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Mathematical statistics algorithm in the bending performance test of corroded reinforced concrete beams under fatigue load

Zhengjian Li
Zhengjian Li
 et 
Lifeng Li
Lifeng Li
   | 30 déc. 2021
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Publié en ligne: 30 déc. 2021
Pages: 695 - 702
Reçu: 17 juin 2021
Accepté: 24 sept. 2021
DOI: https://doi.org/10.2478/amns.2021.2.00142
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© 2021 Zhengjian Li et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

RC beam with diagonal cracks. RC, reinforced concrete
RC beam with diagonal cracks. RC, reinforced concrete

Fig. 2

The stress balance condition and stress Mohr circle of the tiny body
The stress balance condition and stress Mohr circle of the tiny body

Fig. 3

Schematic diagram of beam principal stress and force balance
Schematic diagram of beam principal stress and force balance

Fig. 4

The distribution of experimental test values in the confidence interval of the probability model
The distribution of experimental test values in the confidence interval of the probability model

Fig. 5

The distribution of the calculated value of the deterministic model in the confidence interval of the probability model
The distribution of the calculated value of the deterministic model in the confidence interval of the probability model

Fig. 6

Calibration of the calculation accuracy of the deterministic model
Calibration of the calculation accuracy of the deterministic model

Basic parameters of corroded RC beams and test values of shear capacity test

Numbering b/mm h/mm λ ρ1/(%) fvy/Mpa Vn1 Vn2 Vn3 Vn4
1 100 175 1.5 1.94 0.44 49.71 52.87 23.68 27.07
2 100 175 2.5 1.94 0.44 50.71 48.93 21.47 38
3 100 175 1.5 1.94 0.44 59.92 50.16 22.78 26.69
4 100 175 2.5 1.94 0.44 52.44 48.96 20.21 37.92
5 100 175 2.5 1.94 0.44 54.05 51.79 20.75 38.84
6 100 175 1.5 1.94 0.44 61.91 58.13 22.99 28.22
7 100 175 2.5 1.94 0.44 53.28 54.07 21.05 39.91
8 100 175 2.5 1.94 0.44 53.25 49.48 20.22 38.7
9 100 175 2.5 1.94 0.44 52.79 48.96 20.21 38.21
10 100 175 2.5 1.94 0.44 53.65 50.5 20.5 38.7
11 100 175 1.5 1.94 0.44 62.65 65.86 22.74 29.84
12 100 175 1.5 1.94 0.44 63.53 67.28 22.99 30.02
13 100 175 1.5 1.94 0.44 65.29 74.67 22.99 31.97
14 100 175 2.5 1.94 0.44 53.73 48.96 20.21 38.98
15 100 175 1.5 1.94 0.44 66.06 76.02 23.19 32.12
16 100 175 1.5 1.94 0.44 66.76 77.86 23.36 33.26
17 120 200 2 1.92 0.32 73.84 52.86 30.01 39.34
18 100 175 2.5 1.94 0.44 58.13 56.18 21.66 41.39
19 100 175 1.5 1.94 0.44 68.06 77.52 23.36 33.53
20 120 200 2 1.92 0.32 77.74 73.12 30.32 42.34

Probability model parameter K − S test D value

Parameter β1 β2 β3 β4
Lognormal distribution 0.032 0.047 0.049 0.05
Weibull distribution 0.067 0.053 0.058 0.059
index distribution 0.055 0.506 0.541 0.56
Gamma distribution 0.031 0.039 0.045 0.048
Normal distribution 0.03 0.037 0.036 0.042
Parameter β5 β6 β7 β8
Lognormal distribution × 0.038 0.064 ×
Weibull distribution × 0.068 0.048 ×
Index distribution × 0.586 0.473 ×
Gamma distribution × 0.037 0.053 ×
Normal distribution 0.031 0.035 0.034 0.025
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