Closure to “Instantaneous Stiffness of Cracked Reinforced Concrete Including Steel-Concrete Interface Damage and Long-Term Effects” by Arnaud Castel, Raymond Ian Gilbert, and Gianluca Ranzi

Abstract

The discussed paper assesses the instantaneous response of an existing RC structure under live loading after taking into account the history of both short-term loading and a period of sustained service loading. First, five flexural RC beams were tested in fourpoint bending to analyze the influence of steel-concrete interface damage or cover-controlled cracking on the potential in the cracked state reduction of the instantaneous stiffness in the cracked state. Second, a finite-element approach is proposed and used to model the short-term response by implementing a damage variable to reduce the steel-concrete bond as loading is increased or after a period of sustained loading and shrinkage. The authors should be complimented for providing a detailed paper with interesting and useful information, which can be used in crack deflection control as a criterion for the serviceability and sustainability of RC structures. This is acknowledged by the discusser who would like to offer the following comments for their consideration and response, primarily about the experimental program, and the precracking and long-term test results. The discusser is confused about the beam designations and values of the precracking and sustained loads. It seems that there is no B4 beam, and perhaps Beam B3 in Table 1 is Beam B6 in Fig. 8, and Beam B6 is Beam B3 in Fig. 6. Furthermore, it seems that the maximum loading values for the precracking tests defined in Table 1 do not coincide with the maximum applied loads achieved in the short-term tests as follows: (1) Beam B3 (in Table 1; B6 in Fig. 8) has a defined value of 65 kN in Table 1, whereas it seems that the precracking load reaches 70 kN in Fig. 8; and (2) Beam B5 has a defined value of 70 kN in Table 1, whereas it seems that the precracking load reaches 60 kN in Fig. 7. To offer a better understanding, can the authors confirm the correct values and beam designations? As observed in Figs. 4–8, which show the load versus deflection curves for all the beams obtained before and after the long-term tests, the different unloading/reloading cycles up to the corresponding maximum loading value result in a cloud of load-deflection points for both the precracking and failure tests. However, it is noteworthy for the failure tests that a cloud of points does not appear for Beams B1 and B2, and that the adjustments for Beams B3, B5, and B6 differ. The adjusted line remains within the cloud for Beam B3 (Fig. 8) and is located next to the upper values of the cloud for Beam B5 (Fig. 7), and two adjusted lines appear for Beam B6 (Fig. 6). Moreover, it seems that the long-term effect on Beam B6 (Fig. 6) results in a deflection of approximately 2 mm for the 90-kN sustained load, whereas Beams B2 and B5 display a similar increase in deflection under the 40-kN sustained load and Beam B3 (Fig. 8) shows a greater increase in deflection under the 70-kN sustained load. Fig. 11 shows the total deflection increase after 6 months under sustained loading. The obtained values range from 0.5 to 3 mm. However, the discusser has not found complete correspondence with the values displayed in Figs. 4–8. It seems that Beam B1 offers a deflection of more than 0.5 mm, whereas Beam B3 (Fig. 8) offers one of more than 3.5 mm. This circumstance becomes worse if one believes that the values shown in Fig. 11 correspond only to the increase in deflection (through a long-term test) instead of the total deflection achieved from the beginning of both the shortand longterm tests on the same beam, which should be clarified. The authors state that the amount of concrete cracking resulting from the precracking test and the resulting damage on the concretesteel interface greatly influence the reduction of the long-term instantaneous stiffness, and that stiffness is affected by the number of flexural cracks along the span and eventually by the steel-concrete interface damage associated with increasing the applied loading. However, despite the modified cracking pattern of the beams under sustained loading being especially interesting, which affects the reduction in stiffness, the discusser has found no figures that include details on the experimental crack width and patterns. Additional information on this topic would help gain a better understanding of how the length of the existing cracks increased and/or how the new cracks occurred between existing cracks in the constant bending moment zone with time. Finally, regarding the references related with this paper, the discusser would like to point out that Model Code 1990 [Comite Euro-International du Beton/Federation Internationale de la Precontrainte (CEB-FIP) 1990] is referenced by the authors, whereas there is a later edition, Model Code 2010 [Federation Internationale du Beton (FIB) 2010], that became available before the paper submission date.