# Retrofitting of Steel Structures with CFRP: Literature Review and Research Needs
## 4 Numerical Analysis  
Computational methods present a cost-effective tool for a better understanding of the performance of the retrofitted components. In this regard, many numerical studies have been proposed to investigate the bond behavior of the retrofitted elements with CFRP. [PERSON] [39] investigated a numerical study on the bond behavior of CFRP/steel joints using ANSYS (2009) software for NM and UHM CFRP by analyzing double-strap joint and doubly reinforced steel plates. An eight-node element of SOLID45 was used due to its large deflection and strain capabilities. The CFRP layer and adhesive were modeled as a single layer of elements. The results showed that the numerical element strains are in good agreement with experimental results except at the gap of the joints. Furthermore, the tensile stress obtained from finite element (FE) analysis is less than the experimental ones for ultra-high modulus CFRP. In this study, steel beams strengthened with UHM CFRP were also modeled. Contrary to CFRP/steel joint models, 4-node SHELL181 elements were utilized to simulate beams to reduce the computational costs. However, the proposed model could not predict the failure of the beam or the laminate for strip panel configuration as a result of the simplified assumptions of the SHELL181 element. [PERSON] and [PERSON] [60] modeled CFRP/steel joints using ABAQUS software, utilizing CPE4R elements for the CFRP and steel adherents and COH2D4 elements for the adhesive layer. The tie constraint, used in ABAQUS to establish perfect interface connection, was applied to the CFRP/adhesive and steel/adhesive surfaces. The numerical findings aligned well with experimental results in terms of the ultimate load, and bond-slip relationships. [PERSON] et al. [46] presented a numerical investigation of the effect of high load rates on the bond behavior of CFRP/steel double strap joints using ABAQUS for LM and NM CFRP. The C3D8R, SC8R, and COH3D8 elements were utilized to model steel plates, CFRP laminate, and the adhesive layer, respectively. The tie constraint was also applied to the adhesive layer with steel and CFRP. It was found that the effective bond length for specimens subjected to high loading rates was shorter compared to the specimens tested under quasi-static loading. The flexural behavior of steel beams strengthened with CFRP sheets using ANSYS was studied by [PERSON] et al. [18]. SOLID186 elements were selected to model steel and CFRP sheets. To model the epoxy layer, the INTER204 element was used. The adhesive layer was defined as linear elastic material and the mixed-mode bi-linear cohesive zone model (CZM) was selected to model the bond between steel and CFRP. The parametric study showed that the CFRP system is very efficient in strengthening compact mono-symmetric sections, whereas its effect is very negligible for non-compact sections. The CFRP/steel double overlapped bonded joints were simulated by [PERSON] et al. [77]. It was revealed that the initial stiffness of the load versus slip relationship increases with the elastic modulus of CFRP laminate. [PERSON] et al. [106] carried out a numerical study on the static behavior of the steel beams strengthened with CFRP strips. A standard two nodes beam element was applied to model the beam and a standard eight-node plane stress element was selected to model CFRP strips as well as the adhesive layer. To ensure the compatibility of the deformations of the beams and strips, multipoint constraints were imposed between the beam nodes and the corresponding adhesive nodes. The adhesive stresses estimated by the FE model were in good agreement with their counterparts obtained from the analytical approach. A 2D FE model was proposed by [PERSON] [122] to investigate the debonding strength of steel beams strengthened with CFRP. To this end, the eight-node element with two degrees of freedom at each node was utilized. Furthermore, it was assumed that the CFRP material is isotropic.