PSI - Issue 37

Jamal A. Abdalla et al. / Procedia Structural Integrity 37 (2022) 660–667 Abdalla et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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4. Empirical Prediction Models and Results 4.1. Nonlinear Models

Four empirical models were developed for the specimens based on the strengthening mechanisms used, i.e. 0S0W for unstrengthened and 4S2W, 4S4W, 4S8W for strengthened specimens. The prediction models are based on the experimental results obtained from (Abokwiek et al. 2021). These models, shown in Fig. 3, display exponential decay relationship curves between the eccentricity ratio ( E R ) and the axial load-carrying capacity ratio ( P R = P u /P o ) of the specimens, where P u is the predicted ultimate load and P o is the axial load capacity of the concentrically loaded column without NSM-CFRP strips and without CFRP wraps (0S0W). As the eccentricity ratio increases, the axial capacity ratio of the column decreases exponentially. This behaviour is applicable to all strengthening schemes, however it is steeper for the unstrengthened case comparing with the strengthened specimens at lower eccentricity ratio. On the other hand, the behaviour is more or less the same at higher eccentricity ratio for all the tested columns. The correlation coefficient for all prediction models is close to unity in all cases, which implies that the developed models are capable of predicting the axial capacity of uniaxially loaded columns strengthened with NSM-CFRP strips and confined with CFRP wraps. A summary of other statistical performance measures in terms of correlation coefficient ( R 2 ), mean absolute percent error ( MAPE ), root of the mean square error ( RMSE ) , and the normalized mean square error ( NMSE ) are listed in Table 3.

Table 3. Empirical nonlinear models of capacity ratio ( P R ) and eccentricity ratio ( E R ) Specimen Nonlinear Empirical Models R 2

MAPE 7.76%

RMSE 0.0353

NMSE

0S0W (no Strip, no Wrap) 4S2W (4 Strips, 2 Wraps) 4S4W (4 Strips, 4 Wraps) 4S8W (4 Strips, 8 Wraps)

0.997

0.0116

P P P P P P P P

2.485

E R

−

o u o u o u o u

0.940

PR

e

= =

0.999

3.17%

0.0201

0.0022

2.248

E R

−

1.368

PR

e

= =

0.996

8.35%

0.0521

0.0120

2.304

E R

−

1.416

PR

e

= =

0.992

6.35%

0.0604

0.0179

2.205

E R

−

1.362

PR

e

= =