PSI - Issue 41

Andrea Pranno et al. / Procedia Structural Integrity 41 (2022) 618–630 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Tab. 4: MAC indicator evaluated for the different damage levels and with reference to the undamaged configuration.

L1’-L2’ 0.0000 0.0208 0.9998 0.0942 0.0347 L1’-L4’ 0.0000 0.0159 0.9972 0.0849 0.0448 L1’-L6’ 0.0000 0.0169 0.9965 0.0834 0.0484 L1’-L8’ 0.0000 0.0168 0.9969 0.0863 0.0460 L1’-L10’

L1’-L1’ 0.0000 0.0234 1.0000 0.0976 0.0320 L1’-L3’ 0.0000 0.0166 0.9981 0.0869 0.0418 L1’-L5’ 0.0000 0.0162 0.9966 0.0834 0.0476 L1’-L7’ 0.0000 0.0173 0.9969 0.0854 0.0468 L1’-L9’ 0.0000 0.0162 0.9965 0.0858 0.0466

1.0000 0.0128 0.0000 0.0010 0.0024 0.9989 0.0180 0.0000 0.0011 0.0025 0.9980 0.0199 0.0000 0.0012 0.0026 0.9975 0.0208 0.0000 0.0012 0.0027 0.9968 0.0221 0.0000 0.0012 0.0028

0.0128 1.0000 0.0234 0.0047 0.0264 0.0109 0.9973 0.0262 0.0018 0.0240 0.0096 0.9952 0.0242 0.0011 0.0227 0.0089 0.9956 0.0239 0.0014 0.0232 0.0083 0.9948 0.0253 0.0014 0.0230

0.0010 0.0047 0.0976 1.0000 0.4032 0.0006 0.0054 0.1235 0.9945 0.4001 0.0007 0.0034 0.1436 0.9877 0.3432 0.0008 0.0017 0.1471 0.9839 0.3264 0.0009 0.0018 0.1465 0.9825 0.3267

0.0024 0.0264 0.0320 0.4032 1.0000 0.0024 0.0341 0.0441 0.3524 0.9933 0.0020 0.0363 0.0315 0.3717 0.9919 0.0019 0.0357 0.0262 0.3690 0.9887 0.0019 0.0352 0.0242 0.3552 0.9829

0.9999 0.0145 0.0000 0.0011 0.0024 0.9984 0.0191 0.0000 0.0011 0.0025 0.9977 0.0204 0.0000 0.0012 0.0027 0.9972 0.0215 0.0000 0.0012 0.0027 0.9962 0.0231 0.0000 0.0012 0.0028

0.0123 0.9997 0.0254 0.0037 0.0261 0.0102 0.9959 0.0253 0.0013 0.0231 0.0091 0.9952 0.0235 0.0011 0.0228 0.0086 0.9953 0.0247 0.0014 0.0232 0.0077 0.9937 0.0258 0.0012 0.0228

0.0008 0.0052 0.1039 0.9990 0.4161 0.0007 0.0047 0.1339 0.9919 0.3740 0.0008 0.0021 0.1497 0.9836 0.3231 0.0008 0.0017 0.1455 0.9839 0.3298 0.0009 0.0021 0.1439 0.9805 0.3253

0.0026 0.0290 0.0398 0.3801 0.9985 0.0022 0.0357 0.0389 0.3577 0.9924 0.0019 0.0364 0.0270 0.3792 0.9906 0.0019 0.0356 0.0260 0.3594 0.9858 0.0019 0.0350 0.0225 0.3489 0.9789

0.0000 0.0161 0.9960 0.0855 0.0478

Fig. 5. CDF evaluated for the mode shapes 1, 4, 6, and 7 for all the investigated levels of damage during the unloading phase

4. Conclusions Static and dynamic loads applied monotonically and cyclically can damage reinforced concrete beams commonly used in girder bridges by inducing diffuse cracking effects. Typically, the damage will extend over a larger area as the load level increases until it affects the entire system. Therefore, it is essential to develop a damage model that can