tesi A. Caggiano.pdf - EleA@UniSA - Università degli Studi di Salerno

1.3. Codes and Standards for Fiber-Reinforced Cementitious Compositesa) rigid-plastic b)crack-hardeningf Ftuf Ff Ftuhardening/softening post-crackfcrack-hardeningFtuf Ftsf Fts crack-softeningf Ftu crack-softeningw u ww u wFigure 1.12: Post-cracking constitutive laws for ULS states [fib Model-Code, 2010a].In the above relationships, f F t s is the serviceability residual strength, relative to acrack opening value representative of the SLS analysis, while f F tu represents the postcrackingstrength for the ULS. At last, w u is the maximum crack opening accepted instructural design and its value depends on the required ductility.When concrete cracks are treated by means of classical smeared-crack models, as usuallyaccepted in design procedures, the fracture zone must necessarily be considered asdistributed in a certain region of the body. Based on this, classical models behave witha loss of objectivity under softening responses. Actually, the definition of a stress-strainlaw is based on the identification of a crack width and on the corresponding structuralcharacteristic length. The link between the stress-crack law (σ−w) and the stress-strainconstitutive relationship (σ − ɛ) is given by the introduction of a characteristic length,l cs ,ε = w/l cs . (1.5)The characteristic length, for elements with conventional rebars, may be calculated asl cs = min{s r m , y} (1.6)being s r m the mean distance between two cracks, while y represents the distancebetween neutral axis and the tension side of the cross section. Further details can beobtained into the fib Model-Code [2010a].In bending sections without traditional reinforcement, under combined tensile-flexuralor combined compressive-flexural stresses, with resulting force external to the crosssection,the simplified expression of y = h (being h the specimen height) can be as-21