Bolted joint calculation per VDI 2230
Calculate tightening torque and permissible assembly preload for metric bolts of property classes 8.8, 10.9 and 12.9, or verify a concentrically loaded bolted joint: resiliences, load factor, embedding loss, required preload, surface pressure and slip safety with a traffic-light assessment.
Select bolt and friction
Result (90 % yield utilization)
Permissible assembly preload FMzul
43.1 kN
Tightening torque MA
83.6 Nm
Permissible assembly tensile stress
511.6 N/mm²
Calculated using the VDI 2230 table logic (Table A1) with head bearing diameter dw = 16.6 mm and medium clearance hole dh = 13.5 mm. Valid for standard head bearing areas without washers or flange bolts.
Formulas and fundamentals
The mechanical model behind VDI 2230 is a preloaded spring system: the bolt acts as a tension spring with resilience δS, the clamped parts as a compression spring with resilience δP. An axial working load FA is shared via the load factor Φ: only the small portion FSA = Φn·FA loads the bolt additionally, the remainder relieves the clamped plates. The load introduction factor n accounts for how close to the interface the working load is applied.
The quick sizing mode answers the most common question in practice: what assembly preload and tightening torque can a bolt take? During tightening, tensile stress and torsional stress from the thread torque act simultaneously. Both are combined into an equivalent stress using the von Mises criterion, which may reach 90 percent of the minimum yield strength. This yields the permissible assembly preload FMzul and, with MA = FMzul·(0.16·P + 0.58·µG·d2 + µK·DKm/2), the tightening torque. These formulas reproduce the well-known VDI 2230 table values (Table A1) to within 1 percent.
Rule of thumb for friction: roughly 85 to 90 percent of the tightening torque is consumed by thread and head friction, only 10 to 15 percent generates preload. The friction coefficient is therefore the dominant uncertainty of any bolt assembly. That is why the tool uses separate friction coefficients for the thread (µG), the head bearing surface (µK) and the interface (µT).
In verification mode the resiliences are computed explicitly: δS as a series connection of head, shank, free loaded thread, engaged thread and nut or tapped-hole region; δP via the equivalent deformation cone of the clamped parts, distinguishing whether the compression cone can develop fully or splits into cone and sleeve. From δS and δP follow the load factor ΦK = δP/(δS + δP) and the additional bolt load.
After assembly the joint loses preload through embedding, the plastic flattening of roughness peaks. The embedding amount fZ depends on surface roughness, load type and the number of contact surfaces and is converted into a force loss via FZ = fZ/(δS + δP). The required minimum assembly preload is FMmin = FKerf + (1 − Φn)·FAmax + FZ. The scatter of the tightening method is captured by the tightening factor αA: the bolt must withstand FMmax = αA·FMmin, and the verification reads FMzul ≥ FMmax.
Four further verifications are performed: the static working-stress check using the equivalent stress with half the assembly torsion retained, the fatigue check with the permissible stress amplitude σASV = 0.85·(150/d + 45) for bolts heat-treated before thread rolling and a required safety SD ≥ 1.2, the surface pressure under the head bearing area against the limiting surface pressure pG of the softest clamped material, and the slip safety for shear transfer by friction grip.
Deliberate simplifications compared with the full guideline: the tool covers concentrically clamped and concentrically loaded single-bolt joints without one-sided opening. Eccentric clamping, temperature effects, multi-layer stacks of different materials, fine-pitch threads and reduced-shank bolts are not included. Tightening factors, embedding amounts and limiting surface pressures are tabulated guide values, and the chamfer diameter of the head bearing area is simplified to the clearance hole. For verifications that must be documented, the calculation per the full VDI 2230 Part 1 remains authoritative.
Worked example
Reference example, shear-loaded joint: a bracket transfers a static transverse force of 3 kN per bolt by friction grip (µT = 0.12, required slip safety 1.2). Selected is an M12 hexagon bolt as a tapped-hole joint in C45 steel, clamp length 30 mm (20 mm of which is shank), tightened with a torque wrench (αA = 1.6), µG = µK = 0.12.
The required clamp load is FKQerf = 1.2·3000/0.12 = 30,000 N. With the resiliences δS = 2.26·10⁻⁶ mm/N and δP = 0.33·10⁻⁶ mm/N and an embedding amount of 10 µm (shear, Rz 16), the embedding loss is about 3,870 N. This gives FMmin = 33,870 N and FMmax = 1.6·FMmin = 54,190 N.
An M12 of class 8.8 is not sufficient: its permissible assembly preload of 43.1 kN is below FMmax. Only class 10.9 with FMzul = 63.3 kN passes the verification; the corresponding tightening torque is 123 Nm. The case illustrates a typical eye-opener: transferring shear by friction grip consumes enormous preload and is a frequent cause of undersized joints.
Frequently asked questions
What tightening torque does an M10 of class 8.8 need?
At the usual friction coefficient µ = 0.12 the result is about 48 Nm tightening torque and 29.6 kN permissible assembly preload (90 percent yield utilization). At µ = 0.14 the torque rises to about 54 Nm while the achievable preload drops. The tool computes these values live for M4 to M36 and classes 8.8, 10.9 and 12.9 using the formula behind the VDI table values.
What does the tightening factor αA mean?
αA = FMmax/FMmin describes the scatter of the achieved preload caused by the tightening method. A torque wrench with an estimated friction coefficient scatters with αA ≈ 1.6 to 2.0, an impact wrench without control up to 4.0, elongation-controlled tightening only 1.1 to 1.2. The larger αA, the larger the bolt must be sized to reliably reach the required minimum clamp load.
Why is the friction coefficient so decisive?
Roughly 85 to 90 percent of the tightening torque is consumed by thread and head friction; only the remainder generates preload. A misjudged friction coefficient therefore translates almost one to one into the achieved preload. Surface and lubrication condition should be known, for example via the friction classes (class B with µ = 0.08 to 0.16 is the most common case).
What is the difference between a through-bolted and a tapped-hole joint?
In a through-bolted joint (DSV) the bolt is clamped with a nut and the compression cone can develop from both sides. In a tapped-hole joint (ESV) the internal thread sits directly in the component and the cone develops from the head side only. This changes the plate resilience, the number of embedding bearing surfaces and the cone angle formula, which is why the tool treats both cases separately.
Why does a bolted joint lose preload after assembly?
Through embedding: the roughness peaks in the thread, under the head and in the interfaces flatten plastically. Depending on roughness and load type a few micrometres are lost, which directly cost preload via the resiliences (FZ = fZ/(δS + δP)). Short clamp lengths are particularly sensitive because the same embedding amount meets a stiffer joint.
Does the tool replace a full verification per VDI 2230?
No. The tool follows the guideline's methodology for concentrically clamped and loaded joints and uses validated formulas and tabulated guide values. Eccentric clamping with one-sided opening, temperature effects, multi-layer stacks of different materials and the guideline's exact load introduction factors are deliberately excluded. For verifications that must be documented, the calculation per VDI 2230 Part 1 is authoritative; responsibility remains with the user.
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