Effectiveness Factor of Concrete in Continuous Deep Beams

An upper-bound analysis of reinforced-concrete continuous deep beams is presented. The concrete is assumed as a rigid–perfectly plastic material obeying the modified Coulomb failure criteria with zero tension cutoff. Two collapse modes are considered, each idealized as an assemblage of rigid blocks moving in plane, separated by yield zones. These zones are idealized as lines, the limiting case of narrow zones of failing material undergoing very high strains. Calibration of the computed failure loads against the experimental failure loads for 20 test beams produces the value of the effectiveness factor for concrete in compression for this type of structure. The effectiveness factor may be allowed to vary with the concrete strength and the amount of web reinforcement, but this provides little improvement over the adoption of a uniform value. The effect of the horizontal and vertical web reinforcement on the load capacity is mainly influenced by the shear span to depth ratio. The deeper the beam, the less effective the vertical web reinforcement, and the more effective the horizontal web reinforcement.