Issue 52

H. EL-Emam et al., Frattura ed Integrità Strutturale, 52 (2020) 197-210; DOI: 10.3221/IGF-ESIS.52.16 205 N UMERICAL M ODEL he three dimensional (3-D) finite element (FE) analysis software ANSYS [28] was used for the analysis of the reinforced beams strengthened with NSM GFRP rods. Fig. 9(a) presents the modeled beam, supports and loading plates. The dimensions of the full-size beams were 2300 mm × 200 mm × 300 mm and the span between the supports was 2200 mm, while, Fig. 9(b) shows the structural model and mesh used in this study. The element size has been adopted to be 25 mm based on the mesh sensitivity. Solid element (Solid 65) has been used to define the 3-D of the structural reinforced concrete. Solid 65 able to crack in tension and crush in compression. This element was simulated by 8-nodes and three translational degrees of freedom at each node. However, the steel reinforcement was modeled using LINK 180. Furthermore, 3-D structural solid element (Solid 45) was used to model the loading plate and supports. Tab. 2 presents the mechanical properties of the materials used in the numerical modeling. Material Properties Unit Data Concrete Compression strength MPa 31.0 Tensile strength MPa 2.0 Young’s modulus, E c MPa 17500 Passion’s ratio 0.2 Main Steel Young’s modulus, E s MPa 196000 Yield stress, f y MPa 480 Passion’s ratio 0.2 Stirrups Young’s modulus, E s MPa 196000 Yield stress, f y MPa 250 Passion’s ratio 0.2 GFRP rod Young’s modulus MPa 56000 Tensile ultimate strength MPa 750 Passion’s ratio 0.2 Epoxy resin Young’s modulus MPa 3780 Tensile yield strength MPa 30 Passion’s ratio 0.35 Table 2: Material properties used in the numerical study. C OMPARISON OF EXPERIMENTAL AND NUMERICAL RESULTS Load – Deflection Curve he load-deflection curves which obtained for Group-B and Group-C from the experimental results and the FE models are shown in (Fig. 10). It is clear that the experimental and numerical load-deflection results were in good agreement. So, the FE models demonstrated the ability to simulate the behavior of reinforced concrete beams strengthened by the NSM technique. The simulation perfectly reflected the bonding between concrete, steel reinforcement and strengthening by NSM-GFRP rods. Moreover, the FE models result in confirming to affect the flexural capacity of beams strengthened with alteration of the concrete cover. With the aid of Fig. 6, it can be concluded that the effect of increasing the amount of tensile reinforcing steel on the efficiency of strengthened beams is more pronounced in the case of short GFRP bar length. Strain distribution on along NSM GFRP bars Fig. 11 illustrates strains distribution along the GFRP bars by FE models compared to the strains measured experimentally. Good agreement between the experimental and predicted numerically GFRP rods are observed. T T