PSI - Issue 44

Roselena Sulla et al. / Procedia Structural Integrity 44 (2023) 998–1005 Sulla et al./ Structural Integrity Procedia 00 (2022) 000–000 where:   and   are the diagonal cracking tensile strength and the corresponding masonry reference shear strength, respectively;  = ℎ/ , ranging from 1 to 1.5, is a correction coefficient related to the stress distribution on the section, depending on the panel aspect ratio; ℎ is the panel height. In particular, in the case of masonry spandrels, the parameter   , that may usually be neglected, is the greater between the horizontal and the vertical mean compressive stresses. In the case of regular masonry, Eq. (6) may be applied to evaluate the shear strength in a simplified way. However, it may be assessed through the following most complete relation:   =      +    ≤  , (7) where:   is the masonry shear strength;  is the friction coefficient;  is the interlocking coefficient defined as the ratio of the block height to the minimum overlapping length of two units belonging to two consecutive joints;  , is a limit value that can be approximated as function of the blocks tensile failure   , and taking into account the panel geometry. The equation to evaluate  , for standard shape blocks is:  , =      . 1 +     (8) 3. Discussion of the strength models considered The previous strength models considered for piers and spandrels may be reviewed in a dimensionless form as follows. Regarding masonry piers bending strength, Eq. (1) expresses the relationship between the axial load and the bending moment, representing their interaction domain. By defining the dimensionless normal stress  =   /0.85  , ranging between 0 to 1, Eq. (1) may be rewritten as:      .  =   1 −  (9) The dimensionless interaction domain, independent on the masonry type, pier thickness and length, is reported in Fig. 1a. As it may be expected, the domain starts from the origin, since no tensile strength is considered. The maximum flexural strength is reached when  = 0.5 . As regards masonry piers shear sliding, the strength is depending on l’ , that is the length of the masonry pier compressed part, where the shear strength is exerted. Therefore, by assuming a linear distribution of the normal stress acting on l’ , starting from Eq. (2) and considering the Eq. (4), as upper limit of Eq. (3) we obtain:      , =    , = 3    −    (10) where   is the mean shear strength (calculated with respect to the total length l ),  is the eccentricity, i.e. the distance between the pier axis and the compressive force, varying in a range between 0 and the masonry pier half length /2 . Hence, the ratio / varies from 0 to 0.5. Eq. (10) shows, in a dimensionless form, that the shear strength depends linearly on the ratio / , varying from 1.5 (if / = 0, i.e. the case when only axial load is applied) to 0 ( / = 0.5 when the eccentricity equals /2 ). The linear relationship is plotted in Fig. 1b. It is clear to note that it is independent from any parameter regarding masonry type and element geometry. 1001 4