This study evaluated the effectiveness of carbon fiber-reinforced polymer (CFRP) composites in strengthening RC beams for a simple span overhanging from both ends and subjected to equal concentrated forces at each end. This innovative loading configuration allows for investigating the performance of CFRP composites under pure moment within the middle span and ensuring continuity of the moment over the supports, which cannot be captured using the classical simple span with four-point loading configuration. A nonlinear finite-element analysis (NLFEA) using Abaqus software was carried out to accomplish the objectives of this study. The NLFEA models were verified initially based on independent experimental results from the literature to calibrate the NLFEA models in terms of the material constitutive models, boundary conditions, and meshing. Then 12 NLFEA models were created with different strengthening schemes of CFRP strips, varying in terms of length and number of layers, in addition to a control beam. All the evaluated RC beams were similar in terms of length and cross-sectional dimensions, material properties, and steel reinforcement. The results revealed that the developed NLFEA models can reasonably simulate the flexural behavior and failure mode of the studied RC beams, which are significantly affected by the configuration and length of the CFRP strips. The results also indicated that it is essential to extend the CFRP strips from the middle span toward the overhanging span to provide continuity and allow the CFRP strips to contribute effectively to the flexural strength.