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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 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.

With discussion by Milik Tichy. Evolution of moments distribution in reinforced concrete indeterminate structures is followed by means of real moment-rotation curves and imposition of compatibility conditions. Theory shows that such a redistribution begins at appearance of first crack and that its amount is already considerable at service load. Redistribution is present also if the structure is designed for bending moments by elastic theory; Therefore in this case its effect is unfavorable. Tests on 2 continuous beams (with measure of reactions) confirm the results of theory and show that the assumption of an elastic distribution of moments can lead to an overestimation of carrying capacity of structures. This danger is particularly important when a high percentage of reinforcement or the presence of axialload considerably reduce the rotation capacity of individual sections (brittle sections). The real behavior of such structures can be easily followed when they are not too complex. The method of "imposed rotations" applied to the tested continuous beams-involves considering inelastic rotations as rotations artificially imposed on critical sections of the structure, which is still considered to be acting elastically. The conclusion is that elastic distribution of moments is not a suitable basis for limit design of reinforced concrete structures and that inelastic calculations seem necessary in all cases. If certain conditions are fulfilled avoiding brittle sections, a great freedom in design seems possible, without any control of compatibility. In the other cases, the proposed method can be used if structures are not too complex; for complex frames simple rules can be found by further research.