Issue 30

A. Fernàndez-Canteli et alii, Frattura ed Integrità Strutturale, 30 (2014) 327-339; DOI: 10.3221/IGF-ESIS.30.40 329 (cdf) at any of the intervening stress ranges seems to be applicable only when a large number of results are at disposal, as this is the case, with an extensive amount of data. Nevertheless, it does not fulfil “a priori” the requested physical and statistical requirements for a model to be valid, in particular, the compatibility between the cumulative distribution functions of the number of cycles given stress range F[N;Δσ] and of the stress range given number of cycles E[Δσ;N] . As an alternative, the S-N resulting under consideration of the Weibull (or Gumbel) probabilistic model proposed by Castillo and Fernández-Canteli is shown in Fig. 2. The parameters estimated using the latter model allows us to define the normalized variable V=(log N-B)(log  -C) as a Weibull (or Gumbel) distribution for minima, thus facilitating the relation of the V values to the probability of failure. Figure 2: S-N field fitted with the Weibull model of Castillo-Canteli [6] for the normalized fatigue results for concrete under compression from Holmen [4]. S Number of cycles to failure 0.95 257; 74; 105; 120; 206; 83; 123; 109; 37; 76; 143; 85; 203; 72; 217 0.90 356; 201; 295; 252; 680; 509; 540; 311; 257; 457; 216; 226; 451; 1129; 342 0.825 1246; 2590; 5560; 4820; 2410; 2400; 4110; 3590; 3330; 1460; 1258; 5598; 3847; 1492; 2903 0.75 16190; 27940; 67340; 1860; 12600; 6710; 26260; 50090; 15570; 9930; 20300; 48420; 24900; 36350; 17280 0.675 3294820; 1459140; 1329780; 1241760; 339830; 896330; 280320; 102950; 658960; 1399830; Run-Out; 485620; 366900; 1250200; 11784100 (Run-Out); Run-Out Table 1: Results of the fatigue tests under constant stress range loading for S min =0.05. From Holmen [4]. Load collective and basic loading block used When a continuous load collective is used for fatigue design or fatigue testing as a practical representation of the real random or pseudo-random load history, it may be discretized as a histogram and handled as a multi-step load sequence. In the variable amplitude tests of Holmen’s investigation [4], the histogram called loading model 3, represented in Fig. 3a,