BIZOMAT MAKEOS · Fasteners
Turn-of-Nut Angle for Bolt Preload
Through what angle must the nut turn to reach this preload, or what preload does a given turn give?
Nut rotation for a target bolt preload by the handbook’s turn-of-nut relation, using the bolt’s elastic elongation over its shank and threaded lengths, with optional joint compliance, or the preload from a specified turn angle.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Solve for | choice | Find the angle for a preload, or the preload for an angle. |
| Target preload | kN | Preload required. |
| Turn angle (preload mode) | ° | Nut turn from the snug position. |
| Thread lead | mm | Thread lead (pitch × starts). |
| Nominal (shank) diameter | mm | Nominal diameter, for the shank area. |
| Tensile stress area | mm² | Tensile stress area of the thread. |
| Unthreaded shank length in the grip | mm | Length of plain shank within the grip. |
| Threaded length in the grip | mm | Length of loaded thread within the grip (often plus about half a nut height for the thread engagement). |
| Bolt elastic modulus | GPa | Elastic modulus of the bolt. |
| Joint stiffness (0 = rigid joint) | kN/mm | Stiffness of the clamped parts; 0 reproduces the handbook relation, which ignores joint compression. |
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: Solve for
- What it is
- Whether to find the nut rotation from snug that produces a target preload, or the preload that a specified rotation produces.
- Units and format
- Choose one of 2 options from the list: Turn angle for a preload; Preload from a turn angle.
- Example
- The form opens with “Turn angle for a preload” selected as a worked example. Choose the option that matches your case.
What this means: Target preload
- What it is
- The clamping tension you want in the bolt after tightening, used when solving for the turn angle.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 35 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The turn angle rises in proportion.
- Get it right
- It is the tension in one bolt, not the total clamping force of the joint.
What this means: Turn angle (preload mode)
- What it is
- The rotation of the nut beyond the snug-tight position, used when solving for the preload.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0.000001° to 3600°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The preload rises in proportion while the bolt stays elastic.
- Get it right
- Measure from snug, not from finger-tight; one full turn is 360°.
What this means: Thread lead
- What it is
- The axial distance the nut advances in one full turn: thread pitch times the number of thread starts.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 50 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
- The turn angle for a given preload is inversely proportional to the lead.
- Get it right
- For a single-start thread the lead equals the pitch; check the starts on multi-start threads.
What this means: Nominal (shank) diameter
- What it is
- The nominal diameter of the bolt, used to work out the cross-sectional area of the plain shank.
- 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.
- Get it right
- If the shank is reduced below nominal, use the actual shank diameter.
What this means: Tensile stress area
- What it is
- The tensile stress area of the threaded section, the effective area used for stretch along the threaded length and for the thread stress.
- Units and format
- Enter a number in mm²: square millimetres. The form accepts 0.000001 mm² to 1000000 mm². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 58 mm² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the thread standard for the size and pitch.
What this means: Unthreaded shank length in the grip
- What it is
- The length of unthreaded shank lying within the clamped grip, which stretches with the shank area.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Threaded length in the grip
- What it is
- The length of threaded bolt lying within the grip, between the end of the shank and the nut, which stretches with the tensile stress area.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 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.
- Get it right
- Thread that projects beyond the nut carries no preload and is not counted.
What this means: Bolt elastic modulus
- What it is
- The elastic (Young’s) modulus of the bolt material, which sets how far the bolt stretches for a given preload.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 205 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- On a rigid joint the bolt stretch and turn angle are inversely proportional to it.
- Get it right
- Enter GPa, not MPa; take it from the bolt material data.
What this means: Joint stiffness (0 = rigid joint)
- What it is
- The compressive stiffness of the clamped parts under the bolt; the nut must also take up their compression. Zero treats the joint as rigid, as in the handbook relation.
- Units and format
- Enter a number in kN/mm: kN/mm. The form accepts 0 kN/mm to 1000000 kN/mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 kN/mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Real joints compress, so zero understates the turn needed; estimate it with a joint stiffness calculation.
Method and formulas
- Bolt elongation B = F_t (L_s ÷ A_s + L_t ÷ A_t) ÷ E.
- Handbook: θ = 360 B ÷ l, with l the lead (θ = 360 F_t L_B ÷ E l).
- With joint compliance the nut also takes up the joint compression: θ = 360 (B + F_t ÷ k_j) ÷ l.
- Example: 35 kN in an M10 bolt with a 1.5 mm lead needs 22.716° from snug on a rigid joint.
Limitations
- Elastic region; yield-tightening needs empirical angles.
- Not valid for gaskets or soft joints without measured joint stiffness; establish angles on a simulated joint.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set an angle-tightening specification for a bolted joint
- Check what preload a turn angle produces
- Compare angle and torque tightening
Who it is for
- Design engineers
- Assembly engineers
- Maintenance fitters
What you get
- Bolt elongation
- Turn angle or preload
- Bolt stiffness
Interpreting the result
- Find the snug point consistently; most of the scatter in angle tightening comes from where counting starts.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1522–1528. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Stretch and angle: setting preload closer to the bolt, and checking it
In Bolted Joints by the Numbers
What it covers: How bolt stretch and nut rotation relate to preload, why the snug point matters, how torque-angle tightening narrows scatter, and how measured stretch verifies preload.
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