Issue 51

G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 294 have been adopted to calculate the confining stress, l f . The effective confining stress (namely , l eff f ) depends on additional parameters not involving the characteristics of the composite system. Semi-empirical formulations available in the scientific literature provide this stress as a function of key efficiency parameters. According to classical formulation [31] the effective confining stress, , l eff f under passive confinement, can be assessed as follow: , 1 2 l eff l eff f f eff f f f k E k          (13) where, f E is the Young’s modulus of the fiber, f  is the ultimate design strain of the fiber (for the following experimental comparisons, it is equal to the average ultimate strain, without any safety factor) and f  is the confinement volumetric ratio of the strengthening system. The calculation of f  depends on the characteristics of the strengthened cross section: 4 f f f f t b D p      for circular wrapped cross-section (14)   4 max , f f f f t b b d p      for rectangular cross-section (15) where, f t is the thickness of the confined layer, f b is the width of the wrap, f p is the spacing between the wraps, D is the diameter of the circular cross-section, b and d are the dimensions of the rectangular cross-section. The coefficient, eff k depends on efficiency of the strengthening system; it can be assumed as follow: eff h v k k k k     (16) where the three coefficients, h k , v k and k  can be easily assessed according to the formulations reported in the CNR guidelines [31]. They depend on geometrical and mechanical parameters; h k is the coefficient of horizontal efficiency: '2 '2 1 3 h m b d k A     (17) where the dimensions ' b and ' d provide the sizes of the effectively confined core (external dimensions minus the radii of the rounded corners), and m A is the area of the gross cross-section and assumes unitary value also for circular confined columns. The coefficient v k represents the vertical efficiency that assumes unitary value for continuous wrapping systems ( f f b p  ). The coefficient k  is the efficiency due to the inclination of the fibers. In the present paper, the strengthening was carried out without inclination of fibers, justifying the assumption of 1 k   . A second approach [32] has been used to estimate the lateral stress, , l eff f on the confined members, as follows: , 2 l eff l eff f f f eff b d f f k t E k b d           (18) For circular confined cross-sections, the dimensions, b and d assume the value of the diameter, D . The coefficient, eff k can be calculated with the same previous formulations [31].