A bolt with 20 kN of preload must absorb an 8 kN external load per bolt without the joint opening. Does the joint hold?
Two boundaries, not one
After assembly, a bolt loses part of its preload to embedding loss F_Z: F_V,rest = F_V − F_Z. While the joint remains closed, the load factor φ splits the load: the residual clamp force drops to F_KR = F_V,rest − (1 − φ)·F_A, while the bolt force rises to F_S,max = F_V,rest + φ·F_A. Both boundary cases have to hold — one protects the joint against opening, the other protects the bolt against yielding.
Worked example: 20 kN preload, 8 kN load
With A_s = 84.3 mm², Rp0.2 = 900 N/mm², F_V = 20 kN, F_Z = 1 kN, φ = 0.25 and F_A = 8 kN, F_V,rest = 19 kN follows. Under full load: F_KR = 19 − 0.75·8 = 13 kN (above the required 10 kN, so the joint stays closed) and F_S,max = 19 + 0.25·8 = 21 kN, giving σ_S = 21,000/84.3 ≈ 249.1 N/mm² — a static safety factor of 900/249.1 ≈ 3.6. These two ideal static checks pass at the assumed preload; this is not a complete verification of the joint.
Separation invalidates the closed-joint model
With F_V = 5 kN, F_Z = 0.5 kN and φ = 0.3, F_V,rest = 4.5 kN. The separation threshold is F_A,sep = 4.5/(1 − 0.3) ≈ 6.43 kN. At F_A = 200 kN this threshold is far exceeded: residual clamp force is zero. A negative result from the closed-joint formula only signals that the model no longer applies. Do not then use F_V,rest + φ·F_A to determine bolt force, stress or safety. The calculator suppresses bolt force, stress and safety factor at and beyond the separation threshold (F_KR ≤ 0). Perform a separate analysis of the opened joint.
Assumptions and applicability limits
This is Mechify’s simplified model for a closed, concentrically loaded static joint, not an official ‘lite’ variant of VDI 2230. Eccentric or bending loads, transverse load with its friction-grip check, fatigue/alternating stress, the embedding-loss table (F_Z is taken as input here) and torsional stress during tightening fall outside this model. For critical or dynamically loaded joints, use the full VDI 2230.