PSI - Issue 44

Sara S. Lucchini et al. / Procedia Structural Integrity 44 (2023) 2286–2293 Lucchini et al. / Structural Integrity Procedia 00 (2022) 000–000

2288

3

θ=min arctan  f ct +σ 0 b∙v cr  ;90° ≥arctan  h L  with v cr = f ct b ∙  1+ σ 0 f ct

(4)

Sliding shear resistance The sliding shear is governed by the shear friction mechanism. Thus, the total resisting force related to the sliding mechanism (V R,s ) is equal to: V R,s =x s ∙  v s,coat ∙n∙t coat +v s,m ∙t m  +V d (5) where x s is the length of the compressed zone and V d is the shear resisting force by dowel action of reinforcing bars, if any, estimated according to NTC (2018). The frictional strength of SFRM (v s,coat ) and URM (v s,m ) can be estimated according to the formulations reported by the NTC (2018), respectively as follows: v s,coat =0.5∙η∙f c ; v s,m =0.4σ 0,s +f v0 (6) where η=0.6(1-f ck /250) is the strength reduction factor, f c is the cylindrical compressive strength of SFRM, f ck is the corresponding characteristic value expressed in MPa, σ 0,s =N/(x s ·t m ) and f v0 is the sliding shear strength of unit-to mortar interface at zero compression. Finally, the length of the compressed zone x s results from the following quadratic equation: 1 6 x s 2 ∙f Ft ∙nt coat +x s  βh∙  v s,coat ∙nt coat +f v0 ∙t m  + 1 3 f Ft ∙nt coat ∙L+ N 3  +N  0.4·βh- L 2  - 1 2 f Ft ∙nt coat ∙L 2 =0 (7) where βh is the lever arm of the lateral load, with β=1 for a cantilever wall and β=0.5 for a double fixed-end wall. Note that the tensile resistance provided by fibers along the cracked section was considered constant and equal to f Ft . 2.2. Flexural resistance Based on the assumption of perfect bond between masonry and coating, the flexural resistance was calculated by equilibrium. The neutral axis (x f ) must be first calculated so that the applied axial force (N) is in equilibrium with the internal forces. Thus, the following equation is obtained: N=α∙λ∙x f ∙(f m ∙t m +f c ∙nt coat )-f Ftu ∙nt coat ∙(L-x f ) +∑ (A' sn ∙σ' sn n1 -A sn ∙σ sn ) (8) where f Ftu is the residual tensile strength of SFRM significant for ultimate conditions; A sn and A’ sn are the total area of the n th vertical rebar placed in the tensile and compressed zone respectively; σ sn and σ’ sn are the corresponding stresses;  =0.8 is the factor defining the effective height of the compressed zone of masonry and SFRM and  =0.85 is the coefficient taking into account the long term effects on the compressive strength. Finally, the resisting moment (M R ) can be evaluated as follows: M R =- α∙ ( f m ∙t m +f c ∙nt coat ) ∙(λx f ) 2 2 + f Ftu ∙  L 2 -x f 2  2 ∙nt coat + ∑ (A sn ∙σ sn ∙ n1 d n -A' sn ∙σ' sn ∙d' n ) + N∙L 2 (9) where d n and d’ n are the effective depths of tensile and compressed rebars respectively. 3. Case studies 3.1. In-plane capacity of a test building To validate the analytical model proposed by the Authors and briefly presented in the previous section, it was applied to the full-scale two-story masonry building tested at the University of Brescia and described in Lucchini et