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SP12 Contains the proceedings of the 1964 International Symposium on Flexural Mechanics of Reinforced Concrete. In addition to providing a more basic understanding of the complex, non-ideal flexural behavior of reinforced concrete, this publication aims to further both immediate and long-range objectives in improving the analytical and statistical basis for the flexural design of reinforced concrete.

With discussion by Edward G. Nawy, H.A. Sawyer, M.Z. Cohn, and E.F.P. Burnett and C.W. Yu. An attempt is made to evaluate our present knowledge with regard to the analysis and design of reinforced concrete linear structural systems at ultimate load. The fundamental difference between the moment curvature concept and moment rotation concept is emphasized and discussed in detail. The authors have attempted to outline previous significant work, to underline a few basic principles, bearing in mind the difference between these two concepts, and to indicate the present extent of our knowledge of this subject with an appreciation of the assumptions and simplifications that are entailed. Readers are assumed to have some basic knowledge of some of the better known work on the subject, such as Sawyer’s or Baker’s work.

With discussion by Theodore Zsutty, Jack R. Benjamin, C. Allen Cornell, and Milik Tichy and Milos Vorlicek. Because the ultimate strength and deformation ability of critical sections are random variables, the ultimate strength of a structure must likewise be a random variable. If the structure is subjected to load from one source and there is only one possible collapse mechanism, the determination of the ultimate strength ZU of the structure is simple. If the structure is subjected to load from one source but there are m possible collapse mechanisms, it becomes necessary to analyze the structure with the aid of equations of the type given herein. The ultimate strengthZUj, for j = 1, 2, . . . , m of the structure is determined by means of each of these equations assuming the occurrence of the j-th collapse mechanism. The probability pUj that the structure will change into the jth mechanism may be ascertained for a definite value of the load for each random variable ZUj But the actual probability of failure must be expressed with the aid of the so-called conditional probabilities since the individual mechanisms are not always statistically independent. If the structure is subjected to load from v sources and there are m possible collapse mechanisms an equation for the jth mechanism will graphically be represented by an interaction diagram. For a given population of structures, identical according to the design, there exists a number of possible combinations of load with a corresponding probability of failure pU. Geometrically speaking, they are points in the v - dimensional space. Their locus is the so called boundary of the safe domain IImin. When the deformation ability of a structure is considered, the system of equations forms the starting point. In this instance the random variable Zuj is a linear combination of ultimate moments MUi and the ultimate plastic rotation 0U of the section. The statistical solution is analogous with the previous one. It may be demonstrated that the variability in ultimate strength of a redundant structure is lower than that of a statically determinate one in all cases. Consequently, the application of the statistical method must result in savings of material in redundant structures.

With discussion by Milik Tichy and Milos Vorlicek; and Herbert A. Sawyer, Jr. Because structural failure generally occurs in successively more severe stages at successively less probable loads, design should ideally account for all stages and be based on comprehensive analysis utilizing a comprehensive, non-linear, force-strain relationship. The criterion for optimum design, using the failure-stage-versus-load profile, is derived. For frames, a method of comprehensive analysis based on a multilinear moment-curvature relationship, using critical moments and "plasticity factors," is presented. Procedures and the relative economics of comprehensive design and its special cases, elastic, plastic, and ultimate strength designs, are compared. A bilinear design procedure for concrete frames, based on two failure stages, is presented.

The object of the paper is to provide a simple, rational technique to check the rotation compatibility of plastic hinges in limit designed reinforced concrete continuous beams proportioned basing on optimum considerations. The relationship between the plastic adaptability and the rotation compatibility is outlined, expressing conveniently both the inelastic rotations and the rotation capacities of critical sections. It is concluded that the compatibility requirement implies only limited adaptability tobe used in the design of concrete structures. Since a similar conclusion can be derived with regard to the serviceability conditions of limit designed structures, adoption of convenient upper bounds for the redistribution factors (or lower bounds for the yield safety parameters) of critical sections will implicitly provide adequate solutions for ultimate safety, compatibility, and serviceability as well. From the practical viewpoint, the significant result follows that for given ( 1) properties of materials, (2) loading conditions, and (3) amount of accepted redistribution, the rotationcompatibility condition to an upper limitation of the steel percentages at critical sections.