International Concrete Abstracts Portal

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.

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.

With discussion by Manuel Xanthakis and Leonard L. Jones. This paper reports certain aspects of the work carried out on yield line analysis at four research centres in Great Britain. Conditions governing the upper bound moment distribution along the yield lines are established and from these nodal force values are obtained. The values obtained agree with those given by Johansen but new restrictive rules are revealed. These rules allow the known anomalies in the equilibrium method for patterns with straight line characteristics to be resolved. By direct appeal to the work method it has also been possible to establish new governing rules for nodal forces at yield line junctions which have moments specified in more than three independent directions. Nodal force values which should be inserted at reinforcement discontinuities are also obtained. These new developments are applied to several specific problems in order to demonstrate their use.

With Discussion by D. H. Clyde, M. P. Nielsen, and R. H. Wood. Yield-line theory for slab design as pioneered by Johansen, has always presented the designer with two alternative methods. The first method is to evaluate the dissipation of energy belonging to any chosen mode of collapse, from which the corresponding collapse load is obtained, the layout of yield lines for the worst mode being found by trial and error. This is known as the "work method" and is on a firm mathematical foundation, even if sometimes slow in application. The second method is the "equilibrium" method using "nodal" forces where yield lines meet, or where they meet edges. This quick method has been popular with designers, but the foundations of the theory are in dispute, and on occasions it gives false results or else provides no results at all. The reasons for breakdown are discussed herein and new techniques are evolved for overcoming the difficulties. In this new outlook there are not, in fact, two separate methods, but merely two mathematical rearrangements of the same approach. The argument brings out the observation that there is a disturbing lack of information on the yield criterion for bending of slabs.

Plastic analysis is applied to evaluation of the membrane action in transversally loaded reinforced concrete slabs with edges restrained against lateral movement. Relations of the large deflection theory of flexure together with the yield condition, appropriate for reinforced concrete slabs, are used in order to obtain the load-deflection curves both in the compressive and tensile membrane action. The membrane action is found to influence considerably the actual carrying capacities of slabs. The developed method yields a continuous transition from the compressive membrane response to the tensile one.