PSI - Issue 19

Sandro Citarelli et al. / Procedia Structural Integrity 19 (2019) 336–345 Sandro Citarelli, Markus Feldmann / Structural Integrity Procedia 00 (2019) 000 – 000

342

7

1 , 2 : ∆ : ∆ :

slopes of fatigue strength curves (3 and 5 according to EC3-1-9) cut- off limit („Variable Amplitude Fatigue Limit = VAFL“) 1 2 (log − log ) + log ∆ fatigue limit („Constant Amplitude Fatigue Limit = CAFL“)

Fig. 10. S-N-curve (median) with normally distributed model parameters The model parameters are adjusted using the maximum likelihood method. The likelihood function, Eq. (3), is iteratively adjusted by modifying the parameter vector until it reaches its maximum according to Eq. (4). ( ) =∏[ ( , )] [1 − ( , )] 1− =1 = { 0 ℎ = 1 ℎ = (3) = ( 1, 2, , , ∆ , ) = max ( ) (4) where = √ 1 2 − 1 2 ( − ) 2 density function (normal distribution) = √ 1 2 ∫ − 1 2 ( − ) 2 −∞ distribution function (normal distribution) : standard deviation By complying with the requirements defined in the standards, the parameter vector can be reduced to the two parameters ∆ and , where defines the standard deviation. This can be assumed to be = 0.0688, taking into account the usual scatter span for welded joints according to (Stahlbau Handbuch, 1996). Using the parameter ∆ estimated from the ML calculation, the median of the characteristic S-N-curve can be determined. The so-called ML profile is then used to determine the fatigue strength for the safety level required in (EN 1993-1-9, 2010). With the help of the ML profile it is approximately possible to determine confidence limits for the estimated parameters. Based on the assumptions described above, this concerns the cut-off limit of the fatigue strength ∆ . By applying the ML quotient over ∆ it can be accessed where the ML profile meets the confidence level 100(1- ) = 75%, see Fig. 11 and Eq. (5).