|عنوان فارسی مقاله:||تحلیل تناوبی قاب های بتن مسلح در مورد به کارگیری روش های مختلف در مدل تار جهت در نظرگیری اثر چسبندگی-لغزش|
|عنوان انگلیسی مقاله:||Cyclic analysis of RC frames with respect to employing different methods in the fiber model for consideration of bond-slip effect|
|رشته های مرتبط:||مهندسی عمران، مدیریت ساخت، زلزله و سازه|
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In this research, based on a nonlinear analysis of reinforced concrete moment-resisting frames, the bondslip effect between concrete and bars along the lengths of beam, column, and joint elements was applied to numerical equations. The governing theory in the numerical equations was similar to that of the fiber model, but the perfect bond assumption between the concrete and bar was removed. The precision of the proposed method in considering the real nonlinear behavior of reinforced concrete frames was compared to the precision of other suggested methods for considering the bond-slip effect in fiber model analysis. Among the capabilities of this method are its ability of modeling the embedded lengths of bars within joints and nonlinear modeling of bond-slip. The precision of the analytical results were compared with the experimental results achieved from 2 specimens under cyclic loading. The comparison showed that the proposed method can model the nonlinear behavior of reinforced concrete frames with very good precision.
Key Words: Bond-slip effect, pull-out effect, cyclic analysis, RC frames
Many analytical models have been devised for the nonlinear analysis of reinforced concrete (RC) frames. Although 2-dimensional and 3-dimensional modeling in a finite element method can make for more accurate analysis, it considerably increases the expense and time of analysis. Therefore, such methods are typically used for modeling structural parts while easier methods are utilized for the full modeling of structures. The one-component model of Clough et al. (1965) is one of the simple models used for nonlinear analysis of RC frames. Various models with concentrated plasticity (Brancaleoni et al., 1983) were presented later and a more accurate description of the nonlinear behavior of the elements of RC frames became available through models with distributed plasticity (Soleimani et al., 1979). Other models (Filippou et al., 1992), including multispring models that use subelements, were devised. One of the most commonly used methods is the fiber model. In this method, an element is divided into a number of concrete and steel fiber lengths, and the element section specifications are worked out by adding up the effects of the fibers’ behavior. This method assumes a perfect bond between concrete and bar (Spacone et al., 1996; Mazars et al, 2006), but this assumption is not very appropriate or realistic and causes a considerable difference between analytical and experimental results (Kwak and Kim, 2006). Belarbi and Hsu (1994), as well as Kwak and Kim (2002), made use of the fiber method, but in order to modify it and reduce the error of analysis resulting from the perfect bond assumption, they modified the stress-strain behavior of the bars. In this way, they drew on an equivalent method. Limkatanyu and Spacone (2002a) used the fiber model but removed the perfect bond assumption. In order to achieve this, they differentiated between the degrees of freedom of the concrete and of the bars in the beam-column elements. This modified method was used for beam-column elements in the present study, but for modeling RC frames, a joint element is also needed. What matters is the compatibility and assimilability of joint elements with beam-column elements. In initial methods of nonlinear analysis of RC frames, the nonlinear effect of beamcolumn joints is considered using calibration of plastic hinges within adjacent beam-column elements (Otani, 1974). In such a situation, the joint element is not modeled separately, but rather its effect on the adjacent elements is considered. From there, the joints of RC frames are located in critical zones and they are affected by different effects such as high shear force and the bond-slip effect, so the joints need more precise modeling (Lee et al., 2009). Based on another approach, the behaviors of each of the elements of joint, beam, and column are separated. The zero-length rotational spring is one such joint element (Alath and Kunnath, 1995). In this kind of modeling, the effect of shear deformation is considered using a spring whose governing behavior is moment-rotation. In another type, as in the previous approach, 2 springs are used in the joint modeling. In one spring, the effect of shear deformation is taken into account, and in the other, the effect of deformation resulting from bar slip is taken into account (Biddah and Ghobarah, 1999). In order to calibrate such joint elements, experimental results or estimated force-deformation relationships at the joints should be used, but a precise calculation of such relationships is not easy, especially in structures that enjoy a high multiplicity of joint element types. Moreover, in such cases, various factors affecting the nonlinear behavior of joints are not separated but are generally applied in the models. In some newer methods, joint elements are modeled as 2- dimensional planes, but in order to use such elements along with adjacent beam-column elements in assembling the whole of the RC frame, transient elements are also utilized so that there will be a connection between the degrees of freedom of joint plane and of adjacent linear elements (Elmorsi et al., 2000). Such elements typically have 2-dimensional formulations and are capable of separately modeling the behavior of concrete and bars and the interactions between them. These elements, however, like finite element methods, increase the modeling time and the amount of calculations. Furthermore, when there is a need for the degrees of freedom of the concrete and bars in the joint element to be compatible with the corresponding degrees of freedom in the adjacent linear beam-column elements, this type of modeling has its own limitations. Another type of joint element is created by assembling a series of one-dimensional components that are used for modeling the dominant behavior of joint elements and whose calibration is carried out through experimental results (Lowes et al., 2004). This kind of modeling relies on the behavior of force deformation for each effective component, and because force-deformation relations are calculated approximately, such modeling will not be completely precise and will need a strong calibration process. Limkatanyu (2000) introduced an interior joint element based on the separation of the degrees of freedom of bars going through the joints and concrete. Although this element can model the interaction between concrete and bars very well, it loses precision because it presupposes identical degrees of freedom for all 4 sides around the joint element and ignores the shear deformation of joint planes. Another important point about the existing types of models is that most of them cannot be used for studying joints in different frame locations. Thus, most of them are useful for only one of various interior, exterior, or corner locations. In the present study, the beam-column element introduced by Limkatanyu and Spacone (2002a) was used for modeling beam and column elements since it enjoys good precision and includes the interaction between the concrete and bars (Limkatanyu and Spacone, 2002b). A joint element was also defined and used, which, in addition to its flexibility in modeling different types of joint elements such as interior, exterior, corner, and footing, is capable of being assembled with the above beam-column element. Moreover, this modeling takes into consideration such factors as the bond-slip effect between the bars that pass through joints, the pull-out effect of bars that are restrained within joints, the nonlinear behavior of materials, and the shear-deformation effect of different beam-column elements. The introduced modeling is easy to use. In order to model the joint elements, a pull-out mechanism, an RC subelement, and a concrete subelement were first defined as the composing parts of the RC joint element. These parts were then assembled to produce 4 types of joint elements to be used along with beam-column elements in the modeling of RC moment-resisting frames. For simplicity’s sake, RCF, RCMRF, BCE, JE, RCSE, and CSE are used in the text instead of reinforced concrete frame, reinforced concrete moment-resisting frame, beam-column element, joint element, reinforced concrete subelement, and concrete subelement, respectively.