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Along with the recent developments in the field, certain doubts were expressed on the practical value of limit design in structural concrete, with particular reference to the following aspects: 1. Limited redistribution in concrete structures due to the variable strength design of members. 2. Lack of economic advantages if additional reinforcement is required at plastic hinges to increase their ductility. 3. More critical service conditions than for structural steel. 4. Special service considerations leading to more complicated analytical work. Similar doubts marked the discussions of the CEB Committee XI at the Monaco Session of the European Concrete Committee in 1961. All these problems can, probably, be summarized as follows: Are there any reasons at all for developing nonlinear analysis and design methods for concrete structures? This writer believes the only reasonable answer to the above question is a straight "of course"! With this he assumes an analysis or design method obviously has to reflect as closely as possible the actual behaviour of the structure. The arguments to follow are but a brief justification of this answer, illustrating the reasons for a nonlinear design of structural concrete from both theoretical and practical considerations.

The purpose of this paper is to review the five papers on experimental investigations presented in Session II, including the prepared and extemporaneous discussions to these papers. An attempt will be made to draw whatever conclusions the results of the studies suggest.

The usage of a high speed digital computer in the investigation of long concrete columns as integral parts of building frames is outlined. Extensive use of the computer was made in both the interpretation of data obtained in physical testing and in analytical studies utilizing idealized mathematical models. Numerical procedures were facilitated by development of a rapid and versatile method for obtaining the relationship between axial load, bending moment, and curvature for rectangular reinforced concrete members. A general program is presented which simulates the behavior of a rectangular frame by use of the method of successive approximations and with predictor and corrector functions based on the axial load-moment-curvature characteristics of both the column and its restraining frame members. The method recognizes the nonlinear characteristics of the problem and considers inelastic action, axial load effects, and the varying reduction instiffness of reinforced concrete members. Verification of many of the analytical procedures was obtained in a series of tests of isolated eccentrically loaded long columns under statically determinate load conditions. A series of tests of columns as integral parts of frames indicated that the analytical procedure can predict the mode of failure and type of long column action to be expected. Quantitative accuracy was shown to be reasonable with major discrepancies directly attributable to shortcomings in the failure criteria postulated for reinforced concrete sections. The analytical procedure showed itself to be a promising tool available for further exploration of long column behavior.

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.

The chairman of this symposium has asked the writer to prepare a general and critical discussion of inelastic reinforced concrete design. This forced him to study more thanadozenof the preprinted papers, in considerable detail, in an attempt to assess the present state of knowledge and of the art.