The object of the paper is to provide a simple, rational technique to check the rotation compatibility of plastic hinges in limit designed reinforced concrete continuous beams proportioned basing on optimum considerations. The relationship between the plastic adaptability and the rotation compatibility is outlined, expressing conveniently both the inelastic rotations and the rotation capacities of critical sections. It is concluded that the compatibility requirement implies only limited adaptability tobe used in the design of concrete structures. Since a similar conclusion can be derived with regard to the serviceability conditions of limit designed structures, adoption of convenient upper bounds for the redistribution factors (or lower bounds for the yield safety parameters) of critical sections will implicitly provide adequate solutions for ultimate safety, compatibility, and serviceability as well. From the practical viewpoint, the significant result follows that for given ( 1) properties of materials, (2) loading conditions, and (3) amount of accepted redistribution, the rotationcompatibility condition to an upper limitation of the steel percentages at critical sections.

With discussion by Peter R. Barnard, George Pincus, Charles A. Rich, and Gerald Sturman, Surendra P. Shah, and George Winter. Inelastic behavior of concrete was studied by direct observations of internal microcracking. Thin slices were made from strained specimens and internal cracks were examined by X-ray and microscope techniques. Bond cracks at the interface between coarse aggregates and mortar, exist in concrete even before any load is applied. Analytical and experimental studies showed that tensile stresses are present at the mortar-aggregate interface because of volume changes of mortar and may be partly responsible for bond cracks in virgin concrete. These bond cracks begin to propagate noticeably at applied compression stresses of one-quarter to one-third of the ultimate strength. At this level the stress-strain curve begins to deviate from a straight line. At about 70% to 90% of ultimate strength cracks through mortar begin to increase noticeably and bridge between bond cracks to form a continuous crack pattern. Upon further load increase this condition eventually leads to a descending stress-strain curve and failure. Other investigators have noted that in that same load range, the volume of concrete begins to increase rather than decrease. An hypothesis explaining this volume expansion and propagation of bond cracks in terms of shear bond strength of the interface and microcracking has been presented. In order to investigate the influence of flexural strain gradients, microcracking and the stress-strain relation of eccentrically loaded specimens were compared with those of concentrically loaded specimens, It was found that a flexural strain gradient definitely retards microcracking, especially mortar cracking as compared to cracking at the same strain in axial compression. The stress-strain curve for eccentric compression, which was computed by an experimental-statistical approach was found to differ materially from that for concentric compression. The peak of the flexural curve was located at a strain about 50% larger and at a stress about 20% larger than the peak of the curve for concentric compression. Structural implications of these findings are briefly examined.

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 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.

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.