KEVOS® MAKEOS · Fasteners
Bolt Torque Coefficient and Yield Clamping Force (JIS Method from Thread and Bearing Friction)
For a metric bolt and nut with known friction in the threads and under the head, what is the torque coefficient K, how is the tightening torque shared between the threads and the bearing face, what clamping force takes the bolt to yield and what torque does that need, and what preload does my tightening torque give?
Torque and tension of a metric fastener by the JIS B 1803 relations the handbook gives: pitch diameter d2 = d − 0.649515 P, stress area As = (π ÷ 4)((d2 + d3) ÷ 2)² with d3 = d1 − H ÷ 6, the lead angle tan β = P ÷ π d and the flank angle in the normal section tan α′ = tan α cos β, the equivalent bearing diameter Dw = (2 ÷ 3)(Do³ − Di³) ÷ (Do² − Di²), the torque coefficient K = (P ÷ π + μs d2 sec α′ + μw Dw) ÷ 2d with Tf = K Ff d, the thread and bearing torques Ts and Tw, the yield clamping force Ffy = σy As ÷ √(1 + 3 [(2 ÷ dA)(P ÷ π + μs d2 sec α′)]²) by the shear strain energy theory and the torque Tfy = K Ffy d to reach it, and the preload and share of the yield clamping force from your tightening torque.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Nominal diameter d | mm | Nominal (major) diameter of the bolt thread. |
| Pitch P | mm | Pitch of the thread. |
| Thread half-angle α | ° | Half the included thread angle: 30° for ISO metric threads. |
| Friction and bearing face | ||
| Friction coefficient in the threads μs | Coefficient of friction between the bolt and nut threads. | |
| Friction coefficient under the head or nut μw | Coefficient of friction between the turning nut or head and the joint face. | |
| Outside diameter of the bearing face Do | mm | Outside diameter of the bearing face in contact; the handbook’s tables take 0.95 × the width across flats. |
| Inside diameter of the bearing face Di (clearance hole) | mm | Inside diameter of the bearing face, usually the clearance hole. |
| Bolt and tightening | ||
| Yield point or proof stress of the bolt σy | MPa | Yield point or proof stress of the bolt material, for example 640 MPa for property class 8.8. |
| Tightening torque you apply | N·m | Torque you apply when tightening; 0 to skip. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Nominal diameter d
- What it is
- Nominal (major) diameter of the bolt thread.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the stress area and the torque for a given preload.
- Get it right
- For example 10 for an M10 bolt.
What this means: Pitch P
- What it is
- Pitch of the thread, from one thread crest to the next.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 20 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the lead angle, the pitch diameter and the stress area.
- Get it right
- 1.5 mm for M10 coarse, 1.25 mm for M10 fine.
What this means: Thread half-angle α
- What it is
- Angle between a thread flank and a line square to the axis.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 5° to 45°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the thread friction torque through sec α′.
- Get it right
- 30° for ISO metric and Unified threads.
Friction and bearing face
What this means: Friction coefficient in the threads μs
- What it is
- Coefficient of friction between the bolt and nut threads.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.12 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises K and lowers the yield clamping force.
- Get it right
- About 0.12 to 0.20 dry or lightly oiled; lower with molybdenum paste.
What this means: Friction coefficient under the head or nut μw
- What it is
- Coefficient of friction between the turning nut or head and the joint face.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.12 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises K and the share of torque lost under the head.
- Get it right
- Often similar to the thread friction; washers and coatings change it.
What this means: Outside diameter of the bearing face Do
- What it is
- Outside diameter of the bearing face under the nut or head.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 16.15 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger bearing face raises the under-head friction torque.
- Get it right
- The handbook tables take 0.95 × the width across flats.
What this means: Inside diameter of the bearing face Di (clearan…
- What it is
- Inside diameter of the bearing face, usually the clearance hole.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 11 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the equivalent bearing diameter with Do.
- Get it right
- Take the clearance hole diameter for the fit class used.
Bolt and tightening
What this means: Yield point or proof stress of the bolt σy
- What it is
- Yield point or proof stress of the bolt material.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 5000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 640 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The yield clamping force rises in proportion.
- Get it right
- 640 MPa for property class 8.8, 940 MPa for 10.9.
What this means: Tightening torque you apply
- What it is
- Torque applied to the nut or head when tightening.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0 N·m to 1000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 35 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the preload and its share of the yield clamping force.
- Get it right
- Enter 0 to skip the preload from torque.
Method and formulas
- d2 = d − 0.649515 P; d1 = d − 1.082532 P; H = 0.866025 P; d3 = d1 − H ÷ 6; As = (π ÷ 4)((d2 + d3) ÷ 2)²; dA = √(4 As ÷ π).
- tan β = P ÷ π d; tan α′ = tan α cos β; Dw = (2 ÷ 3)(Do³ − Di³) ÷ (Do² − Di²).
- K = (P ÷ π + μs d2 sec α′ + μw Dw) ÷ 2d; Ts = (Ff ÷ 2)(P ÷ π + μs d2 sec α′); Tw = (Ff ÷ 2) μw Dw.
- Ffy = σy As ÷ √(1 + 3 [(2 ÷ dA)(P ÷ π + μs d2 sec α′)]²); Tfy = K Ffy d.
- Preload from the applied torque Ff = T ÷ (K d).
- Example: K = 0.16881; the bolt reaches its yield clamping force of 30,454 N at 51.411 N·m.
Limitations
- Friction coefficients vary widely with surface finish, coating and lubricant; measure them for critical joints.
- The handbook’s tables average K over many sizes, so a single size may differ slightly from the table.
- Tightening to yield needs controlled methods; this tool gives the torque at the onset of yield, not a recommended torque.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Work out the nut factor from the thread and under-head friction
- Find the torque that takes a bolt to its yield clamping force
- Check the preload a tightening torque gives against yield
Who it is for
- Machine designers
- Maintenance fitters
- Assembly engineers
What you get
- Pitch diameter, stress area and its equivalent diameter
- Lead angle and flank angle in the normal section
- Equivalent bearing diameter Dw
- Torque coefficient K and the shares of thread and bearing torque
- Yield clamping force and the torque to reach it
- Preload from your torque and its share of the yield clamping force
Interpreting the result
- Usually more than half of the torque goes into friction under the head or nut.
- Higher thread friction lowers the yield clamping force because the bolt also carries torsion.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1529–1531. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Useful alongside · KEVOS® original book
Tightening by torque: the nut factor and its scatter
In Bolted Joints by the Numbers
What it covers: How tightening torque becomes preload through the nut factor, why friction makes that uncertain, how lubricants change it, and how to correct a torque wrench for an adapter.
Also in Designing a tension joint for separation, proof load and scatter
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