PSI - Issue 78

Somayeh Gholami et al. / Procedia Structural Integrity 78 (2026) 1459–1465 1461 • e ∗ is the mass participating in the fundamental vibration mode (estimated according to a triangular mode

shape assumption). = ( +∑ 2 ) 1

(3)

In Equation (3): •

G k is the total characteristic permanent load; • Q k, j are the characteristic variable loads for each area j according to their use; • ψ 2j are the load combination factors for seismic conditions; • g is the gravitational acceleration. As per e* , when information related to the dynamic behaviour of the building is lacking, it can be calculated as a function of the number of stories N using the empirical expression in Equation (4). ∗ = 0.75 + 0.25 −0.75 (4) The resisting shear F LSLS used for determining the spectral acceleration capacity is defined as the minimum value among those calculated at each story level (i) and in each main direction is computed by summing the in-plane shear contributions of the masonry wall panels. The critical value, corresponding to the weakest combination of floor and direction is then selected as the global base shear capacity F LSLS to be used in the seismic capacity evaluation (Equation (5)). = ( , | ) = ( | · | · · | · | · ) (5) Where: • A x|yi is the total shear-resistant area of the walls at level i in the direction x and y, respectively; • τ di is the design shear strength of the masonry panels determined according to Turnšek– Čačovič formulation (6) (Turnsek V and Cacovic, 1971); • ξ xi is a reduction coefficient related to the predominant failure mechanism of the masonry piers at level i (1.0 in case of expected shear failure, and 0.8 in the case of expected bending failure); • ζ is a coefficient that accounts for the effectiveness of the spandrels: it is taken as 1.00 if the spandrels prevent rotation of the upper section of the pier, and 0.80 if such rotations are allowed. • β x|yi is the coefficient accounting for the in-plane stiffness irregularity at level i (Equation (7)), where e i and d i are the distances between the center of stiffness and the center of mass and the outermost wall in the considered direction, respectively; • κ i is the ratio between the resultant of seismic forces acting at the i-th floor and the total seismic force; • μ xi is the coefficient accounting for the homogeneity of stiffness and strength of masonry piers at level i (Equation (8)). = 0 √1+ 0 1.5 0 (6) =1+2 ≤1.25 (7) | =1−0.2√ | ∑ 2 | , 2 | (8) In Equation (8):