VDI 2230 Bolted Joint Verification — Engineering Guide
1 · The spring model of the joint
A preloaded joint is two springs in series. The bolt elongates like a tension spring with compliance δ_S; the clamped plates compress like a much stiffer spring with compliance δ_P. When the external axial load F_A enters the joint, it unloads the plate spring and adds load to the bolt spring in proportion to the load factor:
Φ = δ_P / (δ_S + δ_P) · Φ* = n·Φ · F_SA = Φ*·F_A · F_PA = (1−Φ*)·F_A
Typical steel joints have Φ = 0.15–0.35: only a fraction of the working load reaches the bolt. That is why preload is so effective — but only if it survives settlement and unloading. The plate compliance uses the VDI substitutional deformation cone from the head bearing diameter dw outward at tanφ = 0.5.
The load-plane factor n accounts for where along the grip the external load is introduced. Loading at mid-joint (n = 0.5) is typical for flange-like connections; loading directly at the separating interface (n = 1.0) is the conservative bound for cover bolts.
2 · Assembly preload and tightening scatter
The maximum assembly preload F_Mmax follows from the von Mises combination of tension and thread torsion at a chosen utilization ν of the yield strength:
F_Mmax = ν·Rp0.2·A_s / √(1 + 3·[(3d₂/2d₃)·(P/(πd₂) + 1.155·μ_G)]²)
Torque-controlled tightening cannot hit that value exactly. Friction scatter and tool accuracy give a real preload between F_Mmax and F_Mmin = F_Mmax/α_A. Choosing a precise technique (low α_A) buys clamping reserve for free: at α_A = 1.2 the minimum preload is 83 % of maximum; at α_A = 2.5 only 40 %.
Every real interface settles. Surface roughness flattens, coatings creep, paint squeezes out — typically f_Z = 0.009–0.015 mm per interface pair. The preload loss is F_Z = f_Z/(δ_S+δ_P), which is why short, stiff joints (small l_K, small δ_S) lose a much larger share of preload to the same settlement.
3 · The four service checks
Yield: maximum bolt load F_Smax = F_Mmax + F_SA must keep the stress below Rp0.2 with margin (SF ≥ 1.1 recommended). Residual clamping: after settlement and unloading, F_Krest = F_Mmin − F_Z − F_PA must stay positive (otherwise the joint opens, the bolt sees the full alternating load and gaskets leak) and above any functional requirement F_Kerf. Slip: transverse load must satisfy F_Q ≤ μ_T·F_Krest — a slipped joint loses its geometry and usually its preload. Fatigue: the alternating stress σ_a = F_SA/(2A_s) must stay below the size-dependent endurance σ_ASV (≈ 34–51 MPa for rolled metric threads).
4 · Worked example (defaults)
M12 10.9, μ_G = μ_K = 0.14, α_A = 1.6, l_K = 40 mm steel plates, F_A = 6 kN: the engine finds F_Mmax ≈ 61 kN, M_A ≈ 137 N·m, Φ ≈ 0.30 (Φ* = 0.15 with n = 0.5), F_Smax ≈ 62 kN (SF ≈ 1.3), settlement loss ≈ 3.7 kN, residual clamp ≈ 29 kN and σ_a ≈ 5 MPa — comfortably inside all four limits. Shorten the grip below l_K/d = 3 and the settlement and short-grip warnings appear — try l_K = 24 mm to see both.
5 · FAQ
Why is my tightening torque different from SC-035? SC-035 solves assembly sizing with the combined nut-factor view; this tool splits head and thread friction (μ_K, μ_G) exactly as VDI 2230 does and adds service verification. Small numeric differences are expected and documented in A3.
What if my plates are large flanges? The deformation cone is capped by the actual joint face diameter. If dw + l_K·tanφ exceeds your flange OD, the real plate stiffness is lower and Φ rises — re-run with a reduced effective cone or accept the n = 1.0 conservative setting.
Can I verify a joint with several bolts? Yes — enter per-bolt loads (total axial and transverse load divided by bolt count, worst-case distribution if uneven). The verification is per bolt; the stiffest-loaded bolt governs.
Is this a substitute for the full VDI 2230 worksheet? It covers the standard concentric, single-bolt verification chain. Eccentric loading, prying, bolt bending and multi-stage tightening procedures still need the complete standard or a joint FEA.
