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

7.1. Basic assumptions1997, Stankowski et al., 1993]σ = f t exp(− u cr f tG I f)(7.8)which relation deals with an exponential and negative type expression of the σ − u crrule (Figure 7.4a).σf t (tensile stregnth)2φG fI(fracture energy)yy0φφ(a)u crutot2s(b)utot2Figure 7.4: Cracked hinge: (a) stress-crack opening displacement of plain concrete and (b)main geometrical assumption under deformation.The total crack opening u cr , at the considered strip, is obtained by subtracting theelastic part from the total displacement u tot ,u cr = u tot − s σ SF RC [u cr ]E(7.9)whereu tot = 2 · φ · (y − y 0 ) (7.10)being φ the angular deformation (relative angle of the two end sections of the crackhinge), while y and y 0 deal with the considered strip position and the depth of theneutral axis as depicted in Figure 7.4b. In Eq. (7.9), s represents the hinge length.By solving Eq. (7.9) for σ SF RC and substituting u tot = s · ɛ ∗ , where ɛ ∗ is the meanlongitudinal strain in the considered sectionε ∗ = 2 · φ · (y − y 0)s(7.11)145