PSI - Issue 22

6

H. Daou et al. / Procedia Structural Integrity 22 (2019) 17–24 H. Daou, W. Raphael, A. Chateauneuf, F. Geara/ Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 5. Histogram of moment values

2. Results and discussions

Table 3. Values of the flexural moment and the long term deflection based on deterministic and probabilistic analyses

Probabilistic analysis Minimum value

Deterministic analysis

Average value

Maximum value

Deflection (cm)

9.09

5.02

9.19

14.8

Moment (N.m)

153721

115500

153520

191660

As mentioned previously, the aim of this study is to assess the structural safety of this complex structure using probabilistic approach taking into consideration uncertainty on material properties and loads on the flexural moment and the long-term deflection. For that, a finite element model is performed using Ansys and probabilistic analysis is then performed using a combination of RSM and MCS and taking into consideration the density, the compressive strength and the modulus of elasticity of concrete, the temperature and the wind velocity as variables (see Table 2). Fig. 3 shows the results of the flexural moment of the terminal’s shell at the ultimate state based on the deterministic analysis. The flexural moment and deflection values are calculated based on probabilistic analysis by performing 10 7 Monte Carlo simulations exploiting the response surface (see Fig. 4). The histogram of the moment values obtained is presented in Fig. 5. Table 3 summarizes the values of the flexural moment and the long term deflection based on deterministic and probabilistic analyses. The probabilistic analysis shows that the values of deflection and moment exceed the deterministic values obtained by 63% and 25%, respectively. According to EC2, the required reinforcement ratio based on deterministic analysis is 0.65, which is greater than the existing ratio in the sell (0.15%). Therefore, the reinforcement of the terminal’s shell is not adequate as the calculated flexural moment requires more reinforcement than the existing one. Based on the probabilistic analysis and to have a probability of failure that does not exceed P f target =8.539x10 -6 , the reinforcement ratio should be calculated for moment value M where P(moment>M)=P f ; in our case M = 184747 N.m. Thus, in order to have a reliable and safe structure, the required reinforcement ratio should be equal to 0.79 which is greater approximately by 12% than the reinforcement