Bolt Pre-selection

Preliminary bolt sizing based on the Kübler equation

Bolt Pre-selection (A_{s,erf})

This calculator sizes an axially loaded bolt joint with the Kübler equation (Kübler-Gleichung). From the axial working load F_B, the required clamping force F_{Kl} and the joint geometry, it returns the required thread stress area A_{s,erf} and recommends a metric bolt size. It is for central (concentric) loading of single bolts or multi-bolt joints treated as one equivalent bolt. It does not cover:

• eccentric load
• shear-controlled joints
• steel structures (Eurocode)

The required area follows A_{s,erf} = (F_B + F_{Kl}) / [\,R_{p0.2}/(\kappa \cdot k_A) - \beta \cdot E_S \cdot f_Z / l_k\,]. The numerator is the total bolt force; the denominator is the allowable stress, reduced for the torsion added during tightening (factor \kappa), the preload scatter of the tightening process (factor k_A) and the preload lost to embedding f_Z. Yield strength R_{p0.2} is filled from the chosen strength class (DIN EN ISO 898-1).

Optional checks add:

• bearing pressure
• joint compliance
• static force split
• fatigue safety S_D
• the alternating force

This is a preliminary estimate (±15–20%) for early sizing. For a precise check, use the full VDI 2230-1 method. Data basis:

• DIN 13-1 (ISO 261, thread geometry)
• DIN EN ISO 898-1 (bolt properties)
• VDI 2230-1 (systematic bolt joint calculation)

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