PSI - Issue 64

Francesco Bencardino et al. / Procedia Structural Integrity 64 (2024) 932–943 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

941

10

( ) ( ) 1 f 

1 b b 2 b b + −

k

=

(5)

b

f

Where b f and b are respectively the FRP and concrete width. In this case k b is assumed 1.18 because b f /b<0.25 . With reference to the same C-FRP plate described above (with dimensions of 1.2×100×9800 mm 3 ), used for the rehabilitation intervention, the design strain ε fd of the C-FRP system obtained using the procedure outlined in the CNR-DT 200 R1/2013 results equal to ~0.00278. This value is significantly conservative even compared to the value obtained experimentally on beam A1.1, reinforced with a C-FRP plate only (without anchoring devices), which showed an ultimate strain value of the C-FRP plate, ε fd,exp , equal to 0.0071. In fact, the ratio ε fd,exp / ε fd is approximately 2.55 without the external end anchorages and 3.45 with external end anchorages. In the latter case, the concrete was also able to achieve a maximum compressive strain of 0.0037, higher than the theoretical value of 0.0035 suggested by the European design codes. 3.3. Analysis at ULS: unstrengthened vs. strengthened sections It is interesting to compare the flexural strength of the sections in the unstrengthened and strengthened conditions. The design flexural strength of the C-FRP strengthened RC beam in sections K-K and M-M can be evaluated using the design strain obtained according to the CNR-DT 200 R1/2013 approach ( ε fd =0.00278 ). In addition, the following assumptions were made: (i) no relative slip occurs between the C-FRP plate and the concrete substrate, and (ii) the behavior of the C-FRP system is considered linear until failure and the shear deformation within the adhesive layer can be neglected. Table 5 shows the values of the ultimate bending strength related to pre-strengthening ( M Rd/ex ) and post strengthening ( M Rd/Str ) for section K-K and M-M, respectively, and the corresponding strengthening factor. The maximum tensile strain existing in the RC sections before applying the C-FRP strengthening system was neglected.

Table 5. Values of bending strength for unstrengthened and strengthened RC sections.

Unstrengthened Sections M Rd/ex [kNm]

Strengthened Sections M Rd/Str [kNm]

Strengthening factor M Rd/Str /M Rd/ex

K-K M-M

~87.3 ~301

~117 ~324

1.340 1.076

Overall, it can be seen that even when using a highly conservative design strain value for the C-FRP plate, it is still possible to achieve a relatively good increase in the load-bearing capacity of the structural element. Knowing the ultimate bending strength of the main sections K-K and M-M, with reference to the ULS combination and a linear static analysis, it is possible to evaluate the total factored load that the structure can withstand and subsequently the value of the live load. In this case, the value of the live load that would result in reaching the maximum allowable design strain is approximately 4 times higher than the one that caused the damage. This increase is even greater if the design strain is taken to be the value obtained from the tests carried out on the C-FRP strengthened beam with external end anchorages, which allows a level of utilization of the C-FRP plate strain of approximately 69% (~0.01) of its strain value at failure. The results reported above highlight the importance of considering the presence of anchoring devices when evaluating the design strain of the C-FRP plate. In this context, the conduct of experimental tests plays a crucial role in further (i) refining the currently available design formulae and (ii) increasing the confidence in this type of strengthening intervention. As a result, it may be possible to obtain more representative design values, allowing the designer to consider higher loading levels.