Shear stress in key
-Allowable -; safety factor -Bearing stress
-Allowable -; safety factor -Minimum key length
-Shear -, bearing -Results
| Torque | - |
| Tangential force F = 2T/d | - |
| Key yield strength | - |
| Bearing yield (weaker of key, hub, shaft) | - |
| Key length / shaft diameter | - |
Checks
How the calculator works
The calculator checks a parallel key transmitting steady torque between a shaft and a hub, using the standard textbook model: the torque becomes a tangential force at the shaft surface that is carried by the key in shear across its length and by bearing on the side of the key.
- Force. F = 2T/d, with T the torque and d the shaft diameter. With power P and speed n (rpm), T = 9549·P(kW)/n N·m, or 63025·P(hp)/n lbf·in.
- Shear. τ = F/(b·L), with b the key width and L its effective length. The allowable shear stress is 0.577·Sy/SF (distortion energy theory) with Sy the yield strength of the key.
- Bearing. σb = F/((h/2)·L), assuming the key is half sunk in the shaft and half in the hub. The allowable is Sy/SF using the lowest yield strength of the key, shaft and hub.
- Minimum length. Lshear = F·SF/(0.577·Sy·b) and Lbearing = 2F·SF/(Sy,min·h). The larger governs.
Yield strengths are typical values for cold-drawn or annealed bar: AISI 1018 about 370 MPa (54 ksi), AISI 1045 about 530 MPa (77 ksi), AISI 4140 about 655 MPa (95 ksi), 304 stainless annealed about 215 MPa (31 ksi), 316 stainless annealed about 205 MPa (30 ksi), gray cast iron and aluminium hubs are entered as a lower bearing limit. Use your certified values for critical work. The model does not include stress concentration, misalignment, fits, or load that is not evenly shared along the key.
Worked example: 40 mm shaft, 500 N·m
Shaft d = 40 mm, torque 500 N·m, key 12 × 8 mm, effective length 45 mm, AISI 1045 key (Sy = 530 MPa) in a steel hub of the same strength, safety factor 2. F = 2·500/0.040 = 25 kN. Shear stress = 25000/(12·45) = 46.3 MPa against an allowable 0.577·530/2 = 152.9 MPa, safety factor 6.6. Bearing stress = 25000/(4·45) = 138.9 MPa against 530/2 = 265 MPa, safety factor 3.8. Minimum length: shear 13.6 mm, bearing 23.6 mm (at SF 2): bearing governs, and the 45 mm key is comfortable.
Questions
How do you calculate the length of a key?
The key carries a tangential force F = 2T/d, where T is the torque and d the shaft diameter. Shear needs a length L ≥ F/(b·τallow) and bearing needs L ≥ F/((h/2)·σallow), where b is the key width and h its height. Use the longer of the two. Example: T = 500 N·m on a 40 mm shaft with a 12 × 8 mm AISI 1045 key (yield 530 MPa) and a safety factor of 2 gives F = 25 kN; the minimum length is 13.6 mm for shear and 23.6 mm for bearing, so bearing governs.
Is a key more likely to fail in shear or in bearing?
For standard key sizes, crushing (bearing) of the key side or the keyway wall usually governs, because the contact height is only about half the key height. Shear governs only for keys that are unusually narrow for their length or are made of a strong material in a weak keyway. Always check both.
What key size should I use for a given shaft diameter?
Standard parallel key sizes grow with shaft diameter, for example about 8 × 7 mm on a 22 to 30 mm shaft and 12 × 8 mm on a 38 to 44 mm shaft in ISO 773 / DIN 6885. The calculator suggests the standard size for your diameter. In US inch practice a common rule is a key width of about one quarter of the shaft diameter.
What safety factor should I use for a key?
Use at least 2 for smooth, steady loads and 3 or more for shock, reversing loads or starts under load. Keys are often designed as the weakest link on purpose (a shear pin effect), so check what failure you want.
Does the calculator account for keyway stress concentration in the shaft?
No. A keyway reduces the shaft's bending and torsional strength and adds a stress concentration; this must be checked separately in the shaft design. The key calculation here covers only the key itself and the contact stress at its sides.
Engineering aid for guidance. Static checks of a parallel key only; it does not cover splines, tapered or Woodruff keys, fatigue, shock factors beyond the safety factor you enter, or the strength of the shaft at the keyway. Verify critical designs against the relevant standard (for example ISO 773, DIN 6885 or ANSI B17.1) and your own calculations; you remain responsible for the design. Nothing you enter leaves your browser except through a share link you copy yourself.