Direct design of hollow reinforced concrete beams. Part 1: Design procedure

This paper, Part I, presents a general 'direct design procedure' for the design of reinforced concrete hollow beams subjected to a combined load of bending, shear and torsion. Elastic stress field in conjunction with Nielsen's twodimensional yield criterion for reinforced concrete subjected to in-plane forces were used in the design of reinforcement. This procedure is based on and satisfies the lower bound theorem of the classical theory of plasticity. The main features of this procedure are the precluding of the use of empirical equations as is the case with existing codes of practice and in addition to satisfying the requirements of the theory of plasticity it reduces the ductility demand assumed by this theory. Comparison between the direct design procedure and the truss analogy showed that the direct design procedure leads to steel requirements close to those of the truss analogy when the angle of inclination of the struts is 45°. The direct design procedure produced much less reinforcement than the American Concrete Institute and the British Standards Institute codes.