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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 P. R. Barnard, S. Stockl, Vitelmo Bertero and C. Felippa, and H. E. H. Roy and Mete A. Sozen. In the application of limit design to reinforced concrete structures, it is essential to know the rotation capacity of the connections. The rotation capacity seldom limits complete moment redistribution in moderately reinforced members subjected to transverse loads. However, it may prove to be a limitation for overreinforced members or members subjected to combined axial and transverse loads. Usually the rotation capacity of the section is governed by the ductility of the concrete which can be improved with the use of transverse reinforcement. This paper reports and discusses the effect of rectangular ties on the load-deformation characteristics of concrete.

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 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.

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.