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The lateral deformation behavior of a RC column is particularly important because it not only magnifies the moment but also affects the ability of the column-and, subsequently, the frame-to sway and absorb energy at all stages of loading. The lateral deformation is affected by disturbed regions, such as tensile cracks or compression wedges, which are often simulated with the help of hinges whose properties are derived empirically. Being empirical, these hinges can only be used within the bounds of the tests from which they were derived, and in this respect are of limited use. In this paper, a mechanics-based hinge is developed that can be used at all stages of loading (that is, at serviceability through to ultimate) and also during failure. The mechanics-based model is based on the principle of plane sections remaining plane, shear-friction theory that quantifies the behavior of RC across sliding planes, and partial-interaction theory that allows for slip between the reinforcement and the encasing concrete. Being mechanics based, it can be used for any type of RC column; that is, for any type of reinforcement and for any type of concrete as long as the material properties are known. The mechanics model is shown to be in good agreement with published test results and can simulate not only multiple cracks if necessary but also the formation of wedges. [ABSTRACT FROM AUTHOR]

The ability of a RC beam to rotate is extremely important at both the serviceability and ultimate limit states as it affects deflection, moment redistribution, and the absorption of energy. The rotation in a RC beam can be considered to have two components: the continuous rotation that occurs in the homogenous portions of the beam and that can be determined by straightforward integration of the curvature and the discrete rotation due to the rigid body displacement between crack faces. In this paper, generic closed-form solutions are derived for the discrete rotation across crack faces, which are limited by debonding or fracture of the reinforcement in tension, or softening of the concrete in compression. It is shown how closed-form solutions can be derived for the moment/discrete rotation for the simplest case of a RC beam with a single layer of reinforcement, which could be used as the starting position for much more complex scenarios. The technique developed is generic as it can cope with any type reinforcement and concrete. [ABSTRACT FROM AUTHOR]

Structural engineers have long recognised the importance of ductility in the design of reinforced concrete structures and, as a consequence, the importance of the ability of a reinforced concrete member to redistribute moment to give prior warning of failure, adjust the structural response to allow for variations in applied load and column drift, and to absorb energy during earthquake, blast and other dynamic loadings. Quantifying the ability of a member to redistribute moment, which at first sight appears to be a relatively simple problem, has been difficult and the problem is still unresolved as can be seen by the very wide range of permissible moment redistribution values in national standards. In this paper, established techniques of shear friction, partial interaction and rigid body displacement are combined to develop a novel structural mechanics based mathematical model for moment redistribution that can be applied to any member with any material property such as the use of brittle reinforcement. [ABSTRACT FROM AUTHOR]

Fibre reinforced polymer (FRP) plate reinforcement is a brittle material which has a brittle interfacial bond with concrete. This can lead to the misconception that all FRP retrofitting techniques provide brittle members and, hence, limited rotational capacity which has severe limitations for structural applications. This paper shows that the FRP reinforcement behaviour is but one of three components that govern the rotational capacity of plated reinforced concrete beam hinges. It is shown that FRP retrofitted beams and slabs can achieve ductile behaviour and provide rotational capacity and, furthermore, that the rotational capacity of FRP plated members depends very importantly on the interface bond characteristics. [ABSTRACT FROM AUTHOR]

Abstract: The ability of a reinforced concrete structure to absorb energy and maintain applied loads is a vitally important concept and requirement in structural design and yet, in comparison with strengths, it is little understood and difficult to quantify. This has necessitated the use of empirically based solutions in design that can only be used within the bounds of the tests from which they were developed and tend to be conservative. This has held back the development of new products in particular FRP RC. This paper explains the fundamental mechanisms that control the ductility of all RC members and describes a mechanics based model that can simulate these mechanisms. It is shown that the model can simulate RC with any type of reinforcement, with any type of bond and with any type of concrete including fibre concrete; as such it is ideally suited for simulating FRP RC, as the reinforcement properties and bond vary widely, in order to develop simple design procedures. [Copyright &y& Elsevier]

Abstract: When a concrete member is subjected to a load its response is both instantaneous and time dependent. The influence of time dependent deformation is particularly import because it may lead to serviceability failures in structural members where deflections or crack widths are excessive. Current analysis techniques for reinforced concrete members are built around a moment–curvature (M/χ) approach that is based on the assumption of full-interaction (FI), that is, the reinforcement does not slip relative to the concrete which encases it and, consequently, the widening of cracks and their effect on deflection cannot be simulated directly. Hence in order to determine member deflection, empirically derived expressions for the flexural rigidity of a member (EIemp) are required to allow for the tension stiffening associated with cracking. In contrast to this FI M/χ approach, a moment–rotation (M/θ) approach has been developed which allows for slip between the reinforcement and concrete, that is partial-interaction (PI) and which, consequently, obviates the need for the empirically derived flexural rigidities (EIemp). The PI M/θ approach simulates directly, through partial-interaction structural mechanics, the formation and widening of cracks as the reinforcement pulls from the concrete at crack faces and, consequently, automatically allows for tension stiffening. Hence the PI M/θ approach is a useful improvement of the current FI M/χ approach as it quantifies the flexural rigidities associated with tension stiffening which can then be used in standard analysis techniques. It is also shown in this paper that the moment rotation approach can be used to derive flexural rigidities that account for the long term effects of creep and shrinkage as well as predicting the effects of creep and shrinkage on cracks widths and spacings. [Copyright &y& Elsevier]