W. Zhang/M. Wu/J. Zhu · Evaluation of vehicular dynamic effects for the life cycle fatigue design of short-span bridges
sive environments and the fatigue life for the bridge could be reduced accordingly. Since the fatigue strength exponent should be treated as a random variable, m is assumed to follow a normal distribution in order to improve our understanding of its effects on the DALC. As listed in Table 4, the mean values of the fatigue strength exponent m are set to 3.00 and 3.26, and the COVs are set to 0.00, 0.025, 0.05, 0.075 and 0.10. Similarly, the chi-square tests for the revised equivalent stress range of the whole design life Slc were carried out and the results are listed in Table 4 as well. As shown in the table, when the COV of m is # 0.05, normal distribution is not acceptable for Slc in many cases; only the lognormal distribution is acceptable. The effects of a random fatigue strength exponent m on the DALC are shown in Fig. 3. As shown in the figure, the COV has significant effects on the DALC values and the DALC value could increase by 1.2 when the COV increases from 0.00 to 0.10 for a mean m value of 3.26. In addition, when the mean value of m increases from 3.00 to 3.26, the DALC values increase by about 0.2 for the same COV value of m. Overall, the DALC values will be influenced significantly by the fatigue strength exponent m. Higher mean values and/or higher derivations of m will lead to a larger DALC. Therefore, the fatigue strength exponent m could be a very important parameter for obtaining a reasonable DALC in bridge fatigue design.
Fig. 2. Effects of fatigue strength exponent and corrosion level on DALC Table 4. Chi-square tests for and COVs of m
Slc
with different mean values
Mean value of m COV of m
3.00
3.26
Fig. 3. Effects of random fatigue strength exponent m on DALC
4.3.3 Corrosion parameters Corrosion parameters A and B are obtained from experiments and uncertainties could be introduced into the corrosion model and the DALC. In the present study, to consider the random effects, the corrosion parameters A and B are assumed to follow a normal distribution with the mean values and COVs shown in Table 1. Four cases were defined to calculate the DALC value: both of the parameters A and B are deterministic (case AB-00), only parameter A is random (case AB-10), only parameter B is random (case AB-01), and both parameters A and B are random (case AB-11). Three corrosion environments were adopted for the structural components: rural (low corrosion level), urban (medium) and marine (high). For all of the cases, the fatigue strength exponent m was set as a deterministic value. The chi-square tests of revised equivalent stress range Slc for a medium corrosion level are listed in Table 5. As shown in the Table, both normal and lognormal distributions are acceptable for Slc in different cases with different corrosion parameters A and B. Table 5. Chi-square tests for Slc with different cases of corrosion parameters A and B (N " normal; LN " lognormal) m 2.9
Case AB-00
Case AB-10
Case AB-01
Case AB-11
N
LN
N
LN
N
LN
N
LN
3.8
2.3
1.4
1.8
11.0
7.3
11.7
7.8
3.0
7.2
6.1
6.4
4.8
7.3
4.9
4.9
3.1
3.1
9.4
8.9
7.7
6.0
9.6
7.9
13.8
10.1
3.2
5.8
4.7
4.4
5.7
6.7
4.3
12.3
9.5
Normal
Lognormal
Normal
Lognormal
3.3
8.1
5.7
10.9
7.6
6.4
4.4
10.3
10.0
0.00
7.2
6.1
9.4
6.8
3.4
8.7
5.5
11.6
8.9
13.9
9.9
4.1
2.1
0.025
5.0
5.3
9.3
8.0
3.5
8.3
5.6
3.6
2.8
5.3
5.8
10.3
6.0
0.05
7.4
4.7
12.1
8.6
3.6
9.6
6.4
9.5
7.8
9.2
6.1
10.9
6.2
0.075
14.1
9.5
11.2
7.2
3.7
11.4
8.5
10.4
7.3
7.8
5.8
9.9
8.0
0.10
16.3
10.8
16.9
11.0
3.8
6.4
3.9
11.1
8.4
13.4
9.7
12.1
8.3
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