company method can change the design basis. Enter reviewed values for the actual joint.
Utilization above 1.0× raises a warning for that nominal mode. A separate length warning appears when L_e < L_required. Geometry warnings appear if width or height is at least the shaft diameter; these warnings catch probable unit or geometry mistakes but do not validate more plausible proportions.
Engineering scope and limitations
This calculator is a transparent first-pass nominal stress and required-length check for one straight rectangular sunk parallel key. It excludes:
- automatic selection of key width, height, length, material, fit, or tolerance;
- shaft and hub keyway stress concentration, local notch stress, yielding, plastic redistribution, and fatigue;
- fretting, wear, backlash, contact nonuniformity, misalignment, deformation, and assembly effects;
- multiple keys, Woodruff keys, tapered or gib-head keys, feather keys with sliding contact, pins, splines, serrations, and keyless locking devices;
- axial retention, hub bursting or distortion, shaft strength outside the key, and torque contribution from interference or friction;
- current-standard dimensional compliance, manufacturing feasibility, inspection acceptance, proof testing, or engineering approval.
Use the current standard, manufacturer instructions, controlled drawings, and a qualified machine-design method for the actual key and keyway. Perform separate shaft, hub, fatigue, fit, and system-load checks before release.
Frequently asked questions
What formulas does the shaft key calculator use?
It calculates tangential force as F_t = 2T/d, nominal shear stress as τ = F_t/(bL_e), and nominal bearing stress as σ_b = F_t/((h/2)L_e). The required length is the larger length obtained from the user-entered shear and bearing allowables.
Why does the bearing area use half the key height?
The nominal sunk-key model assigns half the rectangular key height to contact with the shaft and half to contact with the hub. The projected area at one interface is therefore (h/2)L_e. Real contact can be smaller or nonuniform.
What is effective key length?
Effective length is the portion assumed to carry load uniformly. Exclude chamfered, radiused, tapered, relieved, or non-contact end portions rather than entering overall blank length without review.
How should I choose allowable shear and bearing stress?
Establish allowables from the actual key, shaft, and hub materials, condition, duty, applicable factors, failure criteria, and governing design method. The calculator defaults are illustrative and are not material recommendations.
Does this calculator include the shaft or hub keyway stress concentration?
No. It checks nominal average stress in the key and at the projected key contact only. Keyway notch fatigue, local shaft and hub stress, deformation, fretting, and fit require separate evaluation.
Does the calculator select standard key dimensions and tolerances?
No. Enter geometry selected from the current standard, manufacturer data, or controlled drawing applicable to the machine. The calculator neither selects a standard nor verifies keyseat depths, tolerances, chamfers, radii, or manufacturing acceptance.
References and review status
Reviewed . References support the nominal rectangular-key force, shear-area, bearing-area, and unit-conversion relationships. They do not establish the entered geometry or allowables, select a current key standard, verify the shaft or hub keyway, or approve a joint.
- University of Florida ABE 4171 — Keys, Couplings and Seals — University lecture material showing F = T/(D/2), shear area WL, the resulting 2T/(DWL) shear stress, and projected bearing area L(H/2).
- NIST Guide to the SI, Appendix B.8 — Conversion factors — Official conversion reference for pound-force, lbf·in, lbf·ft, psi, and SI units used by the shared unit engine.
- ISO/R 773:1969 — Rectangular or square parallel keys and keyways — Official ISO catalogue record confirming the dimensional subject and withdrawn status of this historical document; it is not used as a current sizing table or acceptance standard here.