P. Visintin

Size-dependent stress-strain model for unconfined concrete

The stress-strain behavior of concrete under compression, both in the ascending and descending branches, is crucial in determining both the strength and ductility of reinforced concrete members. This material property is generally determined directly from compression tests of cylinders or prisms. However, it is widely recognized that this material property depends on both the size and shape of the test specimen and the method of measurement. This paper shows that concrete deformation because of compression is both a material property and a shear-friction mechanism and that by taking both of these deformations into account it is possible to derive a stress-strain relationship that is size-dependent. This paper also shows how the stress-strain from cylinder tests of one specific length can be modified to determine the stress-strain relationship for any size of a cylinder. With this new procedure, the authors reanalyzed the results from 380 published tests on unconfined concrete to extract size-dependent strains at the peak stress and then used these results in existing curve-fitting models to produce size-dependent stress-strain models for unconfined concrete. This paper shows how these size-dependent stress-strain models can be used in a size-dependent deformation-based approach to quantify both the strength and ductility of reinforced concrete members.

Mechanics-Based Hinge Analysis for Reinforced Concrete Columns

AbstractThe 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...

FRP-Reinforced Concrete Beams: Unified Approach Based on IC Theory

In general, steel-reinforced concrete involves a ductile steel material and a very strong and ductile bond between the steel reinforcement and concrete, so that debonding rarely governs the design. In contrast, fiber-reinforced polymer (FRP) reinforcement is a brittle material with a weak and brittle bond, making debonding a major issue. Consequently, there has been an extensive amount of research on FRP debonding and in particular intermediate crack (IC) debonding. This paper shows that the very good research by the FRP research community on the mechanics of IC debonding can be applied to a wide range of apparently disparate reinforced concrete behaviors to produce a unified approach. Hence, a single mechanism, or unified approach, based on IC debonding is proposed in this paper for dealing with moment rotation, tension stiffening and deflections, member ductility and moment redistribution, shear capacity, confinement, and fiber concrete for FRP RC beams.

Incorporating residual strains in the flexural rigidity of RC members with varying degrees of prestress and cracking

The deformation of reinforced concrete columns and beams is controlled by the variation of the flexural rigidity (EI) both along the member and with applied loads and time. Currently, the moment-curvature (M/χ) approach is used to quantify EI. Prior to cracking, the M/χ approach provides a pure mechanics based solution for EI; that is, the only components of the model that have to be determined empirically are the material stress-strain relationships. However after cracking, the M/χ approach has to be semi-empirical, that is EI has to be determined empirically because the M/χ approach cannot simulate the mechanics of tension-stiffening. An alternative approach for quantifying EI using a moment-rotation (M/θ) approach is described in this paper. It is shown that the M/θ approach gives exactly the same results as the M/χ approach prior to cracking but after cracking has an advantage over the M/χ approach in that it can quantify the mechanics of tension-stiffening, that is allow for bond slip and its effect on crack spacing and crack widths. This paper deals with the mechanics of incorporating creep, shrinkage, prestress, relaxation and thermal gradients (broadly referred to as residual strains) on the flexural rigidity of RC beams and columns at all levels of loading prior to concrete softening.

Presliding shear failure in prestressed RC beams. I: partial-interaction mechanism

Despite significant experimental, numerical and analytical research, the shear behavior of reinforced concrete members remains one of the least well understood mechanisms in reinforced concrete. Because of the complexity of shear behavior, empirical or semiempirical analysis approaches have typically been developed and these are widely employed in codes of practice. As with all empirical models, they should only be applied within the bounds of the tests from which they were derived which restricts the wide application of innovative materials as expensive testing must be performed to adjust existing empirical formulae or develop empirical formulae specific to the new materials. There is, therefore, a strong need to develop a generic, mechanics-based model to describe shear failure, which is the subject of this paper. The model is based on the mechanics of partial interaction, that is, slip between reinforcement and adjacent concrete which allows for crack formation and widening and is commonly referred to as tension-stiffening and slip across sliding planes in concrete associated with shear failure, which is referred to as shear friction.

Shear Strength of FRP RC Beams and One-Way Slabs without Stirrups

AbstractDue to the complex mechanism of shear behavior, most current empirical methods do not physically simulate the shear behavior as seen in practice. These approaches, therefore, cannot be directly applied to accommodate advanced technologies such as in the use of fiber-reinforced polymer (FRP) or fiber-reinforced concrete. With FRP reinforcement widely used nowadays, there is a need for a mechanics-based approach to explain and simulate the shear failure mechanism. In this paper and from a mechanics-based segmental approach, a generic closed-form solution is derived for quantifying the shear capacity of RC beams and one-way slabs without stirrups and in theory with any type of reinforcement and concrete. The model is validated with 209 published shear tests of FRP-reinforced specimens with normal concrete and, to show the generic nature of the model, with a further 626 published shear tests on beams with steel reinforcement. The generic closed-form solution is further simplified to facilitate shear d...

