BIZOMAT MAKEOS · Fasteners
Bolted Joint Design Check (Preload, Separation, Proof and Fatigue)
Does this bolt size and tightening torque keep the joint closed and the bolt safe under the working load?
Complete check of a preloaded tension joint: stress area, bolt and member (frustum) stiffness, joint constant, preload and tightening torque from the target share of proof load, preload scatter from the nut factor tolerance, and factors against separation, exceeding proof load and fatigue (Goodman) under a load cycling from zero to the working value.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Bolt | ||
| Nominal diameter | mm | Nominal bolt diameter. |
| Thread pitch | mm | Thread pitch. |
| Proof strength | MPa | Proof strength of the property class (from the bolt standard). |
| Tensile strength | MPa | Minimum tensile strength. |
| Endurance limit of the threaded bolt | MPa | Fully corrected endurance limit of the threaded bolt (rolled or cut threads, from fatigue data). |
| Bolt modulus | GPa | Elastic modulus of the bolt. |
| Joint | ||
| Grip length | mm | Total thickness clamped. |
| Threaded length within the grip | mm | Length of thread inside the grip. |
| Member modulus | GPa | Elastic modulus of the clamped members (the frustum estimate assumes one material). |
| Tightening and load | ||
| Target preload (share of proof load) | % | Preload as a share of proof load (75% is common for reusable joints). |
| Nut factor | Nominal nut factor for the finish and lubrication. | |
| Nut factor scatter (±) | % | Uncertainty in the nut factor, which scatters the preload for a given torque. |
| Working tension load per bolt | kN | External tension load per bolt, cycling from zero. |
| Required factor (separation and fatigue) | Factor you require against separation and fatigue. | |
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.
Bolt
What this means: Nominal diameter
- What it is
- The nominal (major) diameter of the bolt thread, the M size for a metric bolt, used for the shank area and the tightening torque.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Thread pitch
- What it is
- The axial distance between adjacent thread crests of the bolt, which sets the tensile stress area.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.75 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Check whether the bolt is coarse or fine pitch; a finer pitch gives a larger stress area.
What this means: Proof strength
- What it is
- The minimum proof strength of the bolt’s property class, the stress it must withstand without permanent set, from the bolt standard.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 2000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Preload and tightening torque rise in direct proportion to it.
What this means: Tensile strength
- What it is
- The minimum tensile strength of the bolt’s property class, used in the Goodman fatigue check.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 2500 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 830 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Endurance limit of the threaded bolt
- What it is
- The fully corrected endurance limit of the threaded bolt, allowing for rolled or cut threads, size and reliability, from fatigue data for the bolt.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 1000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 129 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the value for the threaded bolt, not the endurance limit of plain material.
What this means: Bolt modulus
- What it is
- The elastic modulus of the bolt material, used to work out the bolt’s stiffness.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 500 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 207 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- In GPa, not MPa.
Joint
What this means: Grip length
- What it is
- The total thickness of the parts clamped between the bolt head and the nut or tapped thread.
- 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 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Include washers; do not include the head or nut height.
What this means: Threaded length within the grip
- What it is
- The length of threaded shank lying inside the grip, between the clamped faces; the rest of the grip is plain shank.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 2000 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
- It cannot exceed the grip; use the full grip if the bolt is threaded right up to the head.
What this means: Member modulus
- What it is
- The elastic modulus of the clamped parts, used in the 30° frustum estimate of joint stiffness.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 500 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 207 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The frustum estimate assumes all clamped parts are one material; mixed-material joints need a fuller stiffness method.
Tightening and load
What this means: Target preload (share of proof load)
- What it is
- The preload you aim for, as a percentage of the bolt’s proof load (proof strength times tensile stress area).
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 10% to 95%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 70% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Preload and torque rise in proportion; a higher preload improves the separation factor but lowers the proof margin.
What this means: Nut factor
- What it is
- The nut factor in T = K F d, which relates tightening torque to preload and depends on thread finish and lubrication.
- Units and format
- Enter a plain number with no unit. The form accepts 0.05 to 0.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Tightening torque is directly proportional to the nut factor.
- Get it right
- Take it from the fastener or lubricant supplier, or from torque–tension tests for your finish and lubricant.
What this means: Nut factor scatter (±)
- What it is
- The uncertainty in the nut factor, as a ± percentage, which spreads the preload actually achieved at the set torque.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 60%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More scatter lowers the minimum preload (separation check) and raises the maximum preload (proof and fatigue checks).
What this means: Working tension load per bolt
- What it is
- The external tensile working load on one bolt, cycling from zero, after the joint load has been shared between the bolts.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Load per bolt, not total joint load: divide the total by the number of bolts where it is shared evenly.
What this means: Required factor (separation and fatigue)
- What it is
- The minimum factor you require against joint separation and against fatigue, from your design code or company practice.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 10. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It does not change the bolt loads; it sets the pass or fail checks for separation and fatigue.
Method and formulas
- A_t = π ÷ 4 (d − 0.9382 P)²; k_b from the shank and threaded lengths; k_m by the 30° frustum: 0.5774 π E d ÷ 2 ln[5 (0.5774 l + 0.5 d) ÷ (0.5774 l + 2.5 d)].
- C = k_b ÷ (k_b + k_m); F_i = share × S_p A_t; torque T = K F_i d; scatter gives F_i ÷ (1 ± scatter).
- Separation factor = F_i,min ÷ [(1 − C) P]; proof factor = (S_p A_t − F_i,max) ÷ C P.
- Fatigue (Goodman): n_f = S_e (S_ut − σ_i) ÷ [σ_a (S_ut + S_e)], σ_a = C P ÷ 2A_t, σ_i = F_i,max ÷ A_t.
- Example: an M12 bolt at 70% of proof needs 84.941 N·m and holds 3.6253 times the separation load.
Limitations
- Concentric tension joint; prying, bending and thermal loads are excluded.
- Frustum stiffness assumes members of one material wider than about three bolt diameters.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Choose bolt size, grade and torque for a joint
- Check a joint after a load increase
- Decide whether torque control is good enough
Who it is for
- Design engineers
- Assembly engineers
- Maintenance engineers
What you get
- Stress area, stiffnesses and joint constant
- Preload range and tightening torque
- Factors against separation, proof and fatigue
Interpreting the result
- If separation fails, raise preload or use more bolts; if fatigue fails, use rolled threads, a longer bolt or a stiffer joint.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1521–1536. 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
Designing a tension joint for separation, proof load and scatter
In Bolted Joints by the Numbers
What it covers: How to choose a target preload that survives its own scatter: separation at the lowest preload, proof load at the highest, fatigue, and why 75% of proof can be too much.
Method explained here · Library collection
Bolted joints that stay tight: preload, torque, fatigue and locking
In Machine Elements and Mechanical Design
What it covers: A bolt holds a joint by clamping it. How preload works, why torque is an unreliable proxy, how to resist fatigue and loosening, and how to specify bolted joints that last in service.
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Open the Bolted Joint Design Check (Preload, Separation, Proof and Fatigue) calculator