amount of the FRP needed on the joints was designed with reference to the weakest joint of the structure at column C8 (i。e。 the original shear strength was 1。82, 1。65 and 1。62 MPa at first, second and third story, respectively)。 The target design was to improve its shear strength up to at least

4。1 MPa, about 2。5 times more than the original shear strength at the third story。 With reference to this joint at the third story (axial load P = 15 650 N), Figure 7 shows the relationship between the inclination of the principal tensile stress, 8, and the shear stress, v, corresponding to any given

state of joint strains for one ply of FRP reinforcement installed (continuous line) and its progress by adding one ply at a time of GFRP quadriaxial laminates up to three plies (dashed line)。

Importantly, the theoretical failure mode was always concrete crushing, assuming that proper anchorage would be ensured to prevent FRP debonding。 Figure 7 clearly shows that the amount of external FRP necessary to pursue the proposed target shear strength was two plies of GFRP quadriaxial laminates with a unit weight of 1140 g/m2。 The results in terms of shear strength, vmax, with reference to each exterior joint, obtained by installing one, two and three plies of quadriaxial GFRP laminates, were computed and reported in the last three columns of Table V。 The results reported in the same table confirm that, in every case, two plies of GFRP laminates are adequate to achieve a shear strength of at least 4。00 MPa。

Since rectangular column C6 has a sectional aspect ratio equal to 3, shear rather than flexure could have controlled its behavior。 Hence, shear FRP retrofit was considered necessary。 It was computed (by using CNR-DT 200/2004 [14] provisions) that totally wrapping the rectangular column C6 along its entire length with two plies of the same quadri-axial GFRP laminates used for the above joints was able to increase the sectional shear strength by about 50% (i。e。 the shear strength is 196 kN by considering concrete and stirrups shear contribution only, and this

values increases up to 286 kN by considering the GFRP effect)。 Importantly, only fibers placed perpendicular to the longitudinal axis of the column and those with a component on that direction were taken into account for calculations。 Thus, the same equations provided for uniaxial laminate shear strengthening were used in calculations。

6。 ASSESSMENT OF THE RETROFITTED STRUCTURE

Nonlinear static pushover analysis was performed on the FRP-confined structure in order to estimate the effectiveness of the proposed retrofit technique on the global structural behavior。 Assuming that the story mass remains constant after the FRP retrofit intervention, the modal displacements of each center of mass in directions X and Y and the corresponding normalized lateral loads are the same as those referred to the ‘as-built’ structure (reported in Table II)。

FRP confinement was taken into account by modifying the inelastic flexural behavior of the elements at the member ends, where the lumped plasticity is assumed。 The bilinear moment–rotation relationship used for each plastic hinge was modified to account for the increases in ultimate curvature $u  (and the related increase in ultimate rotation capacity) due to FRP confinement。  In

particular, yielding curvature, $y, and moment, My, were not modified by FRP confinement, while

the ultimate curvature, $u, and ultimate moment, Mu, were determined on reaching the increased ultimate strains in concrete, nccu, (determined from Equation (5)) or in steel reinforcement, assumed equal to 402 as in the ‘as-built’ structure。 Yielding rotation, ultimate rotation and plastic hinge length were computed by using Equations (1)–(4)。 The knowledge level was again assumed equal