With discussion by P. R. Barnard, S. Stockl, Vitelmo Bertero and C. Felippa, and H. E. H. Roy and Mete A. Sozen. In the application of limit design to reinforced concrete structures, it is essential to know the rotation capacity of the connections. The rotation capacity seldom limits complete moment redistribution in moderately reinforced members subjected to transverse loads. However, it may prove to be a limitation for overreinforced members or members subjected to combined axial and transverse loads. Usually the rotation capacity of the section is governed by the ductility of the concrete which can be improved with the use of transverse reinforcement. This paper reports and discusses the effect of rectangular ties on the load-deformation characteristics of concrete.

With discussion by Peter R. Barnard, HerbertlA. Sawyer,,M.Z. Cohn, and Emilio Rosenblueth and Roger Diaz de Cossio. Failure due to crushing is a case of instability. The traditional nonlinear moment-curvature approach does not hold for systems exhibiting descending (unstable) portions in their force-deformation characteristics. A method based on a moment-rotation approach and an assumed contaminated zone is presented, which takes into account descending branches.

The aim of this work is to predict both the average value and the variance of the creep deflection of reinforced concrete beams under sustained loads. Two quite distinct problems emerge, the determination of a probabilistic model to predict the creep behavior of a concrete prism under axial compression, and the introduction of this description of material behavior into an analysis of the bending of a beam under an arbitrary vertical loading. The model of the creep mechanism of concrete is a simplified version of an earlier model suggested by one of the authors. Stochastic processes, namely varieties of the Markov birth process, are employed to represent both the viscous flow of the cement paste and the delayed-elastic effects caused by fluids -- water and viscous paste-initially trapped within the elastic skeleton of crystals and aggregate. In a manner similar to that developed by another of the authors for the bending of homogeneous beams of stochastically viscoelastic material, the bending of a reinforced concrete beam is formulated. The creep response of a unit length of concrete to a unit stress is assumedto be a stochastic process of the type presented in the first part of the paper. These arguments lead to the desired results, formulas which predict the mean and variance of the deflection of any point on the beam at any time. In addition, spatial and temporal covariance functions are obtained; the latter permits the engineer to take advantage of an early observation of the creep deflection to alter his prediction of later deflections and to reduce the variance of these predictions.

With discussion by Leonard G. Tulin and Kurt H. Gerstle, Ralph M. Richard and Stanley D. Hansen, and Peter R. Barnard. The purpose of this paper is to explain, in the light of recent research into the concrete stress-strain relationship in compression, the flexural behavior of statically indeterminate reinforced conrete beams when loaded to collapse. Based on the concept of concrete as a strain-softening material, it is shown that a length of a beam can continue to rotate when moment is falling off and that rupture will not occur unless the energy balance in the beam ceases to be satisfied. In a comparison between the inelastic behavior of structural steel and reinforced concrete beams, it is shownthat in the latter there is a distinct maximum load which such a beam can withstand; that hinging regions tend to contract rather than spread as in steel; that it is possible for some regions of a beam to be falling off in moment while the total load on the beam is increasing; and that moment redistribution occurs through falloff in moment at some sections as well as through inelastic action. Finally, the possible development of true collapse methods for the analysis or design of indeterminate reinforced concrete beams is discussed.

With discussion by M. Z. Cohn and D.H. Clyde. Existing design code requirements of English-speaking countries permit ultimate strength design. This method replaces the traditional stress analysis criteria of brittle behavior at stress level by brittle behavior at the level of moment capacity, possibly because limit design has been ruled out as unsuitable for rigorous design in reinforced concrete due to the limited ductility of concrete. Nevertheless, ultimate load methods have been proposed which allow limited redistribution by taking advantage of whatever ductility is available at moment level and checking against a deformation criterion. Design methods may be checked for conservatism by reference to the yield criterion (or interaction diagram for reinforced concrete cross sections) and to the theorems of limit design, particularly the lower bound theorem. This provides a necessary but not sufficient check on safety where there is a deformation criterion as well as a stress limit. It is shown that: 1. All methods which use an asymmetrical yield envelope and alternative loading systems can lead to unsafe designs; 2. the ultimate load method can lead to designs which satisfy the limit design uniqueness principle and, hence, violate certain assumptions of the method; and 3. the optimum limit design method, in solutions published by the proposers, violate the lower bound theorem of limit design. The correction of the deficiencies is straightforward in terms of the principles used to examine them but further development of the theories is necessary.