FRP reinforcement at sagging and hogging zones in continuous beams: Iifluence on redistribution of moment

The actual design methodologies, based on the up-to-date codes, very often allow or in some cases require the application of non linear-procedures, particularly in seismic zones. The check of the structural elements is not always related to strength requirements only, but also to ductility aspects. Ductility is a fundamental structural property because it allows stress redistribution and provides warning of oncoming failure. In well-designed steel reinforced concrete beams the failure is announced by yielding of the steel reinforcement, followed after significant deformation with no substantial loss of load carrying capacity, by concrete crushing. The application of external sheets of FRP materials, currently considered an almost common practice in the framework of strengthening and rehabilitation of r.c. structures, can sharply affect the failure mode and the local and global ductility of the structure. Aim of the present paper is an evaluation of the moment redistribution capacity of continuous beams reinforced with longitudinal sheets of FRP at hogging and sagging zones. The study is carried out by adopting an analytical model developed by the authors which allows the definition of the bending moment-mean curvature relationship (for each value of axial force) of a cracked reference element. The tension-stiffening effects, the non linearity of materials, the slips at the interfaces and the strain localizations near the cracks are accounted for. The influence of the FRP location and amount on the bending moment redistribution is examined with reference to different beam schemes and load typologies, in order to check the sensitivity of these parameters. A first typology includes simply supported symmetrical and non-symmetrical two-span beams. A second typology refers to fixed-end beams, which simulates the behaviour of multi-support beams. The analyzed cross-sections are characterized by the same concrete geometry (300 x 500 mm2), but different reinforcement at the top (Ast) and at the bottom (Asb). The obtain results highlight that the application of FRP reinforcement at both sides of the sections causes a reduction of the redistribution factor in any analysed case: the FRP application generally reduces the redistribution factor of about 20% (1 sheet – tf=0.13 mm) up to 50% (4 sheets). Furthermore the effect of the location of the composite material on the redistribution factor is analysed. For the studied schemes, in which the first plastic hinge occurs at the support, no redistribution takes place when the FRP is applied at the hogging zone; on the contrary significant redistributions are allowed when the composite material is at the sagging zones. In the non-symmetrical scheme the reduction of the redistribution factor is about 10-20% for the application of one sheet up to more than 40% when 4 sheets are applied. Furthermore the obtained results show the strong dependence of the redistribution factor on the mean local stiffness of the zones interested by plastic hinges, as highlighted by the cases of reinforcement applied only on the sagging or hogging zones of the beams