Industrial-grade bolted-joint assembly calculator: VDI 2230 permissible assembly preload with torsion, full tightening-torque equation, preload scatter band by tightening technique, implied nut factor, metric coarse thread database and full audit trail.
Decision:Run the stated engineering model, review its assumptions and warnings, then make the release decision against the governing standard and verified source data.
SectorCalc SC-035 applies VDI 2230 Part 1 assembly-level calculations to metric bolted joints: permissible assembly preload FM zul accounting for torsion while tightening, the full tightening-torque equation with thread and head friction, and the preload scatter band FM min = FM max/αA for the selected tightening technique. It also reports the traditional nut factor K so torque values can be compared with legacy shop specifications. Results are assembly reference values — the joint itself (clamped parts, embedment, external loads, fatigue) requires the full VDI 2230 joint calculation, which is a separate verification.
VDI 2230 tightening torque equation
The torque a wrench must deliver splits into a thread-pitch term, thread friction, and head-bearing friction:
Only about 10–15% of the applied torque stretches the bolt (the 0.16·P term). The remaining 85–90% is consumed by friction — which is why two bolts at identical torque can differ by 30% or more in preload when friction differs.
Permissible assembly preload FM zul
Tightening loads the bolt in combined tension and torsion. VDI 2230 reduces the allowable assembly preload below the pure-tension yield load accordingly:
ds = (d2 + d3)/2 · A0 = π/4 · ds² ≈ stress area As
SC-035 then applies the yield utilization: FM max = ν · FM zul with ν = 70–90%. At ν = 90% the bolt reaches about 90% of its torsion-corrected yield at maximum assembly preload — the usual VDI design point for new bolts in controlled assembly.
Tightening factor αA and preload scatter
No tightening method hits the target preload exactly. The tightening factor expresses the scatter between the maximum and minimum preload a method produces at the same nominal torque:
FM min = FM max / αA
Tightening technique
αA (guideline)
Preload scatter
Torque wrench (manual)
1.6 – 2.5
±25–40 %
Impulse / impact driver
2.5 – 4.0
±45 %+
Hydraulic torque / multi-spindle
1.2 – 1.6
±10–20 %
Yield-controlled (torque-angle to yield)
1.1 – 1.3
±5–15 %
Elongation measurement / ultrasonic
1.05 – 1.15
±3–8 %
The joint must still clamp when the preload is at FM min — and the bolt must survive FM max. A torque wrench at αA = 2.0 delivers half the design preload on a bad day: that is the load case the joint verification must satisfy.
Friction classes and why μ dominates
Because friction consumes most of the torque, μ is the single most influential input. Moving from μ = 0.20 (dry galvanised) to μ = 0.10 (oiled) at the same torque nearly doubles achieved preload. Practical rules:
Never mix "as-received" fasteners from different suppliers in one joint without confirming the friction class — plating and lubricant vary.
Specify the friction window in the work instruction (e.g. "μtot = 0.10–0.16, oiled") and torque for the worst end.
Re-lubricating a dry-spec bolt without re-computing torque is a classic over-tightening failure — preload rises as friction falls at fixed torque.
Nut factor K — the short formula
MA [N·m] = K · FM [N] · d [mm] / 1000
K ≈ 0.20 dry · 0.15 lightly oiled · 0.12 well lubricated
The short formula hides geometry inside K. SC-035 reports the K implied by the full VDI equation for your exact size, friction and DKm — comparing it with a legacy "K = 0.20" specification reveals how much that legacy spec actually under- or over-tightens on your fastener.
Metric coarse thread reference
Size
Pitch P
Stress area As
FM zul 8.8 / 10.9 / 12.9 (μ=0.12)
M6
1.00
20.1 mm²
≈ 9.3 / 13.7 / 16.1 kN
M8
1.25
36.6 mm²
≈ 17.0 / 24.9 / 29.3 kN
M10
1.50
58.0 mm²
≈ 26.9 / 39.5 / 46.5 kN
M12
1.75
84.3 mm²
≈ 39.1 / 57.5 / 67.6 kN
M16
2.00
157 mm²
≈ 72.8 / 107 / 126 kN
M20
2.50
245 mm²
≈ 114 / 167 / 197 kN
M24
3.00
353 mm²
≈ 164 / 241 / 283 kN
M30
3.50
561 mm²
≈ 260 / 383 / 450 kN
M36
4.00
817 mm²
≈ 379 / 557 / 655 kN
Frequently asked questions
Why does the same torque give different preload?
Because 85–90% of tightening torque is eaten by friction in the thread and under the head. Plating, lubricant, surface roughness and washer condition change friction coefficient between bolts of the same batch. At fixed torque, lower friction means higher preload — a dry-spec bolt re-lubricated without changing torque can be stretched past yield.
Should I use the VDI equation or the K-factor short formula?
Use the VDI equation whenever the fastener size, friction class and head-bearing diameter are known — it is geometry-exact for the specified conditions. The K short formula (M = K·F·d with K ≈ 0.15–0.20) is a screening rule only; its implied error can exceed ±25% across sizes. SC-035 reports the K implied by your exact inputs so legacy specifications can be mapped and checked.
Can bolts torqued to 90% utilization be reused?
VDI practice treats bolts tightened to 90% of torsion-corrected yield as single-use for critical joints: residual elongation and thread damage are possible and invisible. For non-critical joints with verified zero permanent set, reuse at reduced utilization (ν = 70%) is common practice. Yield-controlled (torque-to-yield) fasteners are strictly single-use by design.
Does this calculator verify my joint?
No. SC-035 is the assembly-level calculation: how much preload a torque produces and how it scatters. Joint verification under external loads — clamped-part stiffness, load introduction factor, embedment/settlement, minimum residual clamp, bolt fatigue under operating load — is the full VDI 2230 joint calculation (SC-036 scope) and must be run separately for structurally significant joints.
Why is fine pitch not supported?
Fine threads have different pitch diameter, minor diameter and stress area for the same nominal size, changing every term of the torque equation and the permissible preload. Using a coarse-thread table on a fine-pitch bolt under-estimates preload and over-stresses the thread. Fine-pitch support requires its own thread database entry — enter it as a custom case only with verified geometry.
