مقاوم سازی لرزه ای سازه های بتنی با کامپوزیت های پلیمری
Abstract
1- Introduction
2- FRP-confined concrete
3- Reliability-based optimal design problem formulation
4- Explicit formulation of inelastic displacements
5- Reliability-based design procedure
6- An illustrative example
7- Conclusion
References
Abstract
Fiber-reinforced polymer composites can be externally bonded to reinforced concrete members which provide an effective seismic retrofit strategy for reinforced concrete structures. For seismic retrofit of a complex building structure, due to the large number of structural members, an optimum design which ensures the use of the minimum amount of fiber-reinforced polymer to achieve a given level of seismic performance is highly desirable for economic reasons. In addition, such an optimum design approach is best built on a probabilistic basis so that various sources of uncertainties in the design process can be appropriately accounted for. This work therefore studies an efficient reliability-based optimization approach for the seismic retrofit design of reinforced concrete structures using fiber-reinforced polymer composites. The structural performance is assessed at the system level using nonlinear pushover analyses. In the proposed approach, the inelastic interstory drift ratios are modeled as indeterministic variables to consider the uncertainties of earthquake loading. By contrast, the thickness of the fiber-reinforced polymer jacket is considered as a deterministic design variable. The reliability-based design approach is formulated by minimizing fiber-reinforced polymer cost subject to prescribed structural reliability constraints. Using the results of nonlinear static pushover analyses and reliability analyses, the reliability index constraints are explicitly formulated with respect to the deterministic design variables based on the virtual work principle as well as Taylor series expansion. A numerical optimality criteria method is derived and programmed to solve this reliability-based nonlinear retrofit design optimization problem. A design example is included to illustrate the application of the new optimization approach.
Introduction
It is well-known that many uncertainties are involved in structural designs, especially in the case of seismic resistant designs (Beck et al., 1998; Charney, 2000; Frangopol, 1985; Gaxiola-Camacho et al., 2017; Lagaros et al., 2008; Zou et al., 2010). The structural responses under random excitations such as seismic loads cannot be precisely predicted; therefore, such design problems involve considerable uncertainties (Ghobarah et al., 2000). Although the probabilistic approach has been widely adopted in the design codes of most countries, its application in building structures is limited to structural member design using partial safety factors. That is, current design codes primarily focus on the ultimate safety check of structural members including beams and columns. A structural design based on current code procedures may not guarantee a satisfactory level of system reliability. Indeed, a system behavior has been regarded more important than a member behavior because of the high redundancy in building structures (Cheng et al., 1998; Kim and Wen, 1990). Performance-based seismic design, which can buildings by earthquakes, has become a standard for seismic design (Applied Technology Council (ATC), 1996; Chan and Zou, 2004; Fragiadakis et al., 2006; Gaxiola-Camacho et al., 2017; Lagaros et al., 2008; Zameeruddin and Sangle, 2016; Zou et al., 2007a). The pushover analysis method has been widely used in the performance-based design procedure to assess the nonlinear seismic performance of structures (Zou and Chan, 2005; Zou, 2012). Moreover, the performance design procedure should be based on probabilistic approaches, which account for the various sources of uncertainties and approximations as stated in FEMA445 (FEMA, 2006). A system reliability-based design approach should be employed directly, instead of using the member level partial factor approach as adopted in the design codes currently available. Furthermore, since the peak seismic interstory drift over the lifetime of a structure is uncertain, a performance parameter can be used and directly related to the reliability index of interstory drift (Beck et al., 1998).directly address the inelastic deformation induced in