PSI - Issue 75

Florian Kalkowsky et al. / Procedia Structural Integrity 75 (2025) 581–592 Florian Kalkowsky et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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4.2. Derivation of design equation for bearing type connections Based on this calculation method from the FKM-Guideline (2020), a design equation compliant to Eurocode 3 for the nominal stress S-N curve of components in bearing type connections can be derived. This design equation already considers the main influencing parameter of the material strength and stress concentration on the fatigue strength. To derive this design equation for the bearing type connection, the parameters listed in Table 3 were used. These parameters include some conservative assumptions for the determination. The factors to consider the mean stress dependence and the surface roughness are formulated as a function of the tensile strength of the base material. With increasing material strength, a greater sensitivity of these factors exists. Based on the three levels of tensile strength, it was possible to derive a formulation graded according to tensile strength. The surface roughness for mill scales was also conservatively assumed to be z = 200 μm . Additional fatigue strength-increasing or -decreasing effects from a coating layer or surface treatment were not subject of the consideration. For this purpose, the surface treatment factor V and the coating factor S assumed to be V = S = 1 in the calculation. The DC acc. to Eurocode 3 must apply regardless of knowledge of the mean stress level. For this purpose, the equation for overload case F2 ( ≥0.5 ) was used in the calculation. Table 3. Input parameter for the derivation of detail categories ∆ C for components in bearing type connections [N/mm²] , [-] [ μm ] [-] [-] , [-] , , [N/mm²] [-] [-] , [-] [-] [-] [-] I 1000 0.45 200 0.5 2700 0.22 400 1 1 0.646 0.5 0.25 0.69 II 800 0.45 200 0.5 2700 0.22 400 1 1 0.695 0.5 0.18 0.76 III 650 0.45 200 0.5 2700 0.22 400 1 1 0.740 0.5 0.13 0.82 The FKM-Guideline defines the component fatigue endurance limit for non-welded components at D = 1 ∙ 10 6 load cycles. Since the FKM-Guideline and the Eurocode 3 use the same probability of survival of S = 97.5 % the following equation can be used for the calculation of a DC. ∆σ C =2 ∙ √ 1 2 5 ∙ 3+M 3 ∙ (1+M ) 2 ∙ f , ∙ R (K f,zd + K 1 , −1) ∙ K 1 ∙ K (2) Using the equation (2) shown above, the formulations for calculating the DC could be established for three ranges of tensile strength as shown in Table 4. Table 4. Proposal for detail categories ∆σ C of components in bearing type connections depending on the material strength Detail category Constructional detail Description Supplementary requirements 1 = 5 One-sided fully supported or double covered symmetrical joint subject to normal stress with non-preloaded normal bolts in holes with normal clearance or blind rivets without load reversal - Δ to be calculated on the net cross-section - t,zd from diagrams or by FEA - by FEA or = 1

0.54 t,zd u,nom σ +0.55 Independent from u 0.64 t,zd u,nom σ +0.35 360 N/mm² ≤ u < 490 N/mm² 0.59 t,zdu,nom σ +0.43 490 N/mm² ≤ u < 650 N/mm²

- Hole manufacturing by drilling - Structural steels S235 up to S700 - Max. detail category 180 ( 1 = 5) - Positioning of holes: 1 ≥ 1.0 0 | 2 ≥ 1.5 0 1 ≥ 2.2 0 | 2 ≥ 2.4 0

Further limitations should be considered in the design as for example effects from secondary bending, inclination of the fastener or avoiding hole elongation ensure elastic load-bearing behavior. Further information can be found in Kalkowsky (2024).