Size effect on the behavior of reinforced concrete deep beams strengthened with CFRP

Deep beams are members considered to have span to depth ratio less than 4. These beams are widely used in different sorts of structures including dams, reservoirs, silos, caissons and high-rise buildings. The cracking mode of deep beams is mainly dependent on their boundary conditions. Due to the rule of shear failure, deep beams are designed against shear. So, strengthening and repairing these beams has always been important to improve shear resistance. One of the applied methods is the use of CFRP fibers for repairing and strengthening deep beams. These fibers can be fabricated in the form of strips, sheets and rebars. Due to the constructional limitations, CFRP strips are frequently installed on the external surface of beams. For this reason, the failure of strengthened beams coincides with debonding of CFRP strips. The former experiments indicate that strengthening deep beams with CFRP strips is useful for improving their behavior. These experiments also indicated that parameters including strengthening angle, shear span to depth ratio and the method of CFRP installation can affect the strength increment due to CFRP. One of the other remarkable parameters that affects the behavior of reinforced concrete beams is size effect. This parameter matters when the geometry of struts and nodal zones remains slender in deep beams. To assess the intensity of size effect in deep beams, the force strength of beam must be normalized based on the compressive strength of concrete and the beams sections area. This study was conducted to investigate the effect of CFRP strengthening on the size effect on deep beams. It was aimed to use explicit dynamic analysis method in Abaqus software so as to model and analyze 53 CFRP-strengthened deep beams with evaluation of previous experiments. In this method, due to the absence of excessive iterations within each analysis step, the number of analysis steps is increased. The so-called method is also appropriate for simulating quasi static models. To reach the purpose of study, the specimens of three different experiments were modeled and analyzed to evaluate the assumptions of numerical modeling. After the evaluation conditions were satisfied, 53 deep beams were modeled in Abaqus software. The specimens were subjected to two incremental point loads and were divided into four-member groups with depths of 400 mm, 600 mm, 800 mm and 1000 mm. The beams shear span to effective depth ratios are 0.5, 1 and 1.5; The compressive strength of concrete also varied from 24.8 MPa to 35 MPa. Since changing the width of deep beams does not affect the intensity of size effect, the beams width was considered constant and equal to 80 mm.The results of the study indicate that strengthening deep beams with CFRP strip or sheet is suitable for reducing the size effect; In addition, increasing compressive strength of concrete and keeping the loading plate constant can amplify size effect of deep beam. Increasing shear span to effective depth ratio of beam caused the size effect to be decreased. Strengthening deep beams with both angles of 45 and 90 degrees was appropriate for decreasing deep beams size effect.