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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.

With discussion by Milik Tichy. The results of 22 tests of two-span continuous prestressed concrete beams are described and analyzed. The pretensioned beams were loaded to failure with concentrated, stationary loads placed at the middle of each span. The variables in the tests were: Shape of cross section, concrete strength, amount of longitudinal reinforcement, effective depth, and web reinforcement. The behavior of the beams is described in terms of deflections, strains, and crack patterns. The characteristic features of failuresunder the primary influence of shear and of flexure are distinguished. The requirements for moment redistribution are discussed. The phenomenon of inclined tension cracking, of critical importance in moment redistribution, is studied quantitatively. The effect of web reinforcement in compensating for the influence of inclined cracking is evaluated.

With discussion by Kurt H. Gerstle and Leonard G. Tulin, and Hiroyuki Aoyama. The objective of this investigation was to establish moment-curvature relationships of reinforced concrete members subjected to constant axial load and reversal of bending. Both the theoretical and experimental approaches have been made, guided by the results of previous experimental investigations. A method of analysis was developed, based on three assumptions: a linear strain distribution over the section; elasto-plastic stress-strain relationship of steel neglecting the Bauschinger effect; elasto-plastic stress-strain relationship of concrete replacing the real curve and neglecting any stress in tension. The effects of variables were studied using this analysis. Reinforcement ratio and concrete strength had minor effects on the shape of momentcurvature diagram. The amount of axial load and the plastic deformation under the previous loading made drastic change. When the member had no axial load, the diagram had a shape like a parallelogram and larger the plastic deformation, the wider the diagram was in the horizontal direction. When the amount of axial load was small, the moment-curvature diagram had a step in the way of reversal, and the larger plastic deformation made this step larger. When the axial load was higher, this step became smaller and for even higher axial load it vanished completely, making a spindleshaped diagram. Tests were made on three reinforced concrete specimens, making all the measurements in the constant moment region of the specimen. The validity and limitation of theoretical analysis were checked. It was found that the agreement was almost perfect for initial loading and for the first reversal made slightly after the yielding in the initial loading. However, the agreement was not very good for reversals after the first reversal from a point considerably beyond the yielding. Study of this discrepancy indicated some modifications of the method of analysis.