International Concrete Abstracts Portal

With discussion by E. Burnett, D. B. Beal, R. H. Wood, and A. L. L. Baker. The moment-rotation results are presented of tests on beams carried out by a number of laboratories working under the auspices of the European Concrete Committee. Idealized diagrams are plotted for comparison, and the basis of these diagrams is given as defining fundamental moment curvature relationships which may be used in ultimate load calculations of frameworks. A simple trial and adjustment method of design is explained in which compatibility of bending moment values and end-slopes can be established by joint by joint procedure. Simplification is effected by separating the sway angle from the total rotation at hinges. This simplification can either be made by joint trial and adjustment procedure or by using the Miiller-Breslau compatibility equations, separating the sway angle, which greatly simplifies these equations.

With discussion by Chan W. Yu and M. T. Soliman, and Alan H. Mattock. Limit design theories for reinforced concrete statically indeterminate structures require a knowledge of the rotational capacity of hinging regions in reinforced concrete members. An investigation is reported of this rotational capacity in reinforced concrete beams. Thirty-seven beams were tested involving the following variables: concrete strength, depth of beam, distance from point of maximum moment to point of zero moment, and amount and yield point of reinforcement. The data are analyzed and a method is proposed whereby the rotational capacity of a hinging region in a reinforced concrete beam may be calculated.

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.