The difference between rotations of a RC member at the peak moment and at the yielding moment is the so-called rotation capacity, which is a particularly critical property for its relationships with redistribution of internal force, energy absorbability, resistance against imposed deformation, and so on. Owing to the nonlinear stress-strain response of materials and their complicated mutual interaction, the precise prediction about rotation response, especially in plastic range, of a RC member, which is the primary basis of quantifying the rotation capacity, is no easy matter; therefore this issue has still been one of the classic and intractable problems in structural engineering over the past decades.
By investigating the deformation components constituting the rotation capacity and referring to the proposed analytical model to predict the rotation capacity, the improved Tension Chord Model, applied in tension zone and representing the tension stiffening effect in pre-and post-yield stages, and the linear softening model, employed in compression zone and predicting the compressive softening behavior of concrete, are subsequently derived. After that the stress-smeared strain curves of concrete and RC tension chord based on the two models are assembled to predict the advanced moment-curvature response with the standard plane-section analysis. And the evaluation procedures about rotation response of RC flexural members are divided into two cases in terms of the nonexistence and existence of damage zones in compressed concrete at failure. In order to validate the presented model, three-point bending tests with the variables regarding to the reinforcement ratios and ductility parameters of steel have been carried out. The main contents of this dissertation can be summarized as follows:
(1) This paper derives the mean bond stresses in pre-and post-yield phases by resorting to the definition of interfacial fracture energy. Afterwards, the mean bond stresses, associating with the strain (stress) levels of reinforcement at cracks, are employed to simplify the evaluations towards the distributions of reinforcement strain and slip. Moreover, a bond stress-strain model is suggested to estimate the bond behavior of reinforcement in terms of the steel strain instead of the slip. Additionally, the phenomena of a cliff-like drop in bond stress after yielding is illuminated by series. Then the proposed models are utilized to simulate some well-known tests, and a good agreement with the experimental results validates the proposed models. Finally, the mean bond stresses implying several typical strain (stress) levels of reinforced concrete members are presented.
(2) The presented mean bond model are implemented into the Tension Chord Method to investigate the stress and strain distributions of concrete and reinforcement, and tension stiffening effect with analytical method. Furthermore, the simulation results acquired this method agree with the test results.
(3) The essential strategies of the crack band model, devoting to representing the concrete softening response in tensile damage zone, are extended to the concrete in compressive damage zone. As a consequence, the linear softening model for compressed concrete, inferred from the stress-strain response of unaxially compressed concrete, is employed to describe the compressive behavior of concrete in hinge region. Moreover, the Hognestad’s law is used to predict the pre-peak response of compressive concrete. As a result, the combination of two models have got good validation by the comparisons with experimental results.
(4) The proposed models, applied to describe the mechanical behavior in tension zone and in compression zone of RC beams, are assembled to predict the advanced moment-curvature response with the standard plane-section analysis. And the evaluation procedures about rotation response of RC flexural members are divided into two cases in terms of the nonexistence and existence of damage zones in compressed concrete at failure.
For the RC flexural member without strain localization at failure, the compressed concrete can be ideally treated as homogeneous. On the other side, as far as the distribution of steel strain is concerned, the smeared steel strain can be deemed constant along the member. So it can be further inferred that the smeared deformation of any plane-section remains plane in view of the distribution characteristics of concrete strain and smeared steel strain; as a result, the moment-curvature relationship, based on the common plane-section analysis, can be evaluated with the stress-strain curve of concrete material and the stress-smeared strain curve of RC tension chord.
While for the RC flexural member with strain localization at failure, the compressive behavior of concrete cannot be thought of as homogeneous any more due to the existence of strain localization. Under this status, the frequently employed plane-section assumption is not valid any more due to the heterogeneity of compressed concrete caused by strain localization. Hence, the moment-curvature relationship, feasible to the overall RC flexural member, cannot be directly evaluated from the stress-strain response of materials. Whereas the assumption regarding plane-section remains plane is still individually applicable in hinge region and in non-hinge region in terms of smeared strain. Therefore, the advanced moment-curvature relationship considering strain localization, can be separately applied in hinge region and in non-hinge region.
(5) The influence of shear on rotation deformation of RC beams has been analytically investigated. Then the Cracked Membrane Model was modified to consider the effect of stresses at the cracks. Moreover, the spacing of Modified Cracked Membrane Model was suggested. Finally, the modified model was proposed to implement the analysis toward the rotation of RC beams without transverse reinforcement.
(6) A series of three-point bending tests with the variables as to reinforcement ratio and ductility parameter have been implemented, and the presented analytical models have achieved a good validation by the comparisons between the simulations and tests.
(7) The influence of ductility of reinforcement and slenderness on the available rotation capacity and on the required rotation capacity of RC beams is investigated. Moreover, a method whereby the available rotation capacity is compared to the required rotation capacity to determine the available degree of moment redistribution is introduced herein. With the described method, the relation between the available degree of moment redistribution and the maximum relative compressive depth of RC beam section is studied to check the adequacy of the structural design method of linear elastic analysis with moment redistribution.
This paper gives new approaches to analyze the bond behavior, concrete compressive response, and rotation capacity of RC flexural members, which are beneficial to the study towards the basic mechanical response of reinforced concrete. Besides, the presented rotation capacity model can be employed to assess the adequacy of the structural design method of linear elastic analysis with moment redistribution suggested by the codes, and is a good tool to design the safe and economical RC structures.