Engineering task and calculation objective
The module calculates the tightening torque of bolted joints to VDI 2230, the German engineering guideline for high-duty bolted joints. The starting point is the required bolt load in the assembly condition — for example from a flange calculation to AD 2000-Merkblatt B7 or DIN 2505 — supplemented by the thread geometry (pitch diameter, pitch) and the friction coefficients in the thread and under the head or nut bearing face. The module supports rigid bolts (full-shank bolts) as well as reduced-shank (waisted) bolts.
Anyone who wants to specify flange connections, equipment covers or machine bolting for proper assembly has to calculate the tightening torque: the preload required by the strength calculation must be set reproducibly on site with a torque wrench. Since only about one tenth of the applied torque actually generates preload, with the rest lost to thread and bearing friction, the friction coefficients largely decide the result — VDI 2230 provides the recognized calculation procedure for this in mechanical and pressure equipment engineering.
Standard and calculation basis: VDI 2230
Calculation workflow
- Adopt the required assembly preload: The bolt load required in the assembly condition is taken over from the upstream calculation — for flange connections typically from AD 2000-Merkblatt B7 or DIN 2505 — and, if necessary, increased by a tightening factor that covers the scatter of the tightening method.
- Determine the thread geometry: From the thread designation follow the pitch and the pitch diameter d2; for waisted bolts additionally the waist diameter, which limits the allowable preload. For the bearing friction, the effective friction diameter is formed from the head or nut bearing face and the clearance hole.
- Set the friction coefficients: The friction coefficients in the thread and at the bearing face are chosen according to surface condition and lubrication (VDI 2230 gives classes from about 0.04 to above 0.20). They are the most uncertain input and should match the actual assembly condition — oiled, with assembly paste, or dry.
- Calculate the tightening torque: The total torque is composed of the thread torque (pitch and thread friction contributions via the pitch diameter) and the friction torque under the bearing face. The module reports the tightening torque for rigid or waisted bolts.
- Check the bolt stress: Finally, it is verified that the equivalent stress from tension (preload) and torsion (thread torque) in the shank or waist does not exceed the allowable utilization of the bolt property class — per VDI 2230 usually 90 % of the minimum yield strength.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Required bolt force | Max(FSB,FDV,FSP) Freq | N |
| Pitch diameter, effective diameter | d2 | mm |
| Bore-hole diameter | Db | mm |
| Outside diameter of bearing surface of head | Da | mm |
| Friction number (bearing surface of head) | µK | - |
| Friction number (thread) | µG | - |
| Pitch angle (60°= metric ISO thread, 0°= flat thread) | α | ° |
| Pitch diameter | P | mm |
| Thread type | Gewindeart | – |
| Factor | P/(π·d2) ≡ tan(φ) | - |
| Factor | µG/cos(α/2) ≡ tan (ρ') | - |
| Frictional moment of the thread | Mg | N·mm |
| Frictional moment of the head | Mk | N·mm |
| Min. required Bolting torque | Mreq = | N·mm |
| Number of bolts | n | - |
| Min. required Bolting torque | Mreq = | N·m |
| Bolt material | Werkstoffnummer | - |
| Design strength | K K' | N/mm² |
| Design strength | K K' | N/mm² |
| Safety factor | S S' | - |
| Safety factor | S S' | - |
| Minor diameter of the bolt thread | d3 | mm |
| Effective stress | Betrieb | N/mm² |
| Per bolt | Betrieb | N |
Calculation options
Thread type
Metric ISO-Standard · Other · UNC thread
Bolt type
Waisted stud · Bolt
Worked example
For a flange connection, a required assembly preload of FM = 50 kN per bolt was determined to AD 2000-Merkblatt B7. Hexagon bolts M16 (property class 8.8) are used, lightly oiled, with thread and bearing friction coefficients µG = µK = 0.12. Find the tightening torque to VDI 2230 — a worked example of how to calculate the bolt tightening torque.
Given values
| Assembly preload F_M | 50,000 N |
| Thread | M16, pitch P = 2.0 mm |
| Pitch diameter d2 | 14.701 mm |
| Thread friction coefficient µ_G | 0.12 |
| Bearing friction coefficient µ_K | 0.12 |
| Effective bearing friction diameter D_Km | 20.0 mm |
Solution
Torque equation per VDI 2230
MA = FM · (0.16 · P + 0.58 · d2 · µG + DKm/2 · µK)
The first term captures the thread pitch, the second the thread friction at the pitch diameter (the factor 0.58 stems from the half flank angle of the metric thread), the third the friction under the head or nut bearing face.
Inserting the numerical values
Pitch contribution: 0.16 · 2.0 = 0.320 mm
Thread friction: 0.58 · 14.701 · 0.12 = 1.023 mm
Bearing friction: 20.0/2 · 0.12 = 1.200 mm
Sum: 0.320 + 1.023 + 1.200 = 2.543 mm
Tightening torque
MA = 50,000 N · 2.543 mm = 127,159 N·mm ≈ 127 N·m
Only the pitch contribution (0.32 of 2.543, i.e. about 13 %) generates preload — roughly 87 % of the torque is consumed by friction. The value agrees with the tabulated figures for M16 of property class 8.8 at µ = 0.12.
Result
| Tightening torque M_A | ≈ 127 N·m |
| Friction share of the total torque | ≈ 87 % |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
Why does the achieved preload scatter so much when tightening with a torque wrench?
Because around 85 to 90 % of the torque is consumed by friction, scatter in the friction coefficients feeds almost fully through to the preload. VDI 2230 captures this with the tightening factor αA: for torque-controlled tightening it lies at about 1.4 to 1.8 depending on how well the friction coefficients are known, and higher under unfavourable conditions. More accurate methods such as yield-controlled or angle-controlled tightening, and hydraulic tensioning, reduce the scatter considerably.
How do rigid and waisted bolts differ in the calculation?
The torque equation is the same; the difference lies in the governing cross-section and in the resilience. For the waisted bolt, the waist cross-section limits the allowable preload, but its high elastic resilience makes the joint less sensitive to settlement losses and fluctuations in the working load — which is why waisted bolts are preferred for cyclically loaded and sealing-critical flange connections.
Which friction coefficients should I use if no measured values are available?
VDI 2230 assigns friction coefficient classes to surface and lubrication conditions. For lightly oiled, phosphated or zinc-plated bolts, values around 0.10 to 0.16 are common; with MoS2 or ceramic pastes 0.08 to 0.12; dry and bright metallic considerably more. Consistency is key: the calculated torque is only valid for the assumed lubrication condition — if lubrication on site differs from the calculation, the joint ends up over- or under-preloaded. For stainless steel bolts, the tendency to gall must also be considered.
May I simply re-check a previously applied tightening torque for verification?
Only to a limited extent: when re-checking with a torque wrench, static friction acts, which is higher than the sliding friction during tightening — the breakaway or re-tightening torque therefore says little about the preload actually present. In addition, preload is lost after assembly through embedding of the contact surfaces. For sealing-critical joints, defined re-tightening procedures or direct force measurements (e.g. hydraulic re-tensioning, load-indicating bolts) are more meaningful.