An experimental and analytical study of shear strength of lightly reinforced concrete beams.

Designing for shear in reinforced concrete members is a complicated process. The current empirical shear equations were derived from testing hundreds of beams without a real fundamental underst and ing of shear behavior. This study deals with two primary factors; concrete strength and the amount of web reinforcement. One objective of this study was to extend current truss models to predict the complete shear behavior of reinforced concrete beams with and without web reinforcement. Experiments were undertaken on twenty-five short rectangular beams with low longitudinal reinforcement ratios. The stirrup spacing ranged from 0 (no stirrups) to d/3. The beams were designed to fail in shear. Strain gages were attached to the stirrups and longitudinal reinforcement. Targets were fastened to the side of the beam over half the beam span to measure the strain on the face of the beam. Test results indicated that the conservativeness of the ACI Code equations decreases as the concrete strength increases. An equation for minimum transverse reinforcement as a function of the concrete strength was proposed as an alternative to the existing ACI Code Equation. Having obtained the minimum web reinforcement ratio, the experimental and analytical results are used to define the maximum stirrup spacing. It is recommended to reinforce beams with low longitudinal reinforcement ratio ($\\rho\\sb\\omega < 1\\%)$ with a minimum transverse reinforcement ratio irrespective of the shear stress in the beam. Also, equations for predicting the shear strength are proposed. A modified truss model is developed to give a designer a better underst and ing of the behavior of the members, the force flow inside the member and the contribution of each material in resisting the applied forces. An analysis with the truss model using an angle of inclination between 30 and 35 deg. predicts the failure load reasonably well. A truss model for predicting the failure load for beams without transverse reinforcement is also developed. A 35 deg. angle of inclination gives satisfactory results. To maintain an angle above 25 deg. as suggested by Schlaich, Ramirez, and Rogowsky, a concrete tension member is included in the truss model. Thus, it is possible to predict the failure load for any beam with any shear span to depth ratio.Ph.D.Civil engineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/162280/1/9001593.pd