PSI - Issue 68

Aseel Salameh et al. / Procedia Structural Integrity 68 (2025) 166–172 A. Salameh et al. / Structural Integrity Procedia 00 (2025) 000–000

169

4

τ(x) =E ! b ! t ! " " # $ !

(1)

Since strain gauges are distributed at a segment of the CFRP sheet, τ( ) is rewritten discretely (Eq. 2): ( ) = 0.5 % % % [( & − &'( )( & − &'( ) + ( &)( − & )( &)( − & )] The slip between the concrete and CFRP sheet is cumulative and equal to the change in the slip value with the change in the segmental distance which is derived considering the FRP deformation. / = − , note that concrete deformation could be neglected concerning the FRP deformation. Therefore, integrating the FRP deformation concerning the segmental distances. s(x) = s(0) + ∫ ε ! (x)dx (integration from 0 to x) (3) Then, ( ) is rewritten as to calculate the cumulative slip along the proposed segmental distance considering the strain gauges along the segment, ( ) = (0) + 1/2[( & − &'( )( & − &'( ) + ( &)( − & )( &)( − & )] , i from 0 to n (4) Following Eqs. 1-4, three bond-slip models were calculated as shown in Fig. 3 for the three specimens. (2)

0 1 2 3 4 5 6 7 8 0 0,05 0,1 0,15 0,2 Stress (MPa) Slip (mm)

0 1 2 3 4 5 6 7 0 0,05 0,1 0,15 0,2 Stress (MPa) Slip (mm)

0 1 2 3 4 5 6 7 0 0,05 0,1 0,15 0,2 Stress (MPa) Slip (mm)

(a) CB-01

(b) CB-02

(c) CB-03

Fig. 3. Calculated bond-slip models from experimental investigation.

The key parameters for the three models τ max , S max , and S 1 are summarized in Table 1.

Table 1. Key parameters of bond-slip models.

Specimen

τ max (MPa)

S max (mm)

S 1 (mm) 0.0896

CB-01 CB-02 CB-03

6.348 6.768

0.2

0.167 0.196

0.017

6.3988

0.0516

Avg.

6.504933

0.187667

0.052733

3. Finite element analysis A three-dimensional (3-D) nonlinear finite element (FE) model of an externally strengthened concrete prism with CFRP laminate was developed in ANSYS v19.2 (ANSYS, 2019). The model is described in the following subsections.