Presliding Shear Failure in Prestressed RC Beams. II: Behavior

In the companion paper, based on the theories of partial interaction and shear friction, a mechanics-based segmental approach, which can cope with any cross section and material property, was developed to simulate the shear behavior and failure of prestressed concrete beams with and without stirrups. The included equations and mechanisms are purely mechanics-based and independent of empirical material properties. In this paper, this numerical approach has been applied to describe the shear behavior of prestressed RC members. The effect of prestress on the shear behavior is explained, and the results of parametric studies on stirrup effectiveness are also shown. Published test beams with and without stirrups, 102 of them, have been analyzed by the proposed model and analytical results show good agreement with the experimental data. The average predicted results for the beams without stirrups being 96% of the test results and that for the beams with stirrups being 91% with coefficients of variation of 0.10 and 0.08, respectively. The equations provided by the ACI standard have been used to calculate the shear strength of the same test specimens, and the ACI shear provisions are shown to be quite conservative with an average of 67 and 74% and coefficients of variation of 0.29 and 0.18 for beams with and without stirrups. The influence of the random nature of cracks on the shear strength is also investigated.

Short-Term Partial-Interaction Behavior of RC Beams with Prestressed FRP and Steel

AbstractThe deformation of a prestressed concrete (PC) member is controlled by the variation in flexural rigidity (EI) both along the length of the member and with applied loads. Typically, the moment-curvature M/χ approach is used to quantify EI with the analysis being mechanically correct prior to cracking as the only empirically derived components are the material stress-strain relationships. Postcracking, however, the M/χ approach has to be semi-empirical as it cannot directly simulate the effects of tension stiffening. This paper presents a displacement-based M/Θ approach for determining the behavior of PC members, with and without supplementary tension reinforcement. Applying the mechanics of partial-interaction (PI) theory, the approach directly simulates the formation and widening of cracks as the reinforcement pulls from the crack face, thus directly allowing for tension stiffening. The PI M/Θ approach can quantify the equivalent flexural rigidities (EIequ) associated with tension-stiffening whic...

Flexural Strength and Ductility of FRP-Plated RC Beams: Fundamental Mechanics Incorporating Local and Global IC Debonding

AbstractReinforced concrete (RC) beams and slabs are frequently strengthened or stiffened in flexure by adhesively bonding fiber-reinforced polymer (FRP) plates to their surfaces using a strain-based moment-curvature design technique. This design technique is generally based on the intermediate crack (IC) debonding strain of the FRP reinforcement, that is, on the start of IC debonding; from this analysis it is often deduced that FRP plating is ineffective at the ultimate limit state because FRP debonding occurs before yield of the steel reinforcement. In this paper, it is shown that the strain-based approach is generally a lower bound at the ultimate limit state. Instead, a displacement-based approach is described that shows that FRP plated beams can be designed to achieve a higher strength than that of the RC beam by itself no matter when IC debonding first occurs. The mechanics of the analysis approach developed here treat the FRP debonded plate as a FRP prestressing tendon with a force equal to the IC ...

Size dependent axial and lateral stress strain relationships for actively confined concrete

The axial and lateral stress/strain behaviour of concrete under compression, both in the ascending and descending branches, is crucial in determining both the strength and ductility of reinforced concrete members, particularly when confined. Both the axial and lateral stress/strain relationships for concrete under any degree of confinement are generally considered as material properties which are usually determined directly from compression tests of cylinders or prisms. It is also widely recognised that these material properties are both dependent on the size and shape of the specimen from which they are extracted and on the method of measurement of strains. In this paper, the global deformation of concrete subjected to compressive forces is considered to comprise of two separate components; the local deformation of the material which is size independent; and the local deformation due to the shear-friction mechanism associated with the formation of wedges which is size dependent. It is shown that by separating the size independent and size dependent components of the deformation, it is possible to derive size dependent stress-strain relations for confined concrete from tests using one specimen size and to derive the dilatory deformation directly from the axial deformation. This should considerably reduce the amount of testing required for new concretes as only one size of specimen need be tested to obtain stress-strain relationships for all sizes. The proposed approach has been used to reanalyse 692 published test results on confined concrete to provide size dependent stress/strain relationships for both axial and dilatory strains in both the ascending and falling branches and for a wide range of confinements. It is also shown that the allowance for the size dependent component of deformation can substantially reduce the scatter.