PSI - Issue 22

404 V.M.G. Gomes et al. / Procedia Structural Integrity 22 (2019) 401–406 V.M.G. Gomes et al. / Structural Integrity Procedia 00 (2018) 000 – 000 where = ( ) and = ( ) , representing the stress range and the number of cycles to fatigue failure. Besides that, it is considered that the dependent variable follows a normal distribution, with a constant variance, along with the variation interval of independent variable, . It is noted that if the linear statistical model is considered, no runouts and/or suspended test data is considered. The rectilinear confidence band is defined, respectively as follows: = − ∙ ± ∙ = ( ± ∙ ) + ∙ (2) where is usually a positive integer number, determining the probability a failure occurring within the confidence intervals of 68.2%, 95,4%, and 99% for = 1 , = 2 , and = 3 , respectively. Finally, the value of the standard deviation is determined by the square root of the variance 2 . 2 = ∑ ( − + ∙ ) 2 =1 − 2 (3) 3. Results and Discussion The fatigue data was used to create S-N curves and compare them with S-N curves provided in Eurocode 3. Fatigue S-N curves were obtained from the statistical method in accordance with ASTM E739-91 (2004). Besides, fatigue failure modes were also compared among different test series. In these comparisons, the experimental S-N curves for single M12 snug tight bolted joints with punched holes is taken as reference. 4

[kN] ∆ [MPa] [cycles] m ∆ [MPa] 18 122 [1.5E6; 5.0E6]

Table 2. Summary of fatigue results, including data and S-N curve parameters in accordance with EC3. Test Series BC Type G Area mm 2 Preload Type Type M. Hole

S S S S S S S S

80×2 80×2 80×2 70×2 80×2 80×2 80×2 80×2

SN SN SN SN SN SN PR PR SN SN SN SN SN

P P P P P P P P P P

0.1 0.1 0.1 0.1 0.3 0.5 0.1 0.1 0.1 0.1 0.1 0.1

S_P_R01_SN

22 26 26 26 26 26 22 50 60 50 60

150 177 208 138 177 150 170 205 170 205 98

[5.0E5; 1.4E6] [7.6E4; 1.5E5] [1.6E5; 4.8E5] [2.8E6; 4.3E6] [7.3E5; 1.0E6] [1,3E6;1,9E6] [6.6E5; 9.1E5] [2,1E5; 2,2E5] [3.2E5; 7.1E5] [2,6E5; 8,3E5] [6.4E4; 1.7E5]

8.03

127

S_P_R01_SN_RA

- - -

- - -

S_P_R03_SN S_P_R05_SN S_P_R01_PR

4.86

144

M_P_R01_SN

M M M M

130×2 130×2 130×2 130×2

9.02

225

M_D_R01_SN

D D

7.92

181

EC3 Detail: Class 90 90 BC Type - Bolted Connection Type; G Area - Gross Cross-Section Area; Type M. Hole – Type of hole manufacturing process; – Maximum Force [kN]; ∆ – Net Stress Range [MPa]; - The number of cycles to fatigue failure [cycles]; – Stress R-Ratio; S – Single; M – Multiple; SN – Snug Tight; PR – Preloaded; P – Punched; D – Drilled; RA – Reduced Area. 3.1. S-N Curves All experimental data the respective mean S-N curves are potted in Fig 2(a). The same information is included in the Fig 2(b), but with the respective confidence bands for = 1, 2, 3 , in accordance with equation 2. Fig. 2(a) also compares the fatigue test data and mean S-N curves (with different parameters) with the S-N curve suggested by Eurocode 3 for bolted joints without preloaded blots. Table 2 informs about the obtained fatigue lives and the presented S - - - - - - 3