【正文】
e wrapped around columns with the fibers oriented in the hoop direction. The consequent increases in the axial pressive strength and the ultimate axial strain of the concrete core depend on several factors, including the thickness, tensile strength and elastic modulus of the confining FRP jacket, unconfined concrete strength and crosssectional shape of the column [7]. For given material properties and crosssectional dimensions, the thickness of the FRP jacket governs the strength and ductility of the confined crosssection.Display Full Size version of this image (11K)Fig. 1.FRPjacketed regions of column for seismic retrofit.This study considers an RC framed structure with Nc columns, Nb beams, and hence 2(Nc+Nb) potential plastic hinges (assuming one hinge at each end of each member). The column is assumed to have a rectangular crosssection, with width Bi and depth Di. Seismic retrofit is achieved with FRP confinement of the potential plastic hinge regions of each column, as shown in Fig. 1. Only the thicknesses of the FRP jackets required for confinement of the plastic hinges are considered as design variables in this study.This approach is realistic and also reduces the design problem to a manageable size. The jacket thicknesses required for shear resistance and for confinement of lap splices are first calculated for each member [5], but these thicknesses are not taken into account in the optimal design procedure presented in this paper. In practical implementation of the seismic retrofit strategy, for any potential plastic hinge region in a column, the total thickness of the FRP jacket should be the sum of those determined for the three failure modes, respectively [5]. This represents a conservative but realistic approach given the current stage of knowledge. The design variables in the optimization process are therefore the thicknesses, ti, of the FRP jackets required for confinement of the plastic hinges in each member. For a given type of FRP material, if the topology of the structure is predefined and each column is assumed to have the same FRP jacket thickness and the same length of the confined region at both ends, the total material cost of the FRP posite used for column confinement is given by(1)where wi is the cost coefficient for the FRP posite, wi=4Lci(Bi+Di)ρ。 ρ is the cost per unit volume of the FRP posite。 and Lci is the length of the primary confinement region at each end of the ith column, which should be the largest of the plastic hinge length, and % of member length [5] and [21]. In practical implementation, a secondary confinement region adjacent to the primary confinement region should also be confined but with the FRP jacket thickness reduced to half of that in the primary confinement region. The amount of FRP required for confining the secondary confinement region is not further considered in this paper.