In this study, the feasibility of utilizing locally produced coarse recycled aggregate (RA) from demolition waste in the UAE for structural applications was investigated. A comprehensive literature review on the subject showed that the shear and flexural responses of reinforced beams utilizing aggregate from concrete demolition waste are greatly dependent on the aggregate replacement ratio and the quality of the recycled aggregate. The experimental program in this study consisted of three phases. Phase I focused on the evaluation of the physical and mechanical characteristics of the RA, Phase II addressed the mix design and fresh and hard properties of the concrete, and Phase III dealt with the flexural and shear behavior of structural members. The research involved twelve 150 mm × 300 mm reinforced concrete beams with a length of 1500 mm or 2000 mm that were made with 0% (control), 50%, or 100% recycled coarse aggregate, replacing natural coarse aggregate (NA). Two target concrete compressive strengths, 25 and 35 MPa, were considered in the investigation. The results showed that the recycled aggregates had lower crushing and LA abrasion values by 40% and 18–28%, respectively, whereas the absorption capacity was 40–300% higher compared to the natural aggregate. In addition, the mechanical properties of the concrete made with different replacement ratios (R%) of RA were either similar or slightly less than those of the control mix. The shear beam tests with fc′ = 25 MPa showed that the 50%- and 100%-replacement-ratio beams demonstrated closely matched normalized shear strength values that exceeded their corresponding NA beam by 12.5%, while the shear beam tests with fc′ = 35 MPa showed that the NA beam exhibited normalized shear strength surpassing the 50% RA and 100% RA beams by 12.5% and 17.5%, respectively. In the flexural beam tests, the flexural strength exhibited minimal disparities for the beams that shared the same RA% but differed in their compressive strength targets, and overall, the variation in the RA% had a marginal impact on the flexural strength of the beams. Further, an increase in the RA% corresponded to an increase in the shear ductility index, which was in contrast with the findings on the flexural ductility index. Furthermore, predictions of flexural strength using the ACI318-19 code and shear strength using the strut-and-tie model yielded comparable results to the experimental ones